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2021年4月1日2021年4月1日

Python（Qiskit）について（３）

概要

Qiskit について, サンプルプログラムを動かしてみた.
動作環境は, Google Colaboratory で行った
実行プログラム, 解説は, 下記の参照サイトをご覧ください

感想

本家のサイトにあるように, 量子ゲートの解説が, 非常に豊富だと驚いた.
時間を見つけて, 今後も, ドキュメントの残りの部分を進めていこうと思う.

量子ゲートのサンプル

事前準備

※参照サイトにあるように, 事前に必要なライブラリを, import させておく.

[編集内容(Import packages)]
# Useful additional packages
import matplotlib.pyplot as plt
%matplotlib inline
import numpy as np
from math import pi

from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister, execute
from qiskit.tools.visualization import circuit_drawer
from qiskit.quantum_info import state_fidelity
from qiskit import BasicAer

backend = BasicAer.get_backend('unitary_simulator')

[編集内容(Import packages)]

# Useful additional packages

import matplotlib.pyplot as plt

%matplotlib inline

import numpy as np

from math import pi

from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister, execute

from qiskit.tools.visualization import circuit_drawer

from qiskit.quantum_info import state_fidelity

from qiskit import BasicAer

backend = BasicAer.get_backend('unitary_simulator')

Identity gate

[編集内容(Bell state)]
q = QuantumRegister(1)
qc = QuantumCircuit(q)
qc.id(q)
qc.draw()

[編集内容(Bell state)]

q = QuantumRegister(1)

qc = QuantumCircuit(q)

qc.id(q)

qc.draw()

      ┌───┐
q0_0: ┤ I ├
      └───┘

┌───┐

q0_0: ┤ I ├

└───┘

U1 gate

[編集内容(U1 gate)]
q = QuantumRegister(1)
qc = QuantumCircuit(q)
qc.u1(pi / 2, q)
qc.draw()

[編集内容(U1 gate)]

q = QuantumRegister(1)

qc = QuantumCircuit(q)

qc.u1(pi / 2, q)

qc.draw()

[出力結果]
/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:3: DeprecationWarning: The QuantumCircuit.u1 method is deprecated as of 0.16.0. It will be removed no earlier than 3 months after the release date. You should use the QuantumCircuit.p method instead, which acts identically.
  This is separate from the ipykernel package so we can avoid doing imports until

      ┌─────────┐
q1_0: ┤ U1(π/2) ├
      └─────────┘

[出力結果]

/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:3: DeprecationWarning: The QuantumCircuit.u1 method is deprecated as of 0.16.0. It will be removed no earlier than 3 months after the release date. You should use the QuantumCircuit.p method instead, which acts identically.

This is separate from the ipykernel package so we can avoid doing imports until

┌─────────┐

q1_0: ┤ U1(π/2) ├

└─────────┘

U1 gate

[編集内容(U1 gate)]
q = QuantumRegister(1)
qc = QuantumCircuit(q)
qc.u(0, 0, pi / 2, q)
qc.draw()

[編集内容(U1 gate)]

q = QuantumRegister(1)

qc = QuantumCircuit(q)

qc.u(0, 0, pi / 2, q)

qc.draw()

[出力結果]
      ┌────────────┐
q3_0: ┤ U(0,0,π/2) ├
      └────────────┘

[出力結果]

┌────────────┐

q3_0: ┤ U(0,0,π/2) ├

└────────────┘

Pauli X, Y, Z, Hadamard, S, S dagger, T, T dagger gate

[編集内容(Pauli X, Y, Z, Hadamard, S, S dagger, T, T dagger gate)]
qr = QuantumRegister(3, 'q')
qc = QuantumCircuit(qr)
qc.x(qr[0])
qc.y(qr[1])
qc.z(qr[2])
qc.h(qr[0])
qc.s(qr[1])
qc.sdg(qr[2])
qc.t(qr[0])
qc.tdg(qr[1])
qc.draw()

[編集内容(Pauli X, Y, Z, Hadamard, S, S dagger, T, T dagger gate)]

qr = QuantumRegister(3, 'q')

qc = QuantumCircuit(qr)

qc.x(qr[0])

qc.y(qr[1])

qc.z(qr[2])

qc.h(qr[0])

qc.s(qr[1])

qc.sdg(qr[2])

qc.t(qr[0])

qc.tdg(qr[1])

qc.draw()

[出力結果]
     ┌───┐ ┌───┐  ┌───┐ 
q_0: ┤ X ├─┤ H ├──┤ T ├─
     ├───┤ ├───┤ ┌┴───┴┐
q_1: ┤ Y ├─┤ S ├─┤ TDG ├
     ├───┤┌┴───┴┐└─────┘
q_2: ┤ Z ├┤ SDG ├───────
     └───┘└─────┘

[出力結果]

┌───┐ ┌───┐ ┌───┐

q_0: ┤ X ├─┤ H ├──┤ T ├─

├───┤ ├───┤ ┌┴───┴┐

q_1: ┤ Y ├─┤ S ├─┤ TDG ├

├───┤┌┴───┴┐└─────┘

q_2: ┤ Z ├┤ SDG ├───────

└───┘└─────┘

Rotation around X, Y, Z-axis

[編集内容(Rotation around X, Y, Z-axis)]
qr = QuantumRegister(3, 'q')
qc = QuantumCircuit(qr)
qc.rx(pi / 1, qr[0])
qc.ry(pi / 2, qr[0])
qc.rz(pi / 3, qr[0])
qc.ry(pi / 4, qr[1])
qc.rz(pi / 5, qr[1])
qc.rx(pi / 6, qr[1])
qc.rz(pi / 7, qr[2])
qc.rx(pi / 8, qr[2])
qc.ry(pi / 9, qr[2])
qc.draw()

[編集内容(Rotation around X, Y, Z-axis)]

qr = QuantumRegister(3, 'q')

qc = QuantumCircuit(qr)

qc.rx(pi / 1, qr[0])

qc.ry(pi / 2, qr[0])

qc.rz(pi / 3, qr[0])

qc.ry(pi / 4, qr[1])

qc.rz(pi / 5, qr[1])

qc.rx(pi / 6, qr[1])

qc.rz(pi / 7, qr[2])

qc.rx(pi / 8, qr[2])

qc.ry(pi / 9, qr[2])

qc.draw()

[出力結果]
      ┌───────┐ ┌─────────┐┌─────────┐
q_0: ─┤ RX(π) ├─┤ RY(π/2) ├┤ RZ(π/3) ├
     ┌┴───────┴┐├─────────┤├─────────┤
q_1: ┤ RY(π/4) ├┤ RZ(π/5) ├┤ RX(π/6) ├
     ├─────────┤├─────────┤├─────────┤
q_2: ┤ RZ(π/7) ├┤ RX(π/8) ├┤ RY(π/9) ├
     └─────────┘└─────────┘└─────────┘

[出力結果]

┌───────┐ ┌─────────┐┌─────────┐

q_0: ─┤ RX(π) ├─┤ RY(π/2) ├┤ RZ(π/3) ├

┌┴───────┴┐├─────────┤├─────────┤

q_1: ┤ RY(π/4) ├┤ RZ(π/5) ├┤ RX(π/6) ├

├─────────┤├─────────┤├─────────┤

q_2: ┤ RZ(π/7) ├┤ RX(π/8) ├┤ RY(π/9) ├

└─────────┘└─────────┘└─────────┘

Controlled X, Y, Z, Hadamard Gates

[編集内容(Controlled X, Y, Z, Hadamard Gates)]
q = QuantumRegister(2)
qc = QuantumCircuit(q)
qc.cx(q[0], q[1])
qc.cy(q[1], q[0])
qc.cz(q[0], q[1])
qc.ch(q[1], q[0])
qc.draw()

[編集内容(Controlled X, Y, Z, Hadamard Gates)]

q = QuantumRegister(2)

qc = QuantumCircuit(q)

qc.cx(q[0], q[1])

qc.cy(q[1], q[0])

qc.cz(q[0], q[1])

qc.ch(q[1], q[0])

qc.draw()

[出力結果]
            ┌───┐   ┌───┐
q10_0: ──■──┤ Y ├─■─┤ H ├
       ┌─┴─┐└─┬─┘ │ └─┬─┘
q10_1: ┤ X ├──■───■───■──
       └───┘

[出力結果]

┌───┐ ┌───┐

q10_0: ──■──┤ Y ├─■─┤ H ├

┌─┴─┐└─┬─┘ │ └─┬─┘

q10_1: ┤ X ├──■───■───■──

└───┘

参照サイト

2021年3月31日

C++ の動作確認をしてみた（４３５）

C++の練習を兼ねて, AtCoder Grand Contest 041 の問題C (Domino Quality) を解いてみた.

■感想.
1. 問題Cは, 解答方針が見えなかったので, 解説を参考に実装して, ようやく, AC版に到達できた.
2. ドミノ牌の敷き詰め方に, 不思議な性質があることを知って, 個人的には, 非常に面白い問題に感じた.
3. 時間を見つけて, 引き続き, 過去問を振り返っていきたいと思う.

本家のサイト AtCoder Grand Contest 041 解説をご覧下さい.

■C++版プログラム(問題C／AC版).

// 解き直し.
// https://img.atcoder.jp/agc041/editorial.pdf
// C++(GCC 9.2.1)
#include <bits/stdc++.h>
using namespace std;
#define repex(i, a, b, c) for(int i = a; i < b; i += c)
#define repx(i, a, b) repex(i, a, b, 1)
#define rep(i, n) repx(i, 0, n)
#define repr(i, a, b) for(int i = a; i >= b; i--)
char ans[1010][1010];

char q31[3][3] = {
    {'a', 'a', '.'},
    {'.', '.', 'a'},
    {'.', '.', 'a'}
};
char q43[4][4] = {
    {'a', 'a', 'b', 'c'},
    {'d', 'd', 'b', 'c'},
    {'b', 'c', 'a', 'a'},
    {'b', 'c', 'd', 'd'}
};
char q53[5][5] = {
    {'a', 'a', 'b', 'b', 'a'},
    {'b', 'c', 'c', '.', 'a'},
    {'b', '.', '.', 'c', 'b'},
    {'a', '.', '.', 'c', 'b'},
    {'a', 'b', 'b', 'a', 'a'}
};
char q63[6][6] = {
    {'a', 'a', 'b', 'c', '.', '.'},
    {'d', 'd', 'b', 'c', '.', '.'},
    {'.', '.', 'a', 'a', 'b', 'c'},
    {'.', '.', 'd', 'd', 'b', 'c'},
    {'b', 'c', '.', '.', 'a', 'a'},
    {'b', 'c', '.', '.', 'd', 'd'}
};
char q73[7][7] = {
    {'a', 'a', 'b', 'b', 'c', 'c', '.'},
    {'d', 'd', '.', 'd', 'd', '.', 'a'},
    {'.', '.', 'd', '.', '.', 'd', 'a'},
    {'.', '.', 'd', '.', '.', 'd', 'b'},
    {'d', 'd', '.', 'd', 'd', '.', 'b'},
    {'.', '.', 'd', '.', '.', 'd', 'c'},
    {'.', '.', 'd', '.', '.', 'd', 'c'}
};

int main(){
    
    // 1. 入力情報.
    int N;
    scanf("%d", &N);
    
    // 2. N = 2.
    if(N == 2){
        puts("-1");
        return 0;
    }
    
    // 3. N = 3.
    if(N == 3){
        rep(i, 3){
            rep(j, 3) printf("%c", q31[i][j]);
            puts("");
        }
        return 0;
    }
    
    // 4. N >= 4.
    // 4-1. x, y を 算出.
    int x = N / 4, y = N - x * 4, s, e;
    if(y < 4) x--, y += 4;
    rep(i, N) rep(j, N) ans[i][j] = '.';
    
    // 4-2. 4 * 4 の マス(x個).
    rep(k, x){
        // 左上が, k番目の場合, (4 * k, 4 * k) ～ (4 * k + 3, 4 * k + 3)
        // の 範囲 を, q43 で 埋めるようにする.
        s = 4 * k;
        e = 4 * (k + 1);
        repx(i, s, e){
            int di = i - s;
            repx(j, s, e){
                int dj = j - s;
                ans[i][j] = q43[di][dj];
            }
        }
    }
    
    // 4-3. y * y の マス(1個).
    s = 4 * x;
    e = N;
    repx(i, s, e){
        int di = i - s;
        repx(j, s, e){
            int dj = j - s;
            if(y == 4) ans[i][j] = q43[di][dj];
            if(y == 5) ans[i][j] = q53[di][dj];
            if(y == 6) ans[i][j] = q63[di][dj];
            if(y == 7) ans[i][j] = q73[di][dj];
        }
    }
    
    // 5. 出力.
    rep(i, N){
        rep(j, N) printf("%c", ans[i][j]);
        puts("");
    }
    return 0;
    
}

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// 解き直し.

// https://img.atcoder.jp/agc041/editorial.pdf

// C++(GCC 9.2.1)

#include <bits/stdc++.h>

using namespace std;

#define repex(i, a, b, c) for(int i = a; i < b; i += c)

#define repx(i, a, b) repex(i, a, b, 1)

#define rep(i, n) repx(i, 0, n)

#define repr(i, a, b) for(int i = a; i >= b; i--)

char ans[1010][1010];

char q31[3][3] = {

{'a', 'a', '.'},

{'.', '.', 'a'},

{'.', '.', 'a'}

};

char q43[4][4] = {

{'a', 'a', 'b', 'c'},

{'d', 'd', 'b', 'c'},

{'b', 'c', 'a', 'a'},

{'b', 'c', 'd', 'd'}

};

char q53[5][5] = {

{'a', 'a', 'b', 'b', 'a'},

{'b', 'c', 'c', '.', 'a'},

{'b', '.', '.', 'c', 'b'},

{'a', '.', '.', 'c', 'b'},

{'a', 'b', 'b', 'a', 'a'}

};

char q63[6][6] = {

{'a', 'a', 'b', 'c', '.', '.'},

{'d', 'd', 'b', 'c', '.', '.'},

{'.', '.', 'a', 'a', 'b', 'c'},

{'.', '.', 'd', 'd', 'b', 'c'},

{'b', 'c', '.', '.', 'a', 'a'},

{'b', 'c', '.', '.', 'd', 'd'}

};

char q73[7][7] = {

{'a', 'a', 'b', 'b', 'c', 'c', '.'},

{'d', 'd', '.', 'd', 'd', '.', 'a'},

{'.', '.', 'd', '.', '.', 'd', 'a'},

{'.', '.', 'd', '.', '.', 'd', 'b'},

{'d', 'd', '.', 'd', 'd', '.', 'b'},

{'.', '.', 'd', '.', '.', 'd', 'c'},

{'.', '.', 'd', '.', '.', 'd', 'c'}

};

int main(){

// 1. 入力情報.

int N;

scanf("%d", &N);

// 2. N = 2.

if(N == 2){

puts("-1");

return 0;

}

// 3. N = 3.

if(N == 3){

rep(i, 3){

rep(j, 3) printf("%c", q31[i][j]);

puts("");

}

return 0;

}

// 4. N >= 4.

// 4-1. x, y を算出.

int x = N / 4, y = N - x * 4, s, e;

if(y < 4) x--, y += 4;

rep(i, N) rep(j, N) ans[i][j] = '.';

// 4-2. 4 * 4 のマス(x個).

rep(k, x){

// 左上が, k番目の場合, (4 * k, 4 * k) ～ (4 * k + 3, 4 * k + 3)

// の範囲を, q43 で埋めるようにする.

s = 4 * k;

e = 4 * (k + 1);

repx(i, s, e){

int di = i - s;

repx(j, s, e){

int dj = j - s;

ans[i][j] = q43[di][dj];

}

// 4-3. y * y のマス(1個).

s = 4 * x;

e = N;

repx(i, s, e){

int di = i - s;

repx(j, s, e){

int dj = j - s;

if(y == 4) ans[i][j] = q43[di][dj];

if(y == 5) ans[i][j] = q53[di][dj];

if(y == 6) ans[i][j] = q63[di][dj];

if(y == 7) ans[i][j] = q73[di][dj];

}

// 5. 出力.

rep(i, N){

rep(j, N) printf("%c", ans[i][j]);

puts("");

}

return 0;

}

[入力例]
6

[出力例]
aabb..
b..zz.
ba....
.a..aa
..a..b
..a..b
※AtCoderテストケースより

※但し, 上記のプログラムでは, 以下の内容が出力される.
aabc..
ddbc..
..aabc
..ddbc
bc..aa
bc..dd

[入力例]
2

[出力例]
-1
※AtCoderテストケースより

[入力例]
3

[出力例]
aa.
..a
..a

[入力例]
7

[出力例]
aabbcc.
dd.dd.a
..d..da
..d..db
dd.dd.b
..d..dc
..d..dc

[入力例]
8

[出力例]
aabc....
ddbc....
bcaa....
bcdd....
....aabc
....ddbc
....bcaa
....bcdd

[入力例]
9

[出力例]
aabc.....
ddbc.....
bcaa.....
bcdd.....
....aabba
....bcc.a
....b..cb
....a..cb
....abbaa

[入力例]
10

[出力例]
aabc......
ddbc......
bcaa......
bcdd......
....aabc..
....ddbc..
......aabc
......ddbc
....bc..aa
....bc..dd

[入力例]
11

[出力例]
aabc.......
ddbc.......
bcaa.......
bcdd.......
....aabbcc.
....dd.dd.a
......d..da
......d..db
....dd.dd.b
......d..dc
......d..dc

[入力例]
33

[出力例]
aabc.............................
ddbc.............................
bcaa.............................
bcdd.............................
....aabc.........................
....ddbc.........................
....bcaa.........................
....bcdd.........................
........aabc.....................
........ddbc.....................
........bcaa.....................
........bcdd.....................
............aabc.................
............ddbc.................
............bcaa.................
............bcdd.................
................aabc.............
................ddbc.............
................bcaa.............
................bcdd.............
....................aabc.........
....................ddbc.........
....................bcaa.........
....................bcdd.........
........................aabc.....
........................ddbc.....
........................bcaa.....
........................bcdd.....
............................aabba
............................bcc.a
............................b..cb
............................a..cb
............................abbaa


[入力例]
55

[出力例]
aabc...................................................
ddbc...................................................
bcaa...................................................
bcdd...................................................
....aabc...............................................
....ddbc...............................................
....bcaa...............................................
....bcdd...............................................
........aabc...........................................
........ddbc...........................................
........bcaa...........................................
........bcdd...........................................
............aabc.......................................
............ddbc.......................................
............bcaa.......................................
............bcdd.......................................
................aabc...................................
................ddbc...................................
................bcaa...................................
................bcdd...................................
....................aabc...............................
....................ddbc...............................
....................bcaa...............................
....................bcdd...............................
........................aabc...........................
........................ddbc...........................
........................bcaa...........................
........................bcdd...........................
............................aabc.......................
............................ddbc.......................
............................bcaa.......................
............................bcdd.......................
................................aabc...................
................................ddbc...................
................................bcaa...................
................................bcdd...................
....................................aabc...............
....................................ddbc...............
....................................bcaa...............
....................................bcdd...............
........................................aabc...........
........................................ddbc...........
........................................bcaa...........
........................................bcdd...........
............................................aabc.......
............................................ddbc.......
............................................bcaa.......
............................................bcdd.......
................................................aabbcc.
................................................dd.dd.a
..................................................d..da
..................................................d..db
................................................dd.dd.b
..................................................d..dc
..................................................d..dc

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[入力例]

[出力例]

aabb..

b..zz.

ba....

.a..aa

..a..b

※AtCoderテストケースより

※但し, 上記のプログラムでは, 以下の内容が出力される.

aabc..

ddbc..

..aabc

..ddbc

bc..aa

bc..dd

[入力例]

[出力例]

-1

※AtCoderテストケースより

[入力例]

[出力例]

aa.

..a

[入力例]

[出力例]

aabbcc.

dd.dd.a

..d..da

..d..db

dd.dd.b

..d..dc

[入力例]

[出力例]

aabc....

ddbc....

bcaa....

bcdd....

....aabc

....ddbc

....bcaa

....bcdd

[入力例]

[出力例]

aabc.....

ddbc.....

bcaa.....

bcdd.....

....aabba

....bcc.a

....b..cb

....a..cb

....abbaa

[入力例]

[出力例]

aabc......

ddbc......

bcaa......

bcdd......

....aabc..

....ddbc..

......aabc

......ddbc

....bc..aa

....bc..dd

[入力例]

[出力例]

aabc.......

ddbc.......

bcaa.......

bcdd.......

....aabbcc.

....dd.dd.a

......d..da

......d..db

....dd.dd.b

......d..dc

[入力例]

[出力例]

aabc.............................

ddbc.............................

bcaa.............................

bcdd.............................

....aabc.........................

....ddbc.........................

....bcaa.........................

....bcdd.........................

........aabc.....................

........ddbc.....................

........bcaa.....................

........bcdd.....................

............aabc.................

............ddbc.................

............bcaa.................

............bcdd.................

................aabc.............

................ddbc.............

................bcaa.............

................bcdd.............

....................aabc.........

....................ddbc.........

....................bcaa.........

....................bcdd.........

........................aabc.....

........................ddbc.....

........................bcaa.....

........................bcdd.....

............................aabba

............................bcc.a

............................b..cb

............................a..cb

............................abbaa

[入力例]

[出力例]

aabc...................................................

ddbc...................................................

bcaa...................................................

bcdd...................................................

....aabc...............................................

....ddbc...............................................

....bcaa...............................................

....bcdd...............................................

........aabc...........................................

........ddbc...........................................

........bcaa...........................................

........bcdd...........................................

............aabc.......................................

............ddbc.......................................

............bcaa.......................................

............bcdd.......................................

................aabc...................................

................ddbc...................................

................bcaa...................................

................bcdd...................................

....................aabc...............................

....................ddbc...............................

....................bcaa...............................

....................bcdd...............................

........................aabc...........................

........................ddbc...........................

........................bcaa...........................

........................bcdd...........................

............................aabc.......................

............................ddbc.......................

............................bcaa.......................

............................bcdd.......................

................................aabc...................

................................ddbc...................

................................bcaa...................

................................bcdd...................

....................................aabc...............

....................................ddbc...............

....................................bcaa...............

....................................bcdd...............

........................................aabc...........

........................................ddbc...........

........................................bcaa...........

........................................bcdd...........

............................................aabc.......

............................................ddbc.......

............................................bcaa.......

............................................bcdd.......

................................................aabbcc.

................................................dd.dd.a

..................................................d..da

..................................................d..db

................................................dd.dd.b

..................................................d..dc

■参照サイト
AtCoder Grand Contest 041

2021年3月30日2021年3月30日

Python（Qiskit）について（２）

概要

Qiskit について, サンプルプログラムを動かしてみた.
動作環境は, Google Colaboratory で行った
実行プログラム, 解説は, 下記の参照サイトをご覧ください

感想

本家のサイトにあるように, 実行結果が, 立体的なグラフで表現されたりと, 非常に高機能だと驚いた.
時間を見つけて, 今後も, ドキュメントの残りの部分を進めていこうと思う.

Qiskit Visualizations

Qiskit のサンプルプログラム

[編集内容(Bell state)]
from qiskit import *
from qiskit.visualization import plot_histogram
from qiskit.tools.monitor import job_monitor

# quantum circuit to make a Bell state
bell = QuantumCircuit(2)
bell.h(0)
bell.cx(0, 1)

meas = QuantumCircuit(2)
meas.measure_all()

# execute the quantum circuit
backend = BasicAer.get_backend('qasm_simulator') # the device to run on
circ = bell + meas
result = execute(circ, backend, shots=10000).result()
counts  = result.get_counts(circ)
print(counts)

[編集内容(Bell state)]

from qiskit import *

from qiskit.visualization import plot_histogram

from qiskit.tools.monitor import job_monitor

# quantum circuit to make a Bell state

bell = QuantumCircuit(2)

bell.h(0)

bell.cx(0, 1)

meas = QuantumCircuit(2)

meas.measure_all()

# execute the quantum circuit

backend = BasicAer.get_backend('qasm_simulator') # the device to run on

circ = bell + meas

result = execute(circ, backend, shots=10000).result()

counts = result.get_counts(circ)

print(counts)

[出力結果]
※実行するごとに, 測定結果が変わってくる.
{'11': 4880, '00': 5120}

[出力結果]

※実行するごとに, 測定結果が変わってくる.

{'11': 4880, '00': 5120}

グラフ描画

[編集内容(Bell state graph)]
from qiskit.visualization import plot_state_city, plot_bloch_multivector
from qiskit.visualization import plot_state_paulivec, plot_state_hinton
from qiskit.visualization import plot_state_qsphere

# execute the quantum circuit
backend = BasicAer.get_backend('statevector_simulator') # the device to run on
result = execute(bell, backend).result()
psi  = result.get_statevector(bell)
plot_state_city(psi)

[編集内容(Bell state graph)]

from qiskit.visualization import plot_state_city, plot_bloch_multivector

from qiskit.visualization import plot_state_paulivec, plot_state_hinton

from qiskit.visualization import plot_state_qsphere

# execute the quantum circuit

backend = BasicAer.get_backend('statevector_simulator') # the device to run on

result = execute(bell, backend).result()

psi = result.get_statevector(bell)

plot_state_city(psi)

[出力結果]
※グラフが描画された.

1 2	[出力結果] ※グラフが描画された.

Qiskit のサンプルプログラム

[編集内容(3-qubit GHZ state)]
from qiskit import *
from qiskit.visualization import plot_histogram
from qiskit.tools.monitor import job_monitor

# quantum circuit to make a GHZ state
ghz = QuantumCircuit(3)
ghz.h(0)
ghz.cx(0, 1)
ghz.cx(0, 2)

meas = QuantumCircuit(3)
meas.measure_all()

# execute the quantum circuit
backend = BasicAer.get_backend('qasm_simulator') # the device to run on
circ = ghz + meas
result = execute(circ, backend, shots=10000).result()
counts  = result.get_counts(circ)
print(counts)

[編集内容(3-qubit GHZ state)]

from qiskit import *

from qiskit.visualization import plot_histogram

from qiskit.tools.monitor import job_monitor

# quantum circuit to make a GHZ state

ghz = QuantumCircuit(3)

ghz.h(0)

ghz.cx(0, 1)

ghz.cx(0, 2)

meas = QuantumCircuit(3)

meas.measure_all()

# execute the quantum circuit

backend = BasicAer.get_backend('qasm_simulator') # the device to run on

circ = ghz + meas

result = execute(circ, backend, shots=10000).result()

counts = result.get_counts(circ)

print(counts)

[出力結果]
※実行するごとに, 測定結果が変わってくる.
{'000': 5044, '111': 4956}

[出力結果]

※実行するごとに, 測定結果が変わってくる.

{'000': 5044, '111': 4956}

グラフ描画

[編集内容(3-qubit GHZ state graph)]
from qiskit.visualization import plot_state_city, plot_bloch_multivector
from qiskit.visualization import plot_state_paulivec, plot_state_hinton
from qiskit.visualization import plot_state_qsphere

# execute the quantum circuit
backend = BasicAer.get_backend('statevector_simulator') # the device to run on
result = execute(ghz, backend).result()
psi  = result.get_statevector(ghz)
plot_state_city(psi)

[編集内容(3-qubit GHZ state graph)]

from qiskit.visualization import plot_state_city, plot_bloch_multivector

from qiskit.visualization import plot_state_paulivec, plot_state_hinton

from qiskit.visualization import plot_state_qsphere

# execute the quantum circuit

backend = BasicAer.get_backend('statevector_simulator') # the device to run on

result = execute(ghz, backend).result()

psi = result.get_statevector(ghz)

plot_state_city(psi)

[出力結果]
※グラフが描画された.

1 2	[出力結果] ※グラフが描画された.

Single-Qubit Gates

量子ゲート(1ビット)

[編集内容(u3 gates)]
import matplotlib.pyplot as plt
%matplotlib inline
import numpy as np
from math import pi
from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister, execute
from qiskit.tools.visualization import circuit_drawer
from qiskit.quantum_info import state_fidelity
from qiskit import BasicAer

backend = BasicAer.get_backend('unitary_simulator')

q = QuantumRegister(1)
qc = QuantumCircuit(q)

# /usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:14: DeprecationWarning: 
# The QuantumCircuit.u3 method is deprecated as of 0.16.0. 
# It will be removed no earlier than 3 months after the release date. 
# You should use QuantumCircuit.u instead, which acts identically. 
# Alternatively, you can decompose u3 in terms of QuantumCircuit.p and QuantumCircuit.sx: 
# u3(ϴ,φ,λ) = p(φ+π) sx p(ϴ+π) sx p(λ) (2 pulses on hardware).
# qc.u3(0, pi/4, pi/3, q)
qc.u(0, pi/4, pi/3, q)
qc.draw()

[編集内容(u3 gates)]

import matplotlib.pyplot as plt

%matplotlib inline

import numpy as np

from math import pi

from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister, execute

from qiskit.tools.visualization import circuit_drawer

from qiskit.quantum_info import state_fidelity

from qiskit import BasicAer

backend = BasicAer.get_backend('unitary_simulator')

q = QuantumRegister(1)

qc = QuantumCircuit(q)

# /usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:14: DeprecationWarning:

# The QuantumCircuit.u3 method is deprecated as of 0.16.0.

# It will be removed no earlier than 3 months after the release date.

# You should use QuantumCircuit.u instead, which acts identically.

# Alternatively, you can decompose u3 in terms of QuantumCircuit.p and QuantumCircuit.sx:

# u3(ϴ,φ,λ) = p(φ+π) sx p(ϴ+π) sx p(λ) (2 pulses on hardware).

# qc.u3(0, pi/4, pi/3, q)

qc.u(0, pi/4, pi/3, q)

qc.draw()

[出力結果]
       ┌──────────────┐
q68_0: ┤ U(0,π/4,π/3) ├

[出力結果]

┌──────────────┐

q68_0: ┤ U(0,π/4,π/3) ├

量子ゲート(1ビット)

[編集内容(u2 gates)]
import matplotlib.pyplot as plt
%matplotlib inline
import numpy as np
from math import pi
from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister, execute
from qiskit.tools.visualization import circuit_drawer
from qiskit.quantum_info import state_fidelity
from qiskit import BasicAer

backend = BasicAer.get_backend('unitary_simulator')

q = QuantumRegister(1)
qc = QuantumCircuit(q)

# /usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:15: 
# DeprecationWarning: The QuantumCircuit.u2 method is deprecated as of 0.16.0. 
# It will be removed no earlier than 3 months after the release date. 
# You can use the general 1-qubit gate QuantumCircuit.u instead: u2(φ,λ) = u(π/2, φ, λ). 
# Alternatively, you can decompose it interms of QuantumCircuit.p and QuantumCircuit.sx: 
# u2(φ,λ) = p(π/2+φ) sx p(λ-π/2) (1 pulse on hardware).
#  from ipykernel import kernelapp as app
# qc.u2(pi/4, pi/3, q)
qc.u(pi/2, pi/4, pi/3, q)
qc.draw()

[編集内容(u2 gates)]

import matplotlib.pyplot as plt

%matplotlib inline

import numpy as np

from math import pi

from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister, execute

from qiskit.tools.visualization import circuit_drawer

from qiskit.quantum_info import state_fidelity

from qiskit import BasicAer

backend = BasicAer.get_backend('unitary_simulator')

q = QuantumRegister(1)

qc = QuantumCircuit(q)

# /usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:15:

# DeprecationWarning: The QuantumCircuit.u2 method is deprecated as of 0.16.0.

# It will be removed no earlier than 3 months after the release date.

# You can use the general 1-qubit gate QuantumCircuit.u instead: u2(φ,λ) = u(π/2, φ, λ).

# Alternatively, you can decompose it interms of QuantumCircuit.p and QuantumCircuit.sx:

# u2(φ,λ) = p(π/2+φ) sx p(λ-π/2) (1 pulse on hardware).

# from ipykernel import kernelapp as app

# qc.u2(pi/4, pi/3, q)

qc.u(pi/2, pi/4, pi/3, q)

qc.draw()

[出力結果]
       ┌────────────────┐
q73_0: ┤ U(π/2,π/4,π/3) ├
       └────────────────┘

[出力結果]

┌────────────────┐

q73_0: ┤ U(π/2,π/4,π/3) ├

└────────────────┘

参照サイト

2021年3月30日2021年3月30日

C++ の動作確認をしてみた（４３４）

C++の練習を兼ねて, AtCoder Beginner Contest 197 の問題E (Traveler) を解いてみた.

■感想.
1. 問題Eは, 解答方針が見えなかったので, 解説を参考に実装して, ようやく, AC版に到達できた.
2. 苦手なdpの訓練を積めたので, 非常に良かったと思う.
3. 時間を見つけて, 引き続き, 過去問を振り返っていきたいと思う.

本家のサイト AtCoder Beginner Contest 197 解説の各リンクをご覧下さい.

■C++版プログラム(問題E／AC版).

// 解き直し.
// https://atcoder.jp/contests/abc197/editorial/995
// C++(GCC 9.2.1)
#include <bits/stdc++.h>
using namespace std;
using LL = long long;
using vl = vector<LL>;
using vvl = vector<vl>;
#define repex(i, a, b, c) for(int i = a; i < b; i += c)
#define repx(i, a, b) repex(i, a, b, 1)
#define rep(i, n) repx(i, 0, n)
#define repr(i, a, b) for(int i = a; i >= b; i--)
#define pb push_back
#define all(x) x.begin(), x.end()
LL dp[202020][2];

int main(){
    
    // 1. 入力情報.
    int N;
    scanf("%d", &N);
    vvl v(N + 2);
    rep(i, N){
        LL x;
        int c;
        scanf("%lld %d", &x, &c);
        v[c].pb(x);
    }
    
    // 2. 番兵(ボールの色: N + 1).
    // -> 原点を保存.
    v[N + 1].pb(0);
    
    // 3. sort.
    rep(i, N + 2) sort(all(v[i]));
    
    // 4. dp更新.
    LL befL = 0, befR = 0, curL, curR, d1, d2;
    repx(i, 1, N + 2){
        // 4-1. ボールの有無を保存.
        int f = v[i].size();
        
        // 4-2. ボールあり.
        if(f){
            // 今回分更新.
            curL = v[i].front();
            curR = v[i].back();
            
            // 色 i を回収して, 左側にいる場合.
            d1 = dp[i - 1][0];
            d1 += (befL > curR) ? (befL - curL) : ((curR - befL) + (curR - curL));
            d2 = dp[i - 1][1];
            d2 += (befR > curR) ? (befR - curL) : ((curR - befR) + (curR - curL));
            dp[i][0] = min(d1, d2);
            
            // 色 i を回収して, 右側にいる場合.
            d1 = dp[i - 1][0];
            d1 += (befL > curL) ? ((befL - curL) + (curR - curL)) : (curR - befL);
            d2 = dp[i - 1][1];
            d2 += (befR > curL) ? ((befR - curL) + (curR - curL)) : (curR - befR);
            dp[i][1] = min(d1, d2);
            
            // 前回分更新.
            befL = curL;
            befR = curR;
        }
        
        // 4-3. ボールなし.
        if(!f){
            dp[i][0] = dp[i - 1][0];
            dp[i][1] = dp[i - 1][1];
        }
    }
    
    // 5. 出力.
    printf("%lld\n", min(dp[N + 1][0], dp[N + 1][1]));
    return 0;
    
}

// 解き直し.

// https://atcoder.jp/contests/abc197/editorial/995

// C++(GCC 9.2.1)

#include <bits/stdc++.h>

using namespace std;

using LL = long long;

using vl = vector<LL>;

using vvl = vector<vl>;

#define repex(i, a, b, c) for(int i = a; i < b; i += c)

#define repx(i, a, b) repex(i, a, b, 1)

#define rep(i, n) repx(i, 0, n)

#define repr(i, a, b) for(int i = a; i >= b; i--)

#define pb push_back

#define all(x) x.begin(), x.end()

LL dp[202020][2];

int main(){

// 1. 入力情報.

int N;

scanf("%d", &N);

vvl v(N + 2);

rep(i, N){

LL x;

int c;

scanf("%lld %d", &x, &c);

v[c].pb(x);

}

// 2. 番兵(ボールの色: N + 1).

// -> 原点を保存.

v[N + 1].pb(0);

// 3. sort.

rep(i, N + 2) sort(all(v[i]));

// 4. dp更新.

LL befL = 0, befR = 0, curL, curR, d1, d2;

repx(i, 1, N + 2){

// 4-1. ボールの有無を保存.

int f = v[i].size();

// 4-2. ボールあり.

if(f){

// 今回分更新.

curL = v[i].front();

curR = v[i].back();

// 色 i を回収して, 左側にいる場合.

d1 = dp[i - 1][0];

d1 += (befL > curR) ? (befL - curL) : ((curR - befL) + (curR - curL));

d2 = dp[i - 1][1];

d2 += (befR > curR) ? (befR - curL) : ((curR - befR) + (curR - curL));

dp[i][0] = min(d1, d2);

// 色 i を回収して, 右側にいる場合.

d1 = dp[i - 1][0];

d1 += (befL > curL) ? ((befL - curL) + (curR - curL)) : (curR - befL);

d2 = dp[i - 1][1];

d2 += (befR > curL) ? ((befR - curL) + (curR - curL)) : (curR - befR);

dp[i][1] = min(d1, d2);

// 前回分更新.

befL = curL;

befR = curR;

}

// 4-3. ボールなし.

if(!f){

dp[i][0] = dp[i - 1][0];

dp[i][1] = dp[i - 1][1];

}

// 5. 出力.

printf("%lld\n", min(dp[N + 1][0], dp[N + 1][1]));

return 0;

}

[入力例]
5
2 2
3 1
1 3
4 2
5 3

[出力例]
12
※AtCoderテストケースより

[入力例]
9
5 5
-4 4
4 3
6 3
-5 5
-3 2
2 2
3 3
1 4

[出力例]
38
※AtCoderテストケースより

[入力例]
25
-36 22
51 25
52 13
113 8
-35 20
62 15
119 13
-104 5
110 2
91 17
-125 4
-71 11
60 19
89 22
-58 8
-7 12
-20 6
-110 20
-70 13
28 25
84 8
120 20
-37 14
-56 22
-72 7

[出力例]
2020

[入力例]
50
-900094 26
-712369 24
443734 20
-219850 20
746600 4
443548 10
201076 43
200562 19
1054193 28
-1066985 7
-217953 12
-282472 15
-324321 14
-196387 25
-697769 41
1213776 6
-1048894 12
-565530 11
279075 16
60507 5
443964 24
-268933 50
-562404 27
208251 19
-414540 10
-334856 6
184481 40
-1065994 11
572836 25
-382416 40
-1142099 37
724968 50
827501 9
-816595 10
-650848 7
-392826 44
-151981 17
-1232079 36
-614437 37
825447 12
1056309 4
309613 22
-525126 46
-1043184 22
-1176284 17
-1158708 33
-347587 16
-819143 44
949645 15
626133 50

[出力例]
33996956

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

[入力例]

2 2

3 1

1 3

4 2

5 3

[出力例]

※AtCoderテストケースより

[入力例]

5 5

-4 4

4 3

6 3

-5 5

-3 2

2 2

3 3

1 4

[出力例]

※AtCoderテストケースより

[入力例]

-36 22

51 25

52 13

113 8

-35 20

62 15

119 13

-104 5

110 2

91 17

-125 4

-71 11

60 19

89 22

-58 8

-7 12

-20 6

-110 20

-70 13

28 25

84 8

120 20

-37 14

-56 22

-72 7

[出力例]

2020

[入力例]

-900094 26

-712369 24

443734 20

-219850 20

746600 4

443548 10

201076 43

200562 19

1054193 28

-1066985 7

-217953 12

-282472 15

-324321 14

-196387 25

-697769 41

1213776 6

-1048894 12

-565530 11

279075 16

60507 5

443964 24

-268933 50

-562404 27

208251 19

-414540 10

-334856 6

184481 40

-1065994 11

572836 25

-382416 40

-1142099 37

724968 50

827501 9

-816595 10

-650848 7

-392826 44

-151981 17

-1232079 36

-614437 37

825447 12

1056309 4

309613 22

-525126 46

-1043184 22

-1176284 17

-1158708 33

-347587 16

-819143 44

949645 15

626133 50

[出力例]

33996956

■参照サイト
AtCoder Beginner Contest 197（Sponsored by Panasonic）

2021年3月29日

Python（Qiskit）について（１）

概要

Qiskit について, サンプルプログラムを動かしてみた.
動作環境は, Google Colaboratory で行った
実行プログラム, 解説は, 下記の参照サイトをご覧ください

感想

量子物理学に関する知識(用語, 数式の意味ほか)は, 徐々に身につけていく必要があると感じた.
時間を見つけて, 今後も, ドキュメントの残りの部分を進めていこうと思う.

Installing Qiskit

Qiskit のインストール

[編集内容(qiskit install)]
!pip install qiskit

1 2	[編集内容(qiskit install)] !pip install qiskit

[出力結果]
Collecting qiskit
  Downloading https://files.pythonhosted.org/packages/f7/4c/2d3065e1feca573a6f9f5f53d6d9db3896d50b6575191e33401956608955/qiskit-0.24.1.tar.gz
Collecting qiskit-terra==0.16.4
  Downloading https://files.pythonhosted.org/packages/89/64/d70a10bce894ec81a227aabc47305449b48bcffd7dde76d30e7cea6c9786/qiskit_terra-0.16.4-cp37-cp37m-manylinux2010_x86_64.whl (8.5MB)
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Collecting qiskit-aer==0.7.6
  Downloading https://files.pythonhosted.org/packages/03/98/735a869724392a8fa084a65d601a8c8940aacdc4c245aba9a65d9a2669ec/qiskit_aer-0.7.6-cp37-cp37m-manylinux2010_x86_64.whl (17.6MB)
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Collecting qiskit-ibmq-provider==0.12.2
  Downloading https://files.pythonhosted.org/packages/08/ac/69bb35892303c3a4a52eaaf7ea95431dd3f57963b580a011ee92693a7fcc/qiskit_ibmq_provider-0.12.2-py3-none-any.whl (198kB)
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Collecting qiskit-ignis==0.5.2
  Downloading https://files.pythonhosted.org/packages/b2/1d/d5df8cf48cf20a26deb6e0535f020cd2ad625cb27457abb0ab39c2104e38/qiskit_ignis-0.5.2-py3-none-any.whl (203kB)
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Collecting qiskit-aqua==0.8.2
  Downloading https://files.pythonhosted.org/packages/0e/82/528741676960a7fd1c75151639601826118f2729ad53034fa3b39290c056/qiskit_aqua-0.8.2-py3-none-any.whl (2.1MB)
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Collecting ply>=3.10
  Downloading https://files.pythonhosted.org/packages/a3/58/35da89ee790598a0700ea49b2a66594140f44dec458c07e8e3d4979137fc/ply-3.11-py2.py3-none-any.whl (49kB)
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Requirement already satisfied: jsonschema>=2.6 in /usr/local/lib/python3.7/dist-packages (from qiskit-terra==0.16.4->qiskit) (2.6.0)
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Requirement already satisfied: scipy>=1.4 in /usr/local/lib/python3.7/dist-packages (from qiskit-terra==0.16.4->qiskit) (1.4.1)
Collecting retworkx>=0.5.0
  Downloading https://files.pythonhosted.org/packages/1b/92/f007f8b9d88dcd5b90e363967e5d54431a68c5fe06d83400732e3b438084/retworkx-0.8.0-cp37-cp37m-manylinux2010_x86_64.whl (1.0MB)
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Requirement already satisfied: sympy>=1.3 in /usr/local/lib/python3.7/dist-packages (from qiskit-terra==0.16.4->qiskit) (1.7.1)
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Collecting fastjsonschema>=2.10
  Downloading https://files.pythonhosted.org/packages/89/1c/8be51fa42aadc1c1611a52b866e1a5a1032a504f24789cf140b4e6d7c940/fastjsonschema-2.15.0-py3-none-any.whl
Collecting python-constraint>=1.4
  Downloading https://files.pythonhosted.org/packages/37/8b/5f1bc2734ca611943e1d6733ee244238679f6410a10cd45ede55a61a8402/python-constraint-1.4.0.tar.bz2
Requirement already satisfied: cython>=0.27.1 in /usr/local/lib/python3.7/dist-packages (from qiskit-aer==0.7.6->qiskit) (0.29.22)
Collecting pybind11>=2.4
  Downloading https://files.pythonhosted.org/packages/8d/43/7339dbabbc2793718d59703aace4166f53c29ee1c202f6ff5bf8a26c4d91/pybind11-2.6.2-py2.py3-none-any.whl (191kB)
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Requirement already satisfied: urllib3>=1.21.1 in /usr/local/lib/python3.7/dist-packages (from qiskit-ibmq-provider==0.12.2->qiskit) (1.24.3)
Requirement already satisfied: requests>=2.19 in /usr/local/lib/python3.7/dist-packages (from qiskit-ibmq-provider==0.12.2->qiskit) (2.23.0)
Collecting requests-ntlm>=1.1.0
  Downloading https://files.pythonhosted.org/packages/03/4b/8b9a1afde8072c4d5710d9fa91433d504325821b038e00237dc8d6d833dc/requests_ntlm-1.1.0-py2.py3-none-any.whl
Collecting websockets>=8
  Downloading https://files.pythonhosted.org/packages/5a/0b/3ebc752392a368af14dd24ee041683416ac6d2463eead94b311b11e41c82/websockets-8.1-cp37-cp37m-manylinux2010_x86_64.whl (79kB)
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Requirement already satisfied: setuptools>=40.1.0 in /usr/local/lib/python3.7/dist-packages (from qiskit-ignis==0.5.2->qiskit) (54.1.2)
Collecting yfinance
  Downloading https://files.pythonhosted.org/packages/a7/ee/315752b9ef281ba83c62aa7ec2e2074f85223da6e7e74efb4d3e11c0f510/yfinance-0.1.59.tar.gz
Requirement already satisfied: pandas in /usr/local/lib/python3.7/dist-packages (from qiskit-aqua==0.8.2->qiskit) (1.1.5)
Collecting docplex==2.15.194
  Downloading https://files.pythonhosted.org/packages/9b/76/ebf5b75a25c4357c9a4758cae7fea778dd7f282b83c2f22e150dc7e3c852/docplex-2.15.194.tar.gz (582kB)
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Collecting dlx
  Downloading https://files.pythonhosted.org/packages/54/c0/b8fb5bb727e983b6f5251433ef941b48f38c65bb0bd6ec509e9185bcd406/dlx-1.0.4.tar.gz
Requirement already satisfied: h5py in /usr/local/lib/python3.7/dist-packages (from qiskit-aqua==0.8.2->qiskit) (2.10.0)
Requirement already satisfied: fastdtw in /usr/local/lib/python3.7/dist-packages (from qiskit-aqua==0.8.2->qiskit) (0.3.4)
Collecting quandl
  Downloading https://files.pythonhosted.org/packages/8b/2b/feefb36015beaecc5c0f9f2533e815b409621d9fa7b50b2aac621796f828/Quandl-3.6.1-py2.py3-none-any.whl
Requirement already satisfied: decorator>=4.3.0 in /usr/local/lib/python3.7/dist-packages (from networkx>=2.2->qiskit-terra==0.16.4->qiskit) (4.4.2)
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Requirement already satisfied: idna<3,>=2.5 in /usr/local/lib/python3.7/dist-packages (from requests>=2.19->qiskit-ibmq-provider==0.12.2->qiskit) (2.10)
Requirement already satisfied: certifi>=2017.4.17 in /usr/local/lib/python3.7/dist-packages (from requests>=2.19->qiskit-ibmq-provider==0.12.2->qiskit) (2020.12.5)
Collecting cryptography>=1.3
  Downloading https://files.pythonhosted.org/packages/b2/26/7af637e6a7e87258b963f1731c5982fb31cd507f0d90d91836e446955d02/cryptography-3.4.7-cp36-abi3-manylinux2014_x86_64.whl (3.2MB)
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Collecting ntlm-auth>=1.0.2
  Downloading https://files.pythonhosted.org/packages/ff/84/97c550164b54942b0e908c31ef09d9469f3ba4cd7332a671e2125732f63b/ntlm_auth-1.5.0-py2.py3-none-any.whl
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Requirement already satisfied: multitasking>=0.0.7 in /usr/local/lib/python3.7/dist-packages (from yfinance->qiskit-aqua==0.8.2->qiskit) (0.0.9)
Collecting lxml>=4.5.1
  Downloading https://files.pythonhosted.org/packages/cf/4d/6537313bf58fe22b508f08cf3eb86b29b6f9edf68e00454224539421073b/lxml-4.6.3-cp37-cp37m-manylinux1_x86_64.whl (5.5MB)
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Collecting inflection>=0.3.1
  Downloading https://files.pythonhosted.org/packages/59/91/aa6bde563e0085a02a435aa99b49ef75b0a4b062635e606dab23ce18d720/inflection-0.5.1-py2.py3-none-any.whl
Requirement already satisfied: more-itertools in /usr/local/lib/python3.7/dist-packages (from quandl->qiskit-aqua==0.8.2->qiskit) (8.7.0)
Requirement already satisfied: cffi>=1.12 in /usr/local/lib/python3.7/dist-packages (from cryptography>=1.3->requests-ntlm>=1.1.0->qiskit-ibmq-provider==0.12.2->qiskit) (1.14.5)
Requirement already satisfied: pycparser in /usr/local/lib/python3.7/dist-packages (from cffi>=1.12->cryptography>=1.3->requests-ntlm>=1.1.0->qiskit-ibmq-provider==0.12.2->qiskit) (2.20)
Building wheels for collected packages: qiskit, python-constraint, yfinance, docplex, dlx
  Building wheel for qiskit (setup.py) ... done
  Created wheel for qiskit: filename=qiskit-0.24.1-cp37-none-any.whl size=2919 sha256=ff29c727e4784ef214489254c465b1fced90c40a7af7c24e7659f4532f94bf1f
  Stored in directory: /root/.cache/pip/wheels/4a/3e/be/606704f95c92255208f2c6c571d95cc075a12d8672515ec7a5
  Building wheel for python-constraint (setup.py) ... done
  Created wheel for python-constraint: filename=python_constraint-1.4.0-py2.py3-none-any.whl size=24079 sha256=bf4f277e7c979232a94c124c9b30df6ae70a1d1cde032a4b6fbc760236adbcb2
  Stored in directory: /root/.cache/pip/wheels/34/31/15/7b070b25d0a549d20ce2e9fe6d727471c2c61ef904720fd40c
  Building wheel for yfinance (setup.py) ... done
  Created wheel for yfinance: filename=yfinance-0.1.59-py2.py3-none-any.whl size=23442 sha256=7377354156be5233a67b078debfeb9242b14297934060f8440ac2c69246b823d
  Stored in directory: /root/.cache/pip/wheels/f8/2a/0f/4b5a86e1d52e451757eb6bc17fd899629f0925c777741b6d04
  Building wheel for docplex (setup.py) ... done
  Created wheel for docplex: filename=docplex-2.15.194-cp37-none-any.whl size=645116 sha256=ef2dfc072d928a4f7db38ec4b0bb54b0825cade9cd274f6dff829df3a96fb379
  Stored in directory: /root/.cache/pip/wheels/ce/fa/5d/8f4d5fed1b8edb72e453cb2ac6fb75c6776b49d7174eb70457
  Building wheel for dlx (setup.py) ... done
  Created wheel for dlx: filename=dlx-1.0.4-cp37-none-any.whl size=5712 sha256=b29aa61a575be43da4cfc7eb11dba7a9079461dc9092f3af879354a7cc1a6b45
  Stored in directory: /root/.cache/pip/wheels/bb/ba/15/fdd0deb104df3254912998150ba9245668db06b00af5912d1a
Successfully built qiskit python-constraint yfinance docplex dlx
Installing collected packages: ply, retworkx, fastjsonschema, python-constraint, qiskit-terra, pybind11, qiskit-aer, cryptography, ntlm-auth, requests-ntlm, websockets, qiskit-ibmq-provider, qiskit-ignis, lxml, yfinance, docplex, dlx, inflection, quandl, qiskit-aqua, qiskit
  Found existing installation: lxml 4.2.6
    Uninstalling lxml-4.2.6:
      Successfully uninstalled lxml-4.2.6
Successfully installed cryptography-3.4.7 dlx-1.0.4 docplex-2.15.194 fastjsonschema-2.15.0 inflection-0.5.1 lxml-4.6.3 ntlm-auth-1.5.0 ply-3.11 pybind11-2.6.2 python-constraint-1.4.0 qiskit-0.24.1 qiskit-aer-0.7.6 qiskit-aqua-0.8.2 qiskit-ibmq-provider-0.12.2 qiskit-ignis-0.5.2 qiskit-terra-0.16.4 quandl-3.6.1 requests-ntlm-1.1.0 retworkx-0.8.0 websockets-8.1 yfinance-0.1.59

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Collecting qiskit

Downloading https://files.pythonhosted.org/packages/f7/4c/2d3065e1feca573a6f9f5f53d6d9db3896d50b6575191e33401956608955/qiskit-0.24.1.tar.gz

Collecting qiskit-terra==0.16.4

Downloading https://files.pythonhosted.org/packages/89/64/d70a10bce894ec81a227aabc47305449b48bcffd7dde76d30e7cea6c9786/qiskit_terra-0.16.4-cp37-cp37m-manylinux2010_x86_64.whl (8.5MB)

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Collecting qiskit-aer==0.7.6

Downloading https://files.pythonhosted.org/packages/03/98/735a869724392a8fa084a65d601a8c8940aacdc4c245aba9a65d9a2669ec/qiskit_aer-0.7.6-cp37-cp37m-manylinux2010_x86_64.whl (17.6MB)

|████████████████████████████████| 17.6MB 211kB/s

Collecting qiskit-ibmq-provider==0.12.2

Downloading https://files.pythonhosted.org/packages/08/ac/69bb35892303c3a4a52eaaf7ea95431dd3f57963b580a011ee92693a7fcc/qiskit_ibmq_provider-0.12.2-py3-none-any.whl (198kB)

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Collecting qiskit-ignis==0.5.2

Downloading https://files.pythonhosted.org/packages/b2/1d/d5df8cf48cf20a26deb6e0535f020cd2ad625cb27457abb0ab39c2104e38/qiskit_ignis-0.5.2-py3-none-any.whl (203kB)

|████████████████████████████████| 204kB 54.2MB/s

Collecting qiskit-aqua==0.8.2

Downloading https://files.pythonhosted.org/packages/0e/82/528741676960a7fd1c75151639601826118f2729ad53034fa3b39290c056/qiskit_aqua-0.8.2-py3-none-any.whl (2.1MB)

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Collecting ply>=3.10

Downloading https://files.pythonhosted.org/packages/a3/58/35da89ee790598a0700ea49b2a66594140f44dec458c07e8e3d4979137fc/ply-3.11-py2.py3-none-any.whl (49kB)

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Requirement already satisfied: jsonschema>=2.6 in /usr/local/lib/python3.7/dist-packages (from qiskit-terra==0.16.4->qiskit) (2.6.0)

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Requirement already satisfied: scipy>=1.4 in /usr/local/lib/python3.7/dist-packages (from qiskit-terra==0.16.4->qiskit) (1.4.1)

Collecting retworkx>=0.5.0

Downloading https://files.pythonhosted.org/packages/1b/92/f007f8b9d88dcd5b90e363967e5d54431a68c5fe06d83400732e3b438084/retworkx-0.8.0-cp37-cp37m-manylinux2010_x86_64.whl (1.0MB)

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Requirement already satisfied: dill>=0.3 in /usr/local/lib/python3.7/dist-packages (from qiskit-terra==0.16.4->qiskit) (0.3.3)

Collecting fastjsonschema>=2.10

Downloading https://files.pythonhosted.org/packages/89/1c/8be51fa42aadc1c1611a52b866e1a5a1032a504f24789cf140b4e6d7c940/fastjsonschema-2.15.0-py3-none-any.whl

Collecting python-constraint>=1.4

Downloading https://files.pythonhosted.org/packages/37/8b/5f1bc2734ca611943e1d6733ee244238679f6410a10cd45ede55a61a8402/python-constraint-1.4.0.tar.bz2

Requirement already satisfied: cython>=0.27.1 in /usr/local/lib/python3.7/dist-packages (from qiskit-aer==0.7.6->qiskit) (0.29.22)

Collecting pybind11>=2.4

Downloading https://files.pythonhosted.org/packages/8d/43/7339dbabbc2793718d59703aace4166f53c29ee1c202f6ff5bf8a26c4d91/pybind11-2.6.2-py2.py3-none-any.whl (191kB)

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Requirement already satisfied: nest-asyncio!=1.1.0,>=1.0.0 in /usr/local/lib/python3.7/dist-packages (from qiskit-ibmq-provider==0.12.2->qiskit) (1.5.1)

Requirement already satisfied: urllib3>=1.21.1 in /usr/local/lib/python3.7/dist-packages (from qiskit-ibmq-provider==0.12.2->qiskit) (1.24.3)

Requirement already satisfied: requests>=2.19 in /usr/local/lib/python3.7/dist-packages (from qiskit-ibmq-provider==0.12.2->qiskit) (2.23.0)

Collecting requests-ntlm>=1.1.0

Downloading https://files.pythonhosted.org/packages/03/4b/8b9a1afde8072c4d5710d9fa91433d504325821b038e00237dc8d6d833dc/requests_ntlm-1.1.0-py2.py3-none-any.whl

Collecting websockets>=8

Downloading https://files.pythonhosted.org/packages/5a/0b/3ebc752392a368af14dd24ee041683416ac6d2463eead94b311b11e41c82/websockets-8.1-cp37-cp37m-manylinux2010_x86_64.whl (79kB)

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Requirement already satisfied: scikit-learn>=0.17 in /usr/local/lib/python3.7/dist-packages (from qiskit-ignis==0.5.2->qiskit) (0.22.2.post1)

Requirement already satisfied: setuptools>=40.1.0 in /usr/local/lib/python3.7/dist-packages (from qiskit-ignis==0.5.2->qiskit) (54.1.2)

Collecting yfinance

Downloading https://files.pythonhosted.org/packages/a7/ee/315752b9ef281ba83c62aa7ec2e2074f85223da6e7e74efb4d3e11c0f510/yfinance-0.1.59.tar.gz

Requirement already satisfied: pandas in /usr/local/lib/python3.7/dist-packages (from qiskit-aqua==0.8.2->qiskit) (1.1.5)

Collecting docplex==2.15.194

Downloading https://files.pythonhosted.org/packages/9b/76/ebf5b75a25c4357c9a4758cae7fea778dd7f282b83c2f22e150dc7e3c852/docplex-2.15.194.tar.gz (582kB)

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Collecting dlx

Downloading https://files.pythonhosted.org/packages/54/c0/b8fb5bb727e983b6f5251433ef941b48f38c65bb0bd6ec509e9185bcd406/dlx-1.0.4.tar.gz

Requirement already satisfied: h5py in /usr/local/lib/python3.7/dist-packages (from qiskit-aqua==0.8.2->qiskit) (2.10.0)

Requirement already satisfied: fastdtw in /usr/local/lib/python3.7/dist-packages (from qiskit-aqua==0.8.2->qiskit) (0.3.4)

Collecting quandl

Downloading https://files.pythonhosted.org/packages/8b/2b/feefb36015beaecc5c0f9f2533e815b409621d9fa7b50b2aac621796f828/Quandl-3.6.1-py2.py3-none-any.whl

Requirement already satisfied: decorator>=4.3.0 in /usr/local/lib/python3.7/dist-packages (from networkx>=2.2->qiskit-terra==0.16.4->qiskit) (4.4.2)

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Collecting cryptography>=1.3

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Building wheels for collected packages: qiskit, python-constraint, yfinance, docplex, dlx

Building wheel for qiskit (setup.py) ... done

Created wheel for qiskit: filename=qiskit-0.24.1-cp37-none-any.whl size=2919 sha256=ff29c727e4784ef214489254c465b1fced90c40a7af7c24e7659f4532f94bf1f

Stored in directory: /root/.cache/pip/wheels/4a/3e/be/606704f95c92255208f2c6c571d95cc075a12d8672515ec7a5

Building wheel for python-constraint (setup.py) ... done

Created wheel for python-constraint: filename=python_constraint-1.4.0-py2.py3-none-any.whl size=24079 sha256=bf4f277e7c979232a94c124c9b30df6ae70a1d1cde032a4b6fbc760236adbcb2

Stored in directory: /root/.cache/pip/wheels/34/31/15/7b070b25d0a549d20ce2e9fe6d727471c2c61ef904720fd40c

Building wheel for yfinance (setup.py) ... done

Created wheel for yfinance: filename=yfinance-0.1.59-py2.py3-none-any.whl size=23442 sha256=7377354156be5233a67b078debfeb9242b14297934060f8440ac2c69246b823d

Stored in directory: /root/.cache/pip/wheels/f8/2a/0f/4b5a86e1d52e451757eb6bc17fd899629f0925c777741b6d04

Building wheel for docplex (setup.py) ... done

Created wheel for docplex: filename=docplex-2.15.194-cp37-none-any.whl size=645116 sha256=ef2dfc072d928a4f7db38ec4b0bb54b0825cade9cd274f6dff829df3a96fb379

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Building wheel for dlx (setup.py) ... done

Created wheel for dlx: filename=dlx-1.0.4-cp37-none-any.whl size=5712 sha256=b29aa61a575be43da4cfc7eb11dba7a9079461dc9092f3af879354a7cc1a6b45

Stored in directory: /root/.cache/pip/wheels/bb/ba/15/fdd0deb104df3254912998150ba9245668db06b00af5912d1a

Successfully built qiskit python-constraint yfinance docplex dlx

Installing collected packages: ply, retworkx, fastjsonschema, python-constraint, qiskit-terra, pybind11, qiskit-aer, cryptography, ntlm-auth, requests-ntlm, websockets, qiskit-ibmq-provider, qiskit-ignis, lxml, yfinance, docplex, dlx, inflection, quandl, qiskit-aqua, qiskit

Found existing installation: lxml 4.2.6

Uninstalling lxml-4.2.6:

Successfully uninstalled lxml-4.2.6

Successfully installed cryptography-3.4.7 dlx-1.0.4 docplex-2.15.194 fastjsonschema-2.15.0 inflection-0.5.1 lxml-4.6.3 ntlm-auth-1.5.0 ply-3.11 pybind11-2.6.2 python-constraint-1.4.0 qiskit-0.24.1 qiskit-aer-0.7.6 qiskit-aqua-0.8.2 qiskit-ibmq-provider-0.12.2 qiskit-ignis-0.5.2 qiskit-terra-0.16.4 quandl-3.6.1 requests-ntlm-1.1.0 retworkx-0.8.0 websockets-8.1 yfinance-0.1.59

Qiskit のバージョン

[編集内容(qiskit version)]
import qiskit
qiskit.__version__

[編集内容(qiskit version)]

import qiskit

qiskit.__version__

[出力結果]
0.16.4

1 2	[出力結果] 0.16.4

Qiskit のサンプルプログラム

[編集内容(qiskit sample)]
import numpy as np
from qiskit import(
  QuantumCircuit,
  execute,
  Aer)
from qiskit.visualization import plot_histogram

# Use Aer's qasm_simulator
simulator = Aer.get_backend('qasm_simulator')

# Create a Quantum Circuit acting on the q register
circuit = QuantumCircuit(2, 2)

# Add a H gate on qubit 0
circuit.h(0)

# Add a CX (CNOT) gate on control qubit 0 and target qubit 1
circuit.cx(0, 1)

# Map the quantum measurement to the classical bits
circuit.measure([0, 1], [0, 1])

# Execute the circuit on the qasm simulator
job = execute(circuit, simulator, shots=1000)

# Grab results from the job
result = job.result()

# Returns counts
counts = result.get_counts(circuit)
print("\nTotal count for 00 and 11 are:",counts)

# Draw the circuit
circuit.draw()

[編集内容(qiskit sample)]

import numpy as np

from qiskit import(

QuantumCircuit,

execute,

Aer)

from qiskit.visualization import plot_histogram

# Use Aer's qasm_simulator

simulator = Aer.get_backend('qasm_simulator')

# Create a Quantum Circuit acting on the q register

circuit = QuantumCircuit(2, 2)

# Add a H gate on qubit 0

circuit.h(0)

# Add a CX (CNOT) gate on control qubit 0 and target qubit 1

circuit.cx(0, 1)

# Map the quantum measurement to the classical bits

circuit.measure([0, 1], [0, 1])

# Execute the circuit on the qasm simulator

job = execute(circuit, simulator, shots=1000)

# Grab results from the job

result = job.result()

# Returns counts

counts = result.get_counts(circuit)

print("\nTotal count for 00 and 11 are:",counts)

# Draw the circuit

circuit.draw()

[出力結果]
※実行するごとに, 測定結果が変わってくる.
Total count for 00 and 11 are: {'00': 472, '11': 528}

     ┌───┐     ┌─┐   
q_0: ┤ H ├──■──┤M├───
     └───┘┌─┴─┐└╥┘┌─┐
q_1: ─────┤ X ├─╫─┤M├
          └───┘ ║ └╥┘
c: 2/═══════════╩══╩═
                0  1

[出力結果]

※実行するごとに, 測定結果が変わってくる.

Total count for 00 and 11 are: {'00': 472, '11': 528}

┌───┐ ┌─┐

q_0: ┤ H ├──■──┤M├───

└───┘┌─┴─┐└╥┘┌─┐

q_1: ─────┤ X ├─╫─┤M├

└───┘ ║ └╥┘

c: 2/═══════════╩══╩═

0 1

Qiskit のサンプルプログラム(Xゲート, Yゲート, Zゲート)

[編集内容(qiskit sample)]
import numpy as np
from qiskit import(
  QuantumCircuit,
  execute,
  Aer)
from qiskit.visualization import plot_histogram

# Use Aer's qasm_simulator
simulator = Aer.get_backend('qasm_simulator')

# Create a Quantum Circuit acting on the q register
circuit = QuantumCircuit(2, 2)

# Add a X or Y or Z gate on qubit 0
# -> コメントアウトを切り替える.
circuit.x(0)
# circuit.y(0)
# circuit.z(0)

# Map the quantum measurement to the classical bits
circuit.measure([0, 1], [0, 1])

# Execute the circuit on the qasm simulator
job = execute(circuit, simulator, shots=1000)

# Grab results from the job
result = job.result()

# Returns counts
counts = result.get_counts(circuit)
print("\nTotal count for 0 and 1 are:", counts)

# Draw the circuit
circuit.draw()

[編集内容(qiskit sample)]

import numpy as np

from qiskit import(

QuantumCircuit,

execute,

Aer)

from qiskit.visualization import plot_histogram

# Use Aer's qasm_simulator

simulator = Aer.get_backend('qasm_simulator')

# Create a Quantum Circuit acting on the q register

circuit = QuantumCircuit(2, 2)

# Add a X or Y or Z gate on qubit 0

# -> コメントアウトを切り替える.

circuit.x(0)

# circuit.y(0)

# circuit.z(0)

# Map the quantum measurement to the classical bits

circuit.measure([0, 1], [0, 1])

# Execute the circuit on the qasm simulator

job = execute(circuit, simulator, shots=1000)

# Grab results from the job

result = job.result()

# Returns counts

counts = result.get_counts(circuit)

print("\nTotal count for 0 and 1 are:", counts)

# Draw the circuit

circuit.draw()

[出力結果]
※実行するごとに, 測定結果は変わらない.
[Xゲートの場合]
Total count for 0 and 1 are: {'01': 1000}

     ┌───┐┌─┐
q_0: ┤ X ├┤M├
     └┬─┬┘└╥┘
q_1: ─┤M├──╫─
      └╥┘  ║ 
c: 2/══╩═══╩═
       1   0 

[Yゲートの場合]
Total count for 0 and 1 are: {'01': 1000}

     ┌───┐┌─┐
q_0: ┤ Y ├┤M├
     └┬─┬┘└╥┘
q_1: ─┤M├──╫─
      └╥┘  ║ 
c: 2/══╩═══╩═
       1   0 

[Zゲートの場合]
Total count for 0 and 1 are: {'00': 1000}

     ┌───┐┌─┐
q_0: ┤ Z ├┤M├
     └┬─┬┘└╥┘
q_1: ─┤M├──╫─
      └╥┘  ║ 
c: 2/══╩═══╩═
       1   0

[出力結果]

※実行するごとに, 測定結果は変わらない.

[Xゲートの場合]

Total count for 0 and 1 are: {'01': 1000}

┌───┐┌─┐

q_0: ┤ X ├┤M├

└┬─┬┘└╥┘

q_1: ─┤M├──╫─

└╥┘ ║

c: 2/══╩═══╩═

1 0

[Yゲートの場合]

Total count for 0 and 1 are: {'01': 1000}

┌───┐┌─┐

q_0: ┤ Y ├┤M├

└┬─┬┘└╥┘

q_1: ─┤M├──╫─

└╥┘ ║

c: 2/══╩═══╩═

1 0

[Zゲートの場合]

Total count for 0 and 1 are: {'00': 1000}

┌───┐┌─┐

q_0: ┤ Z ├┤M├

└┬─┬┘└╥┘

q_1: ─┤M├──╫─

└╥┘ ║

c: 2/══╩═══╩═

1 0

Circuit Basics

Qiskit のサンプルプログラム

[編集内容(GHZ state)]
import numpy as np
from qiskit import *
%matplotlib inline

# Create a Quantum Circuit acting on a quantum register of three qubits
circ = QuantumCircuit(3)

# Add a H gate on qubit 0, putting this qubit in superposition.
circ.h(0)

# Add a CX (CNOT) gate on control qubit 0 and target qubit 1, putting
# the qubits in a Bell state.
circ.cx(0, 1)

# Add a CX (CNOT) gate on control qubit 0 and target qubit 2, putting
# the qubits in a GHZ state.
circ.cx(0, 2)

# Visualize Circuit
# ImportError: The class MatplotlibDrawer needs pylatexenc. to install, run "pip install pylatexenc".
# circ.draw('mpl')
circ.draw()

[編集内容(GHZ state)]

import numpy as np

from qiskit import *

%matplotlib inline

# Create a Quantum Circuit acting on a quantum register of three qubits

circ = QuantumCircuit(3)

# Add a H gate on qubit 0, putting this qubit in superposition.

circ.h(0)

# Add a CX (CNOT) gate on control qubit 0 and target qubit 1, putting

# the qubits in a Bell state.

circ.cx(0, 1)

# Add a CX (CNOT) gate on control qubit 0 and target qubit 2, putting

# the qubits in a GHZ state.

circ.cx(0, 2)

# Visualize Circuit

# ImportError: The class MatplotlibDrawer needs pylatexenc. to install, run "pip install pylatexenc".

# circ.draw('mpl')

circ.draw()

[出力結果]
     ┌───┐          
q_0: ┤ H ├──■────■──
     └───┘┌─┴─┐  │  
q_1: ─────┤ X ├──┼──
          └───┘┌─┴─┐
q_2: ──────────┤ X ├
               └───┘

[出力結果]

┌───┐

q_0: ┤ H ├──■────■──

└───┘┌─┴─┐ │

q_1: ─────┤ X ├──┼──

└───┘┌─┴─┐

q_2: ──────────┤ X ├

└───┘

Qiskit のサンプルプログラム

[編集内容(GHZ state)]
import numpy as np
from qiskit import *
%matplotlib inline

# Create a Quantum Circuit acting on a quantum register of five qubits
circ = QuantumCircuit(5)

# Add a H gate on qubit 0, putting this qubit in superposition.
circ.h(0)

# Add a CX (CNOT) gate on control qubit 0 and target qubit 1, putting
# the qubits in a Bell state.
circ.cx(0, 1)

# Add a CX (CNOT) gate on control qubit 0 and target qubit 2, putting
# the qubits in a GHZ state.
circ.cx(0, 2)

# Add a CX (CNOT) gate on control qubit 0 and target qubit 3, putting
# the qubits in a ??? state.
circ.cx(0, 3)

# Add a CX (CNOT) gate on control qubit 0 and target qubit 4, putting
# the qubits in a ??? state.
circ.cx(0, 4)

# Visualize Circuit
circ.draw()

[編集内容(GHZ state)]

import numpy as np

from qiskit import *

%matplotlib inline

# Create a Quantum Circuit acting on a quantum register of five qubits

circ = QuantumCircuit(5)

# Add a H gate on qubit 0, putting this qubit in superposition.

circ.h(0)

# Add a CX (CNOT) gate on control qubit 0 and target qubit 1, putting

# the qubits in a Bell state.

circ.cx(0, 1)

# Add a CX (CNOT) gate on control qubit 0 and target qubit 2, putting

# the qubits in a GHZ state.

circ.cx(0, 2)

# Add a CX (CNOT) gate on control qubit 0 and target qubit 3, putting

# the qubits in a ??? state.

circ.cx(0, 3)

# Add a CX (CNOT) gate on control qubit 0 and target qubit 4, putting

# the qubits in a ??? state.

circ.cx(0, 4)

# Visualize Circuit

circ.draw()

[出力結果]
     ┌───┐                    
q_0: ┤ H ├──■────■────■────■──
     └───┘┌─┴─┐  │    │    │  
q_1: ─────┤ X ├──┼────┼────┼──
          └───┘┌─┴─┐  │    │  
q_2: ──────────┤ X ├──┼────┼──
               └───┘┌─┴─┐  │  
q_3: ───────────────┤ X ├──┼──
                    └───┘┌─┴─┐
q_4: ────────────────────┤ X ├
                         └───┘

[出力結果]

┌───┐

q_0: ┤ H ├──■────■────■────■──

└───┘┌─┴─┐ │ │ │

q_1: ─────┤ X ├──┼────┼────┼──

└───┘┌─┴─┐ │ │

q_2: ──────────┤ X ├──┼────┼──

└───┘┌─┴─┐ │

q_3: ───────────────┤ X ├──┼──

└───┘┌─┴─┐

q_4: ────────────────────┤ X ├

└───┘

参照サイト

2021年3月29日

C++ の動作確認をしてみた（４３３）

C++の練習を兼ねて, AtCoder Regular Contest 116 の問題A (Odd vs Even) ～問題B (Products of Min-Max) を解いてみた.

■感想.
1. 規則性を抽出できたので, AC版まで到達できたと思う.
2. 時間を見つけて, 引き続き, 過去問を振り返っていきたいと思う.

本家のサイト AtCoder Regular Contest 116 解説の各リンクをご覧下さい.

■C++版プログラム(問題A／AC版).

// C++(GCC 9.2.1)
#include <bits/stdc++.h>
using namespace std;
using LL = long long;
#define repex(i, a, b, c) for(int i = a; i < b; i += c)
#define repx(i, a, b) repex(i, a, b, 1)
#define rep(i, n) repx(i, 0, n)
#define repr(i, a, b) for(int i = a; i >= b; i--)

int main(){
    
    // 1. 入力情報.
    int T;
    scanf("%d", &T);
    rep(i, T){
        // 与えられた整数.
        LL N;
        scanf("%lld", &N);
        
        // 倍数をチェック.
        int f = 0;
        if(N % 2 == 0) f++;
        if(N % 4 == 0) f++;
        
        // 出力.
        if(f == 0) puts("Odd");
        if(f == 1) puts("Same");
        if(f == 2) puts("Even");
    }
    return 0;
    
}

// C++(GCC 9.2.1)

#include <bits/stdc++.h>

using namespace std;

using LL = long long;

#define repex(i, a, b, c) for(int i = a; i < b; i += c)

#define repx(i, a, b) repex(i, a, b, 1)

#define rep(i, n) repx(i, 0, n)

#define repr(i, a, b) for(int i = a; i >= b; i--)

int main(){

// 1. 入力情報.

int T;

scanf("%d", &T);

rep(i, T){

// 与えられた整数.

LL N;

scanf("%lld", &N);

// 倍数をチェック.

int f = 0;

if(N % 2 == 0) f++;

if(N % 4 == 0) f++;

// 出力.

if(f == 0) puts("Odd");

if(f == 1) puts("Same");

if(f == 2) puts("Even");

}

return 0;

}

[入力例]
3
2
998244353
1000000000000000000

[出力例]
Same
Odd
Even
※AtCoderのテストケースより

[入力例]
17
222079
533860
941892
685490
243916
404856
695734
34365
572866
940162
470243
133907
930142
667476
669648
477556
294291

[出力例]
Odd
Even
Even
Same
Even
Even
Same
Odd
Same
Same
Odd
Odd
Same
Even
Even
Even
Odd

[入力例]

998244353

1000000000000000000

[出力例]

Same

Odd

Even

※AtCoderのテストケースより

[入力例]

222079

533860

941892

685490

243916

404856

695734

34365

572866

940162

470243

133907

930142

667476

669648

477556

294291

[出力例]

Odd

Even

Same

Even

Same

Odd

Same

Odd

Same

Even

Odd

■C++版プログラム(問題B／AC版).

// C++(GCC 9.2.1)
#include <bits/stdc++.h>
using namespace std;
using LL = long long;
#define repex(i, a, b, c) for(int i = a; i < b; i += c)
#define repx(i, a, b) repex(i, a, b, 1)
#define rep(i, n) repx(i, 0, n)
#define repr(i, a, b) for(int i = a; i >= b; i--)
const LL MOD = 998244353;
LL a[202020], sum[202020];

int main(){
    
    // 1. 入力情報.
    int N;
    scanf("%d", &N);
    rep(i, N) scanf("%lld", &a[i]);
    
    // 2. sort.
    sort(a, a + N);
    
    // 3. max(B) の 和 は？
    // ex.
    // a = {a1, a2, a3, a4, a5} の 場合.
    //  min(B)       max(B) の 和.
    //    a1   sum[1] = a1 * 1 + a2 * 1 + a3 * 2 + a4 * 4 + a5 * 8 (16通り)
    //    a2   sum[2] =          a2 * 1 + a3 * 1 + a4 * 2 + a5 * 4  (8通り)
    //    a3   sum[3] =                   a3 * 1 + a4 * 1 + a5 * 2  (4通り)
    //    a4   sum[4] =                            a4 * 1 + a5 * 1  (2通り)
    //    a5   sum[5] =                                     a5 * 1  (1通り)
    // -> 上記から, a1 * sum[1] * ... * a5 * sum[5] (31通りの和) を 計算すれば良さそうに見える.
    sum[N - 1] = a[N - 1];
    repr(i, N - 2, 0){
        sum[i] = sum[i + 1] * 2LL;
        sum[i] += (MOD - a[i + 1]);
        sum[i] += a[i];
        sum[i] %= MOD;
    }
    
    // 4. 集計.
    LL ans = 0;
    rep(i, N) ans += (a[i] * sum[i]), ans %= MOD;
    
    // 5. 出力.
    printf("%lld\n", ans);
    return 0;
    
}

// C++(GCC 9.2.1)

#include <bits/stdc++.h>

using namespace std;

using LL = long long;

#define repex(i, a, b, c) for(int i = a; i < b; i += c)

#define repx(i, a, b) repex(i, a, b, 1)

#define rep(i, n) repx(i, 0, n)

#define repr(i, a, b) for(int i = a; i >= b; i--)

const LL MOD = 998244353;

LL a[202020], sum[202020];

int main(){

// 1. 入力情報.

int N;

scanf("%d", &N);

rep(i, N) scanf("%lld", &a[i]);

// 2. sort.

sort(a, a + N);

// 3. max(B) の和は？

// ex.

// a = {a1, a2, a3, a4, a5} の場合.

// min(B) max(B) の和.

// a1 sum[1] = a1 * 1 + a2 * 1 + a3 * 2 + a4 * 4 + a5 * 8 (16通り)

// a2 sum[2] = a2 * 1 + a3 * 1 + a4 * 2 + a5 * 4 (8通り)

// a3 sum[3] = a3 * 1 + a4 * 1 + a5 * 2 (4通り)

// a4 sum[4] = a4 * 1 + a5 * 1 (2通り)

// a5 sum[5] = a5 * 1 (1通り)

// -> 上記から, a1 * sum[1] * ... * a5 * sum[5] (31通りの和) を計算すれば良さそうに見える.

sum[N - 1] = a[N - 1];

repr(i, N - 2, 0){

sum[i] = sum[i + 1] * 2LL;

sum[i] += (MOD - a[i + 1]);

sum[i] += a[i];

sum[i] %= MOD;

}

// 4. 集計.

LL ans = 0;

rep(i, N) ans += (a[i] * sum[i]), ans %= MOD;

// 5. 出力.

printf("%lld\n", ans);

return 0;

}

[入力例]
3
2 4 3

[出力例]
63
※AtCoderのテストケースより

[入力例]
1
10

[出力例]
100
※AtCoderのテストケースより

[入力例]
7
853983 14095 543053 143209 4324 524361 45154

[出力例]
206521341
※AtCoderのテストケースより

[入力例]
12
31 41 59 26 53 58 97 93 23 84 62 64

[出力例]
10307796

[入力例]

2 4 3

[出力例]

※AtCoderのテストケースより

[入力例]

[出力例]

100

※AtCoderのテストケースより

[入力例]

853983 14095 543053 143209 4324 524361 45154

[出力例]

206521341

※AtCoderのテストケースより

[入力例]

31 41 59 26 53 58 97 93 23 84 62 64

[出力例]

10307796

■参照サイト
AtCoder Regular Contest 116

2021年3月28日

C++ の動作確認をしてみた（４３２）

C++の練習を兼ねて, AtCoder Beginner Contest 197 の問題C (ORXOR) ～問題D (Opposite) を解いてみた.

■感想.
1. 実装に苦労したものの, 解説見る前に, AC版に到達出来たので, 良かったと思う.
2. 時間を見つけて, 引き続き, 過去問を振り返っていきたいと思う.

本家のサイト AtCoder Beginner Contest 197 解説の各リンクをご覧下さい.

■C++版プログラム(問題C／AC版).

// C++(GCC 9.2.1)
#include <bits/stdc++.h>
using namespace std;
using LL = long long;
using vi = vector<int>;
#define repex(i, a, b, c) for(int i = a; i < b; i += c)
#define repx(i, a, b) repex(i, a, b, 1)
#define rep(i, n) repx(i, 0, n)
#define repr(i, a, b) for(int i = a; i >= b; i--)
#define pb push_back
LL a[22];

int main(){
    
    // 1. 入力情報.
    int N;
    scanf("%d", &N);
    rep(i, N) scanf("%lld", &a[i]);
    
    // 2. 2 の 冪乗 を 保存.
    vi cPow2;
    int count = 0;
    cPow2.pb(1);
    while(count < N){
        // 最大値を2倍.
        int p = 2 * cPow2.back();
        
        // 保存.
        cPow2.pb(p);
        
        // インクリメント.
        count++;
    }
    
    // 3. 区間を生成し, 最小値を探索.
    LL ans = 202020202020202020;
    rep(i, 1 << N){
        // 3-1. 区間を生成.
        int bef = -1, cur;
        vi v;
        rep(j, N){
            // 今回分更新.
            cur = (cPow2[N - 1 - j] & i) ? 1 : 0;
            
            // 前回と異なる場合は, 区間開始地点と見て保存.
            if(bef != cur) v.pb(j);
            
            // 前回分更新.
            bef = cur;
        }
        
        // 3-2. 番兵.
        v.pb(N);
        
        // 3-3. XOR生成.
        LL cXOR = 0;
        rep(j, v.size() - 1){
            // 区間開始地点, 区間終了地点.
            LL cOR = 0;
            int s = v[j];
            int e = v[j + 1];
            
            // 区間内の数のビット単位OR を計算.
            repx(k, s, e) cOR |= a[k];
            
            // 全ての値のビット単位XOR を計算.
            cXOR ^= cOR;
        }
        
        // 3-4. 最小値更新.
        ans = min(ans, cXOR);
    }
    
    // 4. 出力.
    printf("%lld\n", ans);
    return 0;
    
}

// C++(GCC 9.2.1)

#include <bits/stdc++.h>

using namespace std;

using LL = long long;

using vi = vector<int>;

#define repex(i, a, b, c) for(int i = a; i < b; i += c)

#define repx(i, a, b) repex(i, a, b, 1)

#define rep(i, n) repx(i, 0, n)

#define repr(i, a, b) for(int i = a; i >= b; i--)

#define pb push_back

LL a[22];

int main(){

// 1. 入力情報.

int N;

scanf("%d", &N);

rep(i, N) scanf("%lld", &a[i]);

// 2. 2 の冪乗を保存.

vi cPow2;

int count = 0;

cPow2.pb(1);

while(count < N){

// 最大値を2倍.

int p = 2 * cPow2.back();

// 保存.

cPow2.pb(p);

// インクリメント.

count++;

}

// 3. 区間を生成し, 最小値を探索.

LL ans = 202020202020202020;

rep(i, 1 << N){

// 3-1. 区間を生成.

int bef = -1, cur;

vi v;

rep(j, N){

// 今回分更新.

cur = (cPow2[N - 1 - j] & i) ? 1 : 0;

// 前回と異なる場合は, 区間開始地点と見て保存.

if(bef != cur) v.pb(j);

// 前回分更新.

bef = cur;

}

// 3-2. 番兵.

v.pb(N);

// 3-3. XOR生成.

LL cXOR = 0;

rep(j, v.size() - 1){

// 区間開始地点, 区間終了地点.

LL cOR = 0;

int s = v[j];

int e = v[j + 1];

// 区間内の数のビット単位OR を計算.

repx(k, s, e) cOR |= a[k];

// 全ての値のビット単位XOR を計算.

cXOR ^= cOR;

}

// 3-4. 最小値更新.

ans = min(ans, cXOR);

}

// 4. 出力.

printf("%lld\n", ans);

return 0;

}

[入力例]
3
1 5 7

[出力例]
2
※AtCoderテストケースより

[入力例]
3
10 10 10

[出力例]
0
※AtCoderテストケースより

[入力例]
4
1 3 3 1

[出力例]
0
※AtCoderテストケースより

[入力例]
5
1 3 12 18 7

[出力例]
24

[入力例]
10
1 2 3 16 17 31 63 1 2 3

[出力例]
32

[入力例]
18
1 2 2 3 4 5 8 9 16 17 32 33 64 65 128 129 256 257

[出力例]
1

[入力例]

1 5 7

[出力例]

※AtCoderテストケースより

[入力例]

10 10 10

[出力例]

※AtCoderテストケースより

[入力例]

1 3 3 1

[出力例]

※AtCoderテストケースより

[入力例]

1 3 12 18 7

[出力例]

[入力例]

1 2 3 16 17 31 63 1 2 3

[出力例]

[入力例]

1 2 2 3 4 5 8 9 16 17 32 33 64 65 128 129 256 257

[出力例]

■C++版プログラム(問題D／AC版).

// C++(GCC 9.2.1)
#include <bits/stdc++.h>
using namespace std;
#define repex(i, a, b, c) for(int i = a; i < b; i += c)
#define repx(i, a, b) repex(i, a, b, 1)
#define rep(i, n) repx(i, 0, n)
#define repr(i, a, b) for(int i = a; i >= b; i--)
const double PI = acos(-1.0);

int main(){
    
    // 1. 入力情報.
    int N;
    scanf("%d", &N);
    double xs, ys, xo, yo;
    scanf("%lf %lf %lf %lf", &xs, &ys, &xo, &yo);
    
    // 2. x1, y1 を 計算.
    // -> 中心を, C(cx, cy)と置いて, ベクトル P[0]C(ux, uy), P[0]P[1](vx, vy) の関係を確認.
    double ux = (xs + xo) / 2.0 - xs;
    double uy = (ys + yo) / 2.0 - ys;
    double theta = PI * (1.0 - 0.5 - 1.0 / (double)N);
    double e = 2.0 * cos(theta);
    double vx = (cos(-theta) * ux - sin(-theta) * uy) * e;
    double vy = (sin(-theta) * ux + cos(-theta) * uy) * e;
    double x1 = xs + vx;
    double y1 = ys + vy;
    
    // 3. 出力.
    printf("%.11lf %.11lf\n", x1, y1);
    return 0;
    
}

// C++(GCC 9.2.1)

#include <bits/stdc++.h>

using namespace std;

#define repex(i, a, b, c) for(int i = a; i < b; i += c)

#define repx(i, a, b) repex(i, a, b, 1)

#define rep(i, n) repx(i, 0, n)

#define repr(i, a, b) for(int i = a; i >= b; i--)

const double PI = acos(-1.0);

int main(){

// 1. 入力情報.

int N;

scanf("%d", &N);

double xs, ys, xo, yo;

scanf("%lf %lf %lf %lf", &xs, &ys, &xo, &yo);

// 2. x1, y1 を計算.

// -> 中心を, C(cx, cy)と置いて, ベクトル P[0]C(ux, uy), P[0]P[1](vx, vy) の関係を確認.

double ux = (xs + xo) / 2.0 - xs;

double uy = (ys + yo) / 2.0 - ys;

double theta = PI * (1.0 - 0.5 - 1.0 / (double)N);

double e = 2.0 * cos(theta);

double vx = (cos(-theta) * ux - sin(-theta) * uy) * e;

double vy = (sin(-theta) * ux + cos(-theta) * uy) * e;

double x1 = xs + vx;

double y1 = ys + vy;

// 3. 出力.

printf("%.11lf %.11lf\n", x1, y1);

return 0;

}

[入力例]
4
1 1
2 2

[出力例]
2.00000000000 1.00000000000
※AtCoderテストケースより

[入力例]
6
5 3
7 4

[出力例]
5.93301270189 2.38397459622
※AtCoderテストケースより

[入力例]
8
3 7
19 25

[出力例]
11.70710678119 3.97918471983

[入力例]
30
2 6
75 51

[出力例]
7.47562561662 -1.09709773136

[入力例]

1 1

2 2

[出力例]

2.00000000000 1.00000000000

※AtCoderテストケースより

[入力例]

5 3

7 4

[出力例]

5.93301270189 2.38397459622

※AtCoderテストケースより

[入力例]

3 7

19 25

[出力例]

11.70710678119 3.97918471983

[入力例]

2 6

75 51

[出力例]

7.47562561662 -1.09709773136

■参照サイト
AtCoder Beginner Contest 197（Sponsored by Panasonic）

2021年3月27日

C++ の動作確認をしてみた（４３１）

C++の練習を兼ねて, AtCoder Grand Contest 041 の問題B (Voting Judges) を解いてみた.

■感想.
1. 問題Bは, 解答方針が見えなかったので, 解説を参考に実装して, ようやく, AC版に到達できた.
2. 実装に苦労したものの, 二分探索の復習が出来たので, 非常に良かったと思う.
3. 時間を見つけて, 引き続き, 過去問を振り返っていきたいと思う.

本家のサイト AtCoder Grand Contest 041 解説をご覧下さい.

■C++版プログラム(問題B／AC版).

// 解き直し.
// https://img.atcoder.jp/agc041/editorial.pdf
// C++(GCC 9.2.1)
#include <bits/stdc++.h>
using namespace std;
using LL = long long;
using vl = vector<LL>;
#define repex(i, a, b, c) for(int i = a; i < b; i += c)
#define repx(i, a, b) repex(i, a, b, 1)
#define rep(i, n) repx(i, 0, n)
#define repr(i, a, b) for(int i = a; i >= b; i--)
#define pb push_back
#define a first
#define b second
#define all(x) x.begin(), x.end()

int main(){
    
    // 1. 入力情報.
    int N, P;
    LL M, V;
    scanf("%d %lld %lld %d", &N, &M, &V, &P);
    vl A;
    rep(i, N){
        LL a;
        scanf("%lld", &a);
        A.pb(a);
    }
    
    // 2. 降順sort.
    sort(all(A));
    reverse(all(A));
    
    // 3. A[Y] + M < A[P] となる Y は？
    int Y = N;
    rep(i, N){
        if(A[i] + M < A[P - 1]){
            Y = i;
            break;
        }
    }
    
    // 4. 二分探索.
    // -> 01-38.txt などで, WA版となったため, ロジック修正.
    // -> l, m, h は, index と見る(問題数 に変換する場合は, +1 を 加算).
    int l = P - 1, h = Y, m;
    auto f = [&](int X) -> bool {
        // 4-1. 問題 1 ～ (P - 1) までの(P - 1)問を, M人 が 投票.
        LL lVote = max(0, P - 1) * M;
        
        // 4-2. 問題 P ～ (X - 1) まで, (A[X] + M - A[i])人 が 投票.
        LL mVote = 0;
        repx(i, P - 1, X) mVote += max(0LL, A[X] + M - A[i]);
        
        // 4-3. 問題 (X + 1) ～ N までの(N - X)問を, M人 が 投票.
        LL rVote = max(0, N - X) * M;
        
        // 4-4. 投票されても構わないかチェック.
        // -> (M * V)未満ならば, 採用される可能性なし.
        LL vote = lVote + mVote + rVote;
        // printf("lVote=%lld mVote=%lld rVote=%lld vote=%lld MV=%lld\n", lVote, mVote, rVote, vote, M * V);
        
        return (vote < M * V);
    };
    // 二分探索で確認してみる.
    while(l + 1 < h){
        m = (h + l) >> 1;
        if(f(m)) h = m;
        else     l = m;
        // printf("h=%lld l=%lld m=%lld\n", h, l, m);
    }
    
    // 5. 出力.
    printf("%d\n", l + 1);
    return 0;
    
}

// 解き直し.

// https://img.atcoder.jp/agc041/editorial.pdf

// C++(GCC 9.2.1)

#include <bits/stdc++.h>

using namespace std;

using LL = long long;

using vl = vector<LL>;

#define repex(i, a, b, c) for(int i = a; i < b; i += c)

#define repx(i, a, b) repex(i, a, b, 1)

#define rep(i, n) repx(i, 0, n)

#define repr(i, a, b) for(int i = a; i >= b; i--)

#define pb push_back

#define a first

#define b second

#define all(x) x.begin(), x.end()

int main(){

// 1. 入力情報.

int N, P;

LL M, V;

scanf("%d %lld %lld %d", &N, &M, &V, &P);

vl A;

rep(i, N){

LL a;

scanf("%lld", &a);

A.pb(a);

}

// 2. 降順sort.

sort(all(A));

reverse(all(A));

// 3. A[Y] + M < A[P] となる Y は？

int Y = N;

rep(i, N){

if(A[i] + M < A[P - 1]){

Y = i;

break;

}

// 4. 二分探索.

// -> 01-38.txt などで, WA版となったため, ロジック修正.

// -> l, m, h は, index と見る(問題数に変換する場合は, +1 を加算).

int l = P - 1, h = Y, m;

auto f = [&](int X) -> bool {

// 4-1. 問題 1 ～ (P - 1) までの(P - 1)問を, M人が投票.

LL lVote = max(0, P - 1) * M;

// 4-2. 問題 P ～ (X - 1) まで, (A[X] + M - A[i])人が投票.

LL mVote = 0;

repx(i, P - 1, X) mVote += max(0LL, A[X] + M - A[i]);

// 4-3. 問題 (X + 1) ～ N までの(N - X)問を, M人が投票.

LL rVote = max(0, N - X) * M;

// 4-4. 投票されても構わないかチェック.

// -> (M * V)未満ならば, 採用される可能性なし.

LL vote = lVote + mVote + rVote;

// printf("lVote=%lld mVote=%lld rVote=%lld vote=%lld MV=%lld\n", lVote, mVote, rVote, vote, M * V);

return (vote < M * V);

};

// 二分探索で確認してみる.

while(l + 1 < h){

m = (h + l) >> 1;

if(f(m)) h = m;

else l = m;

// printf("h=%lld l=%lld m=%lld\n", h, l, m);

}

// 5. 出力.

printf("%d\n", l + 1);

return 0;

}

[入力例]
6 1 2 2
2 1 1 3 0 2

[出力例]
5
※AtCoderテストケースより

[入力例]
6 1 5 2
2 1 1 3 0 2

[出力例]
3
※AtCoderテストケースより

[入力例]
10 4 8 5
7 2 3 6 1 6 5 4 6 5

[出力例]
8
※AtCoderテストケースより

[入力例]
20 3456 8 7
1728 11106 5834 12781 18820 14127 19412 9407 903 18066 14909 10426 10017 16164 21158 4660 18664 20245 3303 5934

[出力例]
10

[入力例]
50 2021 11 13
4365 17834 3440 5625 7833 2260 18430 10630 7648 2337 12612 9640 6127 12345 17602 15202 13456 16161 18060 12345 21191 6149 5440 778 14265 1574 8561 12345 20036 19537 12345 8049 21239 17688 5625 12591 13759 6962 12345 3933 14044 2721 652 12159 10982 19920 11192 5625 22068 9206

[出力例]
17

[入力例]

6 1 2 2

2 1 1 3 0 2

[出力例]

※AtCoderテストケースより

[入力例]

6 1 5 2

2 1 1 3 0 2

[出力例]

※AtCoderテストケースより

[入力例]

10 4 8 5

7 2 3 6 1 6 5 4 6 5

[出力例]

※AtCoderテストケースより

[入力例]

20 3456 8 7

1728 11106 5834 12781 18820 14127 19412 9407 903 18066 14909 10426 10017 16164 21158 4660 18664 20245 3303 5934

[出力例]

[入力例]

50 2021 11 13

4365 17834 3440 5625 7833 2260 18430 10630 7648 2337 12612 9640 6127 12345 17602 15202 13456 16161 18060 12345 21191 6149 5440 778 14265 1574 8561 12345 20036 19537 12345 8049 21239 17688 5625 12591 13759 6962 12345 3933 14044 2721 652 12159 10982 19920 11192 5625 22068 9206

[出力例]

■参照サイト
AtCoder Grand Contest 041

2021年3月26日

C++ の動作確認をしてみた（４３０）

C++の練習を兼ねて, AtCoder Regular Contest 115 の問題D (Odd Degree) を解いてみた.

■感想.
1. 問題Dは, 解答方針が見えなかったので, 解説を参考に実装して, ようやく, AC版に到達できた.
2. 苦手なdpの訓練を積めたので, 非常に良かったと思う.
3. 幅優先探索の復習が出来たので, 非常に良かったと思う.
4. 時間を見つけて, 引き続き, 過去問を振り返っていきたいと思う.

本家のサイト AtCoder Regular Contest 115 解説の各リンクをご覧下さい.

■C++版プログラム(問題D／AC版).

// 解き直し.
// https://atcoder.jp/contests/arc115/editorial/853
// C++(GCC 9.2.1)
#include <bits/stdc++.h>
using namespace std;
using LL = long long;
using P = pair<int, int>;
using vi = vector<int>;
using vvi = vector<vi>;
#define repex(i, a, b, c) for(int i = a; i < b; i += c)
#define repx(i, a, b) repex(i, a, b, 1)
#define rep(i, n) repx(i, 0, n)
#define repr(i, a, b) for(int i = a; i >= b; i--)
#define a first
#define b second
#define pb push_back
const LL MOD = 998244353;
const int LIMIT = 5050;
LL FAC[LIMIT], INV[LIMIT], g[LIMIT][LIMIT], dp[LIMIT][LIMIT];

// Fermat's little theorem から, 大きな冪乗の計算を行う.
// @param a: べき乗したい正整数.
// @param b: 指数.
// @return: べき乗した計算結果(mod版).
LL mPow(LL a, LL b){
    LL t = 1;
    while(b){
        if(b & 1) t = (t * a) % MOD;
        a = a * a % MOD;
        b >>= 1;
    }
    return t % MOD;
}

// 組み合わせ(nCk)計算用(mod版).
// ※配列FAC, INV は, 事前に計算済のものを使う.
// @param n: 対象となる要素の個数.
// @param k: 選択する要素の個数.
// @return: 組み合わせ(nCk)の計算結果(mod版).
LL combination(LL n, LL k){
    if(n < 0 || k < 0 || k > n) return 0;
    LL ret = FAC[n] * INV[k] % MOD * INV[n - k] % MOD;
    return ret;
}

int main(){
    
    // 1. 入力情報.
    int N, M;
    scanf("%d %d", &N, &M);
    vvi G(N);
    vector<P> edges;
    rep(i, M){
        int a, b;
        scanf("%d %d", &a, &b);
        a--;
        b--;
        G[a].pb(b);
        G[b].pb(a);
        edges.pb({a, b});
    }
    FAC[0] = 1;
    repx(i, 1, N + 1) FAC[i] = i * FAC[i - 1] % MOD;
    rep(i, N + 1)     INV[i] = mPow(FAC[i], MOD - 2) % MOD;
    
    // 2. グラフを連結成分に分解.
    // https://ja.wikipedia.org/wiki/幅優先探索
    auto bfs = [&](vvi &G, int s, int* c, int l){
        // 2-1. 空のキュー.
        queue<int> q;
        
        // 2-2. 連結成分番号を設定.
        c[s] = l;
        
        // 2-3. 探索地点 s をキュー q に追加.
        q.push(s);
        while(!q.empty()){
            // 2-4. キューから取り出す.
            int u = q.front();
            q.pop();
            
            // 2-5. 取り出した要素を処理.
            for(auto &e : G[u]){
                // 2-6. 訪問済であれば, 処理をスキップ.
                if(c[e])            continue;
                if(!c[e] && e != s) c[e] = l, q.push(e);
            }
        }
        return;
    };
    int c[N], idx = 0;
    rep(i, N) c[i] = 0;
    rep(i, N) if(!c[i]) bfs(G, i, c, ++idx);
    // rep(i, N) printf("%d ", c[i]);
    // puts("");
    
    // 3. 連結成分ごとの頂点数, 辺数 を 計算.
    set<int> gn[idx]; // 各連結成分に対する頂点.
    int gm[idx];      // 各連結成分に対する辺数.
    rep(i, idx) gm[i] = 0;
    for(auto &e : edges){
        int a, b;
        a = e.a;
        b = e.b;
        int n = c[a] - 1;
        assert(c[a] == c[b]);
        
        // 頂点を保存.
        gn[n].insert(a);
        gn[n].insert(b);
        
        // 辺数をカウント.
        gm[n]++;
    }
    
    // 4. 連結成分ごとに集計.
    rep(i, idx){
        LL m = (LL)gm[i];
        LL n = (LL)gn[i].size();
        LL o = m - n + 1LL;
        rep(k, N + 1){
            // K が 奇数.
            // - >何もしない
            if(k & 1) continue;
            
            // K が 偶数.
            // -> 辺が有る場合は, 全域木を適当に一つ取り, 全域木に含まれない辺を残すかどうか自由に決める.
            LL res = (m == 0) ? 1LL : mPow(2LL, o);
            g[i][k] = res * combination(n, (LL)k) % MOD;
        }
    }
    
    // 5. dp更新.
    int nSum = gn[0].size();
    rep(k, nSum + 1) dp[0][k] = g[0][k];
    repx(i, 1, idx){
        // 5-1. 頂点数設定.
        int nCur = gn[i].size();
        
        // 5-2. (i - 1)番目の状態をベースに, i番目の状態を決定.
        rep(k1, nSum + 1){
            rep(k2, nCur + 1){
                dp[i][k1 + k2] += dp[i - 1][k1] * g[i][k2];
                dp[i][k1 + k2] %= MOD;
            }
        }
        
        // 5-3. 頂点数合計を更新.
        nSum += nCur;
    }
    
    // 6. 出力.
    rep(i, N + 1) printf("%lld\n", dp[idx - 1][i]);
    return 0;
    
}

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// 解き直し.

// https://atcoder.jp/contests/arc115/editorial/853

// C++(GCC 9.2.1)

#include <bits/stdc++.h>

using namespace std;

using LL = long long;

using P = pair<int, int>;

using vi = vector<int>;

using vvi = vector<vi>;

#define repex(i, a, b, c) for(int i = a; i < b; i += c)

#define repx(i, a, b) repex(i, a, b, 1)

#define rep(i, n) repx(i, 0, n)

#define repr(i, a, b) for(int i = a; i >= b; i--)

#define a first

#define b second

#define pb push_back

const LL MOD = 998244353;

const int LIMIT = 5050;

LL FAC[LIMIT], INV[LIMIT], g[LIMIT][LIMIT], dp[LIMIT][LIMIT];

// Fermat's little theorem から, 大きな冪乗の計算を行う.

// @param a: べき乗したい正整数.

// @param b: 指数.

// @return: べき乗した計算結果(mod版).

LL mPow(LL a, LL b){

LL t = 1;

while(b){

if(b & 1) t = (t * a) % MOD;

a = a * a % MOD;

b >>= 1;

}

return t % MOD;

}

// 組み合わせ(nCk)計算用(mod版).

// ※配列FAC, INV は, 事前に計算済のものを使う.

// @param n: 対象となる要素の個数.

// @param k: 選択する要素の個数.

// @return: 組み合わせ(nCk)の計算結果(mod版).

LL combination(LL n, LL k){

if(n < 0 || k < 0 || k > n) return 0;

LL ret = FAC[n] * INV[k] % MOD * INV[n - k] % MOD;

return ret;

}

int main(){

// 1. 入力情報.

int N, M;

scanf("%d %d", &N, &M);

vvi G(N);

vector<P> edges;

rep(i, M){

int a, b;

scanf("%d %d", &a, &b);

a--;

b--;

G[a].pb(b);

G[b].pb(a);

edges.pb({a, b});

}

FAC[0] = 1;

repx(i, 1, N + 1) FAC[i] = i * FAC[i - 1] % MOD;

rep(i, N + 1) INV[i] = mPow(FAC[i], MOD - 2) % MOD;

// 2. グラフを連結成分に分解.

// https://ja.wikipedia.org/wiki/幅優先探索

auto bfs = [&](vvi &G, int s, int* c, int l){

// 2-1. 空のキュー.

queue<int> q;

// 2-2. 連結成分番号を設定.

c[s] = l;

// 2-3. 探索地点 s をキュー q に追加.

q.push(s);

while(!q.empty()){

// 2-4. キューから取り出す.

int u = q.front();

q.pop();

// 2-5. 取り出した要素を処理.

for(auto &e : G[u]){

// 2-6. 訪問済であれば, 処理をスキップ.

if(c[e]) continue;

if(!c[e] && e != s) c[e] = l, q.push(e);

}

return;

};

int c[N], idx = 0;

rep(i, N) c[i] = 0;

rep(i, N) if(!c[i]) bfs(G, i, c, ++idx);

// rep(i, N) printf("%d ", c[i]);

// puts("");

// 3. 連結成分ごとの頂点数, 辺数を計算.

set<int> gn[idx]; // 各連結成分に対する頂点.

int gm[idx]; // 各連結成分に対する辺数.

rep(i, idx) gm[i] = 0;

for(auto &e : edges){

int a, b;

a = e.a;

b = e.b;

int n = c[a] - 1;

assert(c[a] == c[b]);

// 頂点を保存.

gn[n].insert(a);

gn[n].insert(b);

// 辺数をカウント.

gm[n]++;

}

// 4. 連結成分ごとに集計.

rep(i, idx){

LL m = (LL)gm[i];

LL n = (LL)gn[i].size();

LL o = m - n + 1LL;

rep(k, N + 1){

// K が奇数.

// - >何もしない

if(k & 1) continue;

// K が偶数.

// -> 辺が有る場合は, 全域木を適当に一つ取り, 全域木に含まれない辺を残すかどうか自由に決める.

LL res = (m == 0) ? 1LL : mPow(2LL, o);

g[i][k] = res * combination(n, (LL)k) % MOD;

}

// 5. dp更新.

int nSum = gn[0].size();

rep(k, nSum + 1) dp[0][k] = g[0][k];

repx(i, 1, idx){

// 5-1. 頂点数設定.

int nCur = gn[i].size();

// 5-2. (i - 1)番目の状態をベースに, i番目の状態を決定.

rep(k1, nSum + 1){

rep(k2, nCur + 1){

dp[i][k1 + k2] += dp[i - 1][k1] * g[i][k2];

dp[i][k1 + k2] %= MOD;

}

// 5-3. 頂点数合計を更新.

nSum += nCur;

}

// 6. 出力.

rep(i, N + 1) printf("%lld\n", dp[idx - 1][i]);

return 0;

}

[入力例]
3 2
1 2
2 3

[出力例]
1
0
3
0
※AtCoderのテストケースより

[入力例]
4 2
1 2
3 4

[出力例]
1
0
2
0
1
※AtCoderのテストケースより

[入力例]
5 4
1 2
3 2
1 3
4 5

[出力例]
2
0
8
0
6
0

[入力例]
7 8
1 2
2 3
3 4
4 1
3 1
5 6
6 7
7 5

[出力例]
8
0
72
0
152
0
24
0

[入力例]
10 15
1 2
1 3
2 3
1 4
1 5
6 7
6 8
6 9
6 10
7 8
7 9
7 10
8 9
8 10
9 10

[出力例]
128
0
2560
0
14080
0
12800
0
3200
0
0

[入力例]

3 2

1 2

2 3

[出力例]

※AtCoderのテストケースより

[入力例]

4 2

1 2

3 4

[出力例]

※AtCoderのテストケースより

[入力例]

5 4

1 2

3 2

1 3

4 5

[出力例]

[入力例]

7 8

1 2

2 3

3 4

4 1

3 1

5 6

6 7

7 5

[出力例]

152

[入力例]

10 15

1 2

1 3

2 3

1 4

1 5

6 7

6 8

6 9

6 10

7 8

7 9

7 10

8 9

8 10

9 10

[出力例]

128

2560

14080

12800

3200

■参照サイト
AtCoder Regular Contest 115

2021年3月24日

Python（Cirq）について（１６）

概要

Cirq について, QAOA に関するサンプルを動かしてみた.
動作環境は, Google Colaboratory で行った
実行プログラムは, 下記の参照サイトをご覧ください

感想

量子物理学に関する知識(用語, 数式の意味ほか)は, 徐々に身につけていく必要があると感じた.
時間を見つけて, 今後も, ドキュメントの残りの部分を進めていこうと思う.

QAOA: Max-Cut

グラフの頂点数を変えて, 実行結果を確認する

頂点数 3

頂点数 7

頂点数 12

頂点数 18

頂点数 23

参照サイト

QAOA: Max-Cut

概要

感想

量子ゲートのサンプル

参照サイト

C++の練習を兼ねて, AtCoder Grand Contest 041 の 問題C (Domino Quality) を解いてみた.

概要

感想

Qiskit Visualizations

Single-Qubit Gates

参照サイト

C++の練習を兼ねて, AtCoder Beginner Contest 197 の 問題E (Traveler) を解いてみた.

概要

感想

Installing Qiskit

Circuit Basics

参照サイト

C++の練習を兼ねて, AtCoder Regular Contest 116 の 問題A (Odd vs Even) ～ 問題B (Products of Min-Max) を解いてみた.

C++の練習を兼ねて, AtCoder Beginner Contest 197 の 問題C (ORXOR) ～ 問題D (Opposite) を解いてみた.

C++の練習を兼ねて, AtCoder Grand Contest 041 の 問題B (Voting Judges) を解いてみた.

C++の練習を兼ねて, AtCoder Regular Contest 115 の 問題D (Odd Degree) を解いてみた.

概要

感想

QAOA: Max-Cut

参照サイト

C++の練習を兼ねて, AtCoder Grand Contest 041 の問題C (Domino Quality) を解いてみた.

C++の練習を兼ねて, AtCoder Beginner Contest 197 の問題E (Traveler) を解いてみた.

C++の練習を兼ねて, AtCoder Regular Contest 116 の問題A (Odd vs Even) ～問題B (Products of Min-Max) を解いてみた.

C++の練習を兼ねて, AtCoder Beginner Contest 197 の問題C (ORXOR) ～問題D (Opposite) を解いてみた.

C++の練習を兼ねて, AtCoder Grand Contest 041 の問題B (Voting Judges) を解いてみた.

C++の練習を兼ねて, AtCoder Regular Contest 115 の問題D (Odd Degree) を解いてみた.