Python | 個人用メモ帳

2021年5月8日

Python（Qiskit）について（９）

概要

Qiskit について, QAOA の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

本家のサイトが詳しいので, 今後も, どのような機能が利用できるかを, 時間を見つけて, 進めていこうと思う.

QAOA(4頂点)

グラフ

[出力結果]
[[ 0. -5. -6.  0.]
 [-5.  0. -2.  5.]
 [-6. -2.  0.  4.]
 [ 0.  5.  4.  0.]]

[出力結果]

[[ 0. -5. -6. 0.]

[-5. 0. -2. 5.]

[-6. -2. 0. 4.]

[ 0. 5. 4. 0.]]

グラフ描画

グラフの分割(Brute Force)

[出力結果]
Objective value computed by the brute-force method is 3

1 2	[出力結果] Objective value computed by the brute-force method is 3

グラフの分割(QAOA)

[出力結果]
[1. 0. 1. 0.]
Objective value computed by QAOA is 3.0

[出力結果]

[1. 0. 1. 0.]

Objective value computed by QAOA is 3.0

グラフの分割(NumPyMinimumEigensolver)

[出力結果]
[0 0 1 1]
Objective value computed by the NumPyMinimumEigensolver is 3

[出力結果]

[0 0 1 1]

Objective value computed by the NumPyMinimumEigensolver is 3

グラフの分割(VQE)

[出力結果]
[0. 1. 0. 1.]
Objective value computed by VQE is 3.0

[出力結果]

[0. 1. 0. 1.]

Objective value computed by VQE is 3.0

QAOA(6頂点)

グラフ

[出力結果]
[[ 0. -5. -6.  0. -2.  5.]
 [-5.  0.  4.  5. -9.  7.]
 [-6.  4.  0.  5. -6.  0.]
 [ 0.  5.  5.  0.  4.  0.]
 [-2. -9. -6.  4.  0.  3.]
 [ 5.  7.  0.  0.  3.  0.]]

[出力結果]

[[ 0. -5. -6. 0. -2. 5.]

[-5. 0. 4. 5. -9. 7.]

[-6. 4. 0. 5. -6. 0.]

[ 0. 5. 5. 0. 4. 0.]

[-2. -9. -6. 4. 0. 3.]

[ 5. 7. 0. 0. 3. 0.]]

グラフ描画

グラフの分割(Brute Force)

[出力結果]
Objective value computed by the brute-force method is 6

1 2	[出力結果] Objective value computed by the brute-force method is 6

グラフの分割(QAOA)

[出力結果]
[1. 0. 0. 0. 1. 1.]
Objective value computed by QAOA is 6.0

[出力結果]

[1. 0. 0. 0. 1. 1.]

Objective value computed by QAOA is 6.0

グラフの分割(NumPyMinimumEigensolver)

[出力結果]
[0 0 1 1 1 0]
Objective value computed by the NumPyMinimumEigensolver is 6

[出力結果]

[0 0 1 1 1 0]

Objective value computed by the NumPyMinimumEigensolver is 6

グラフの分割(VQE)

[出力結果]
[1. 0. 0. 0. 1. 1.]
Objective value computed by VQE is 6.0

[出力結果]

[1. 0. 0. 0. 1. 1.]

Objective value computed by VQE is 6.0

QAOA(8頂点)

グラフ

[出力結果]
[[  0.  -7.  -9.   0.  -2.   8.   6.   7.]
 [ -7.   0. -14.  10.   8. -10.   0.   6.]
 [ -9. -14.   0.   0.   4.  -2.   0.  12.]
 [  0.  10.   0.   0.   8.   9.  14. -14.]
 [ -2.   8.   4.   8.   0. -10.  -6.   0.]
 [  8. -10.  -2.   9. -10.   0.   0.  13.]
 [  6.   0.   0.  14.  -6.   0.   0.  -2.]
 [  7.   6.  12. -14.   0.  13.  -2.   0.]]

[出力結果]

[[ 0. -7. -9. 0. -2. 8. 6. 7.]

[ -7. 0. -14. 10. 8. -10. 0. 6.]

[ -9. -14. 0. 0. 4. -2. 0. 12.]

[ 0. 10. 0. 0. 8. 9. 14. -14.]

[ -2. 8. 4. 8. 0. -10. -6. 0.]

[ 8. -10. -2. 9. -10. 0. 0. 13.]

[ 6. 0. 0. 14. -6. 0. 0. -2.]

[ 7. 6. 12. -14. 0. 13. -2. 0.]]

グラフ描画

グラフの分割(Brute Force)

[出力結果]
Objective value computed by the brute-force method is 11

1 2	[出力結果] Objective value computed by the brute-force method is 11

グラフの分割(QAOA)

[出力結果]
[1. 1. 1. 0. 0. 1. 0. 1.]
Objective value computed by QAOA is 9.0

[出力結果]

[1. 1. 1. 0. 0. 1. 0. 1.]

Objective value computed by QAOA is 9.0

グラフの分割(NumPyMinimumEigensolver)

[出力結果]
[1 1 1 0 0 0 0 1]
Objective value computed by the NumPyMinimumEigensolver is 11

[出力結果]

[1 1 1 0 0 0 0 1]

Objective value computed by the NumPyMinimumEigensolver is 11

グラフの分割(VQE)

[出力結果]
[1. 0. 1. 0. 1. 1. 0. 0.]
Objective value computed by VQE is 11.0

[出力結果]

[1. 0. 1. 0. 1. 1. 0. 0.]

Objective value computed by VQE is 11.0

	Brute Force	QAOA	NumPyMinimumEigensolver	VQE
4頂点	コスト: 3	分割結果: [1. 0. 1. 0.] コスト: 3.0	分割結果: [0 0 1 1] コスト: 3	分割結果: [0. 1. 0. 1.] コスト: 3.0
6頂点	コスト: 6	分割結果: [1. 0. 0. 0. 1. 1.] コスト: 6.0	分割結果: [0 0 1 1 1 0] コスト: 6	分割結果: [1. 0. 0. 0. 1. 1.] コスト: 6.0
8頂点	コスト: 11	分割結果: [1. 1. 1. 0. 0. 1. 0. 1.] コスト: 9.0 (※分割に失敗しているように見える)	分割結果: [1 1 1 0 0 0 0 1] コスト: 11	分割結果: [1. 0. 1. 0. 1. 1. 0. 0.] コスト: 11.0

参照サイト

Quantum Approximate Optimization Algorithm

2021年4月18日

Python（Qiskit）について（７）

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

本家のサイトが詳しいので, 今後も, どのような機能が利用できるかを, 時間を見つけて, 進めていこうと思う.

Algebraic operations and predicates

to_matrix_op etc

[編集内容(to_matrix_op etc)]
from qiskit.aqua.operators import (StateFn, Zero, One, Plus, Minus, X, H,
                                   DictStateFn, VectorStateFn, CircuitStateFn, OperatorStateFn)

# to_matrix_op
print((Plus ^ 2).to_matrix_op())
print((Minus ^ 2).to_matrix_op())
print((Plus ^ Plus).to_matrix_op())   # equal to Plus ^ 2
print((Plus ^ Minus).to_matrix_op())
print((Minus ^ Plus).to_matrix_op())
print((Minus ^ Minus).to_matrix_op()) # equal to Minus ^ 2

# to_circuit_op
print((Plus ^ 2).to_circuit_op())
print((Minus ^ 2).to_circuit_op())
print((Plus ^ Plus).to_circuit_op())   # equal to Plus ^ 2
print((Plus ^ Minus).to_circuit_op())
print((Minus ^ Plus).to_circuit_op())
print((Minus ^ Minus).to_circuit_op()) # equal to Minus ^ 2

# sample
print((Plus ^ 2).to_matrix_op().sample())
print((Minus ^ 2).to_matrix_op().sample())
print((Plus ^ Plus).to_matrix_op().sample())
print((Plus ^ Minus).to_matrix_op().sample())
print((Minus ^ Plus).to_matrix_op().sample())
print((Minus ^ Minus).to_matrix_op().sample())

[編集内容(to_matrix_op etc)]

from qiskit.aqua.operators import (StateFn, Zero, One, Plus, Minus, X, H,

DictStateFn, VectorStateFn, CircuitStateFn, OperatorStateFn)

# to_matrix_op

print((Plus ^ 2).to_matrix_op())

print((Minus ^ 2).to_matrix_op())

print((Plus ^ Plus).to_matrix_op()) # equal to Plus ^ 2

print((Plus ^ Minus).to_matrix_op())

print((Minus ^ Plus).to_matrix_op())

print((Minus ^ Minus).to_matrix_op()) # equal to Minus ^ 2

# to_circuit_op

print((Plus ^ 2).to_circuit_op())

print((Minus ^ 2).to_circuit_op())

print((Plus ^ Plus).to_circuit_op()) # equal to Plus ^ 2

print((Plus ^ Minus).to_circuit_op())

print((Minus ^ Plus).to_circuit_op())

print((Minus ^ Minus).to_circuit_op()) # equal to Minus ^ 2

# sample

print((Plus ^ 2).to_matrix_op().sample())

print((Minus ^ 2).to_matrix_op().sample())

print((Plus ^ Plus).to_matrix_op().sample())

print((Plus ^ Minus).to_matrix_op().sample())

print((Minus ^ Plus).to_matrix_op().sample())

print((Minus ^ Minus).to_matrix_op().sample())

[出力結果]
VectorStateFn(Statevector([0.5+0.j, 0.5+0.j, 0.5+0.j, 0.5+0.j],
            dims=(2, 2)))
VectorStateFn(Statevector([ 0.5-1.22e-16j, -0.5+1.22e-16j, -0.5+1.22e-16j,
              0.5-1.22e-16j],
            dims=(2, 2)))
VectorStateFn(Statevector([0.5+0.j, 0.5+0.j, 0.5+0.j, 0.5+0.j],
            dims=(2, 2)))
VectorStateFn(Statevector([ 0.5-6.1e-17j, -0.5+6.1e-17j,  0.5-6.1e-17j, -0.5+6.1e-17j],
            dims=(2, 2)))
VectorStateFn(Statevector([ 0.5-6.1e-17j,  0.5-6.1e-17j, -0.5+6.1e-17j, -0.5+6.1e-17j],
            dims=(2, 2)))
VectorStateFn(Statevector([ 0.5-1.22e-16j, -0.5+1.22e-16j, -0.5+1.22e-16j,
              0.5-1.22e-16j],
            dims=(2, 2)))
CircuitStateFn(
     ┌───┐
q_0: ┤ H ├
     ├───┤
q_1: ┤ H ├
     └───┘
)
CircuitStateFn(
     ┌───┐┌───┐
q_0: ┤ X ├┤ H ├
     ├───┤├───┤
q_1: ┤ X ├┤ H ├
     └───┘└───┘
)
CircuitStateFn(
     ┌───┐
q_0: ┤ H ├
     ├───┤
q_1: ┤ H ├
     └───┘
)
CircuitStateFn(
     ┌───┐┌───┐
q_0: ┤ X ├┤ H ├
     ├───┤└───┘
q_1: ┤ H ├─────
     └───┘     
)
CircuitStateFn(
     ┌───┐     
q_0: ┤ H ├─────
     ├───┤┌───┐
q_1: ┤ X ├┤ H ├
     └───┘└───┘
)
CircuitStateFn(
     ┌───┐┌───┐
q_0: ┤ X ├┤ H ├
     ├───┤├───┤
q_1: ┤ X ├┤ H ├
     └───┘└───┘
)
{'00': 0.263671875, '01': 0.259765625, '11': 0.248046875, '10': 0.228515625}
{'10': 0.2734375, '00': 0.26953125, '01': 0.236328125, '11': 0.220703125}
{'11': 0.259765625, '01': 0.2568359375, '10': 0.2451171875, '00': 0.23828125}
{'00': 0.259765625, '11': 0.2587890625, '10': 0.248046875, '01': 0.2333984375}
{'11': 0.259765625, '10': 0.2509765625, '01': 0.2470703125, '00': 0.2421875}
{'01': 0.2822265625, '11': 0.24609375, '00': 0.2373046875, '10': 0.234375}

[出力結果]

VectorStateFn(Statevector([0.5+0.j, 0.5+0.j, 0.5+0.j, 0.5+0.j],

dims=(2, 2)))

VectorStateFn(Statevector([ 0.5-1.22e-16j, -0.5+1.22e-16j, -0.5+1.22e-16j,

0.5-1.22e-16j],

dims=(2, 2)))

VectorStateFn(Statevector([0.5+0.j, 0.5+0.j, 0.5+0.j, 0.5+0.j],

dims=(2, 2)))

VectorStateFn(Statevector([ 0.5-6.1e-17j, -0.5+6.1e-17j, 0.5-6.1e-17j, -0.5+6.1e-17j],

dims=(2, 2)))

VectorStateFn(Statevector([ 0.5-6.1e-17j, 0.5-6.1e-17j, -0.5+6.1e-17j, -0.5+6.1e-17j],

dims=(2, 2)))

VectorStateFn(Statevector([ 0.5-1.22e-16j, -0.5+1.22e-16j, -0.5+1.22e-16j,

0.5-1.22e-16j],

dims=(2, 2)))

CircuitStateFn(

┌───┐

q_0: ┤ H ├

├───┤

q_1: ┤ H ├

└───┘

)

CircuitStateFn(

┌───┐┌───┐

q_0: ┤ X ├┤ H ├

├───┤├───┤

q_1: ┤ X ├┤ H ├

└───┘└───┘

)

CircuitStateFn(

┌───┐

q_0: ┤ H ├

├───┤

q_1: ┤ H ├

└───┘

)

CircuitStateFn(

┌───┐┌───┐

q_0: ┤ X ├┤ H ├

├───┤└───┘

q_1: ┤ H ├─────

└───┘

)

CircuitStateFn(

┌───┐

q_0: ┤ H ├─────

├───┤┌───┐

q_1: ┤ X ├┤ H ├

└───┘└───┘

)

CircuitStateFn(

┌───┐┌───┐

q_0: ┤ X ├┤ H ├

├───┤├───┤

q_1: ┤ X ├┤ H ├

└───┘└───┘

)

{'00': 0.263671875, '01': 0.259765625, '11': 0.248046875, '10': 0.228515625}

{'10': 0.2734375, '00': 0.26953125, '01': 0.236328125, '11': 0.220703125}

{'11': 0.259765625, '01': 0.2568359375, '10': 0.2451171875, '00': 0.23828125}

{'00': 0.259765625, '11': 0.2587890625, '10': 0.248046875, '01': 0.2333984375}

{'11': 0.259765625, '10': 0.2509765625, '01': 0.2470703125, '00': 0.2421875}

{'01': 0.2822265625, '11': 0.24609375, '00': 0.2373046875, '10': 0.234375}

StateFn etc

[編集内容(StateFn etc)]
from qiskit.aqua.operators import (StateFn, Zero, One, Plus, Minus, X, H,
                                   DictStateFn, VectorStateFn, CircuitStateFn, OperatorStateFn)
from qiskit.circuit.library import RealAmplitudes

# StateFn
print(StateFn({'0' : 1}))
print(StateFn({'1' : 1}))
print(StateFn({'0' : 1}) == Zero)
print(StateFn({'0' : 0}) == Zero)
print(StateFn({'1' : 1}) == Zero)
print(StateFn({'1' : 0}) == Zero)
print(StateFn({'0' : 0}) == One)
print(StateFn({'0' : 1}) == One)
print(StateFn({'1' : 0}) == One)
print(StateFn({'1' : 1}) == One)
print(StateFn([0, 1, 1, 0]))
print(StateFn([1, 0, 0, 1]))

# RealAmplitudes
print(StateFn(RealAmplitudes(1)))
print(StateFn(RealAmplitudes(2)))
print(StateFn(RealAmplitudes(3)))

[編集内容(StateFn etc)]

from qiskit.aqua.operators import (StateFn, Zero, One, Plus, Minus, X, H,

DictStateFn, VectorStateFn, CircuitStateFn, OperatorStateFn)

from qiskit.circuit.library import RealAmplitudes

# StateFn

print(StateFn({'0' : 1}))

print(StateFn({'1' : 1}))

print(StateFn({'0' : 1}) == Zero)

print(StateFn({'0' : 0}) == Zero)

print(StateFn({'1' : 1}) == Zero)

print(StateFn({'1' : 0}) == Zero)

print(StateFn({'0' : 0}) == One)

print(StateFn({'0' : 1}) == One)

print(StateFn({'1' : 0}) == One)

print(StateFn({'1' : 1}) == One)

print(StateFn([0, 1, 1, 0]))

print(StateFn([1, 0, 0, 1]))

# RealAmplitudes

print(StateFn(RealAmplitudes(1)))

print(StateFn(RealAmplitudes(2)))

print(StateFn(RealAmplitudes(3)))

[出力結果]
DictStateFn({'0': 1})
DictStateFn({'1': 1})
True
False
False
False
False
False
False
True
VectorStateFn(Statevector([0.+0.j, 1.+0.j, 1.+0.j, 0.+0.j],
            dims=(2, 2)))
VectorStateFn(Statevector([1.+0.j, 0.+0.j, 0.+0.j, 1.+0.j],
            dims=(2, 2)))
CircuitStateFn(
     ┌──────────┐┌──────────┐┌──────────┐┌──────────┐
q_0: ┤ RY(θ[0]) ├┤ RY(θ[1]) ├┤ RY(θ[2]) ├┤ RY(θ[3]) ├
     └──────────┘└──────────┘└──────────┘└──────────┘
)
CircuitStateFn(
     ┌──────────┐     ┌──────────┐     ┌──────────┐     ┌──────────┐
q_0: ┤ RY(θ[0]) ├──■──┤ RY(θ[2]) ├──■──┤ RY(θ[4]) ├──■──┤ RY(θ[6]) ├
     ├──────────┤┌─┴─┐├──────────┤┌─┴─┐├──────────┤┌─┴─┐├──────────┤
q_1: ┤ RY(θ[1]) ├┤ X ├┤ RY(θ[3]) ├┤ X ├┤ RY(θ[5]) ├┤ X ├┤ RY(θ[7]) ├
     └──────────┘└───┘└──────────┘└───┘└──────────┘└───┘└──────────┘
)
CircuitStateFn(
     ┌──────────┐          ┌──────────┐                      ┌──────────┐»
q_0: ┤ RY(θ[0]) ├──■────■──┤ RY(θ[3]) ├──────────────■────■──┤ RY(θ[6]) ├»
     ├──────────┤┌─┴─┐  │  └──────────┘┌──────────┐┌─┴─┐  │  └──────────┘»
q_1: ┤ RY(θ[1]) ├┤ X ├──┼───────■──────┤ RY(θ[4]) ├┤ X ├──┼───────■──────»
     ├──────────┤└───┘┌─┴─┐   ┌─┴─┐    ├──────────┤└───┘┌─┴─┐   ┌─┴─┐    »
q_2: ┤ RY(θ[2]) ├─────┤ X ├───┤ X ├────┤ RY(θ[5]) ├─────┤ X ├───┤ X ├────»
     └──────────┘     └───┘   └───┘    └──────────┘     └───┘   └───┘    »
«                           ┌──────────┐             
«q_0: ──────────────■────■──┤ RY(θ[9]) ├─────────────
«     ┌──────────┐┌─┴─┐  │  └──────────┘┌───────────┐
«q_1: ┤ RY(θ[7]) ├┤ X ├──┼───────■──────┤ RY(θ[10]) ├
«     ├──────────┤└───┘┌─┴─┐   ┌─┴─┐    ├───────────┤
«q_2: ┤ RY(θ[8]) ├─────┤ X ├───┤ X ├────┤ RY(θ[11]) ├
«     └──────────┘     └───┘   └───┘    └───────────┘
)

[出力結果]

DictStateFn({'0': 1})

DictStateFn({'1': 1})

True

False

True

VectorStateFn(Statevector([0.+0.j, 1.+0.j, 1.+0.j, 0.+0.j],

dims=(2, 2)))

VectorStateFn(Statevector([1.+0.j, 0.+0.j, 0.+0.j, 1.+0.j],

dims=(2, 2)))

CircuitStateFn(

┌──────────┐┌──────────┐┌──────────┐┌──────────┐

q_0: ┤ RY(θ[0]) ├┤ RY(θ[1]) ├┤ RY(θ[2]) ├┤ RY(θ[3]) ├

└──────────┘└──────────┘└──────────┘└──────────┘

)

CircuitStateFn(

┌──────────┐ ┌──────────┐ ┌──────────┐ ┌──────────┐

q_0: ┤ RY(θ[0]) ├──■──┤ RY(θ[2]) ├──■──┤ RY(θ[4]) ├──■──┤ RY(θ[6]) ├

├──────────┤┌─┴─┐├──────────┤┌─┴─┐├──────────┤┌─┴─┐├──────────┤

q_1: ┤ RY(θ[1]) ├┤ X ├┤ RY(θ[3]) ├┤ X ├┤ RY(θ[5]) ├┤ X ├┤ RY(θ[7]) ├

└──────────┘└───┘└──────────┘└───┘└──────────┘└───┘└──────────┘

)

CircuitStateFn(

┌──────────┐ ┌──────────┐ ┌──────────┐»

q_0: ┤ RY(θ[0]) ├──■────■──┤ RY(θ[3]) ├──────────────■────■──┤ RY(θ[6]) ├»

├──────────┤┌─┴─┐ │ └──────────┘┌──────────┐┌─┴─┐ │ └──────────┘»

q_1: ┤ RY(θ[1]) ├┤ X ├──┼───────■──────┤ RY(θ[4]) ├┤ X ├──┼───────■──────»

├──────────┤└───┘┌─┴─┐ ┌─┴─┐ ├──────────┤└───┘┌─┴─┐ ┌─┴─┐ »

q_2: ┤ RY(θ[2]) ├─────┤ X ├───┤ X ├────┤ RY(θ[5]) ├─────┤ X ├───┤ X ├────»

└──────────┘ └───┘ └───┘ └──────────┘ └───┘ └───┘ »

« ┌──────────┐

«q_0: ──────────────■────■──┤ RY(θ[9]) ├─────────────

« ┌──────────┐┌─┴─┐ │ └──────────┘┌───────────┐

«q_1: ┤ RY(θ[7]) ├┤ X ├──┼───────■──────┤ RY(θ[10]) ├

« ├──────────┤└───┘┌─┴─┐ ┌─┴─┐ ├───────────┤

«q_2: ┤ RY(θ[8]) ├─────┤ X ├───┤ X ├────┤ RY(θ[11]) ├

« └──────────┘ └───┘ └───┘ └───────────┘

)

PrimitiveOps

Pauli Gates

[編集内容(Pauli Gates)]
from qiskit.aqua.operators import X, Y, Z, I, CX, T, H, S, PrimitiveOp

# Pauli I.
I
print(I.eval('0'), I.eval('1'))
print(I.eval('0').eval('0')) # (1, 1)成分.
print(I.eval('0').eval('1')) # (1, 2)成分.
print(I.eval('1').eval('0')) # (2, 1)成分.
print(I.eval('1').eval('1')) # (2, 2)成分.

# Pauli X.
X
print(X.eval('0'), X.eval('1'))
print(X.eval('0').eval('0')) # (1, 1)成分.
print(X.eval('0').eval('1')) # (1, 2)成分.
print(X.eval('1').eval('0')) # (2, 1)成分.
print(X.eval('1').eval('1')) # (2, 2)成分.

# Pauli Y.
Y
print(Y.eval('0'), Y.eval('1'))
print(Y.eval('0').eval('0')) # (1, 1)成分.
print(Y.eval('0').eval('1')) # (1, 2)成分.
print(Y.eval('1').eval('0')) # (2, 1)成分.
print(Y.eval('1').eval('1')) # (2, 2)成分.

# Pauli Z.
Z
print(Z.eval('0'), Z.eval('1'))
print(Z.eval('0').eval('0')) # (1, 1)成分.
print(Z.eval('0').eval('1')) # (1, 2)成分.
print(Z.eval('1').eval('0')) # (2, 1)成分.
print(Z.eval('1').eval('1')) # (2, 2)成分.

[編集内容(Pauli Gates)]

from qiskit.aqua.operators import X, Y, Z, I, CX, T, H, S, PrimitiveOp

# Pauli I.

print(I.eval('0'), I.eval('1'))

print(I.eval('0').eval('0')) # (1, 1)成分.

print(I.eval('0').eval('1')) # (1, 2)成分.

print(I.eval('1').eval('0')) # (2, 1)成分.

print(I.eval('1').eval('1')) # (2, 2)成分.

# Pauli X.

print(X.eval('0'), X.eval('1'))

print(X.eval('0').eval('0')) # (1, 1)成分.

print(X.eval('0').eval('1')) # (1, 2)成分.

print(X.eval('1').eval('0')) # (2, 1)成分.

print(X.eval('1').eval('1')) # (2, 2)成分.

# Pauli Y.

print(Y.eval('0'), Y.eval('1'))

print(Y.eval('0').eval('0')) # (1, 1)成分.

print(Y.eval('0').eval('1')) # (1, 2)成分.

print(Y.eval('1').eval('0')) # (2, 1)成分.

print(Y.eval('1').eval('1')) # (2, 2)成分.

# Pauli Z.

print(Z.eval('0'), Z.eval('1'))

print(Z.eval('0').eval('0')) # (1, 1)成分.

print(Z.eval('0').eval('1')) # (1, 2)成分.

print(Z.eval('1').eval('0')) # (2, 1)成分.

print(Z.eval('1').eval('1')) # (2, 2)成分.

[出力結果]
PauliOp(Pauli('I'), coeff=1.0)
DictStateFn({'0': (1+0j)}) DictStateFn({'1': (1+0j)})
(1+0j)
0j
0j
(1+0j)
PauliOp(Pauli('X'), coeff=1.0)
DictStateFn({'1': (1+0j)}) DictStateFn({'0': (1+0j)})
0j
(1+0j)
(1+0j)
0j
PauliOp(Pauli('Y'), coeff=1.0)
DictStateFn({'1': 1j}) DictStateFn({'0': -1j})
0j
1j
-1j
0j
PauliOp(Pauli('Z'), coeff=1.0)
DictStateFn({'0': (1+0j)}) DictStateFn({'1': (-1+0j)})
(1+0j)
0j
0j
(-1+0j)

[出力結果]

PauliOp(Pauli('I'), coeff=1.0)

DictStateFn({'0': (1+0j)}) DictStateFn({'1': (1+0j)})

(1+0j)

PauliOp(Pauli('X'), coeff=1.0)

DictStateFn({'1': (1+0j)}) DictStateFn({'0': (1+0j)})

(1+0j)

PauliOp(Pauli('Y'), coeff=1.0)

DictStateFn({'1': 1j}) DictStateFn({'0': -1j})

-1j

PauliOp(Pauli('Z'), coeff=1.0)

DictStateFn({'0': (1+0j)}) DictStateFn({'1': (-1+0j)})

(1+0j)

(-1+0j)

CX Gates etc

[編集内容(Pauli Gates)]
[編集内容(CX Gates etc)]
from qiskit.aqua.operators import X, Y, Z, I, CX, CZ, T, H, S, PrimitiveOp

# CX.
CX
print(CX.eval('00'), CX.eval('01'), CX.eval('10'), CX.eval('11'))
print(CX.eval('00').eval('00'), CX.eval('00').eval('01'), CX.eval('00').eval('10'), CX.eval('00').eval('11')) # (1, 1) - (4, 1)成分.
print(CX.eval('01').eval('00'), CX.eval('01').eval('01'), CX.eval('01').eval('10'), CX.eval('01').eval('11')) # (1, 2) - (4, 2)成分.
print(CX.eval('10').eval('00'), CX.eval('10').eval('01'), CX.eval('10').eval('10'), CX.eval('10').eval('11')) # (1, 3) - (4, 3)成分.
print(CX.eval('11').eval('00'), CX.eval('11').eval('01'), CX.eval('11').eval('10'), CX.eval('11').eval('11')) # (1, 4) - (4, 4)成分.
print(CX)
print(CX.to_matrix().real)

# X ^ Z.
XZ = X ^ Z
XZ
print(XZ.eval('00'), XZ.eval('01'), XZ.eval('10'), XZ.eval('11'))
print(XZ.eval('00').eval('00'), XZ.eval('00').eval('01'), XZ.eval('00').eval('10'), XZ.eval('00').eval('11')) # (1, 1) - (4, 1)成分.
print(XZ.eval('01').eval('00'), XZ.eval('01').eval('01'), XZ.eval('01').eval('10'), XZ.eval('01').eval('11')) # (1, 2) - (4, 2)成分.
print(XZ.eval('10').eval('00'), XZ.eval('10').eval('01'), XZ.eval('10').eval('10'), XZ.eval('10').eval('11')) # (1, 3) - (4, 3)成分.
print(XZ.eval('11').eval('00'), XZ.eval('11').eval('01'), XZ.eval('11').eval('10'), XZ.eval('11').eval('11')) # (1, 4) - (4, 4)成分.
print(XZ)
print(XZ.to_matrix().real)

[編集内容(Pauli Gates)]

[編集内容(CX Gates etc)]

from qiskit.aqua.operators import X, Y, Z, I, CX, CZ, T, H, S, PrimitiveOp

# CX.

print(CX.eval('00'), CX.eval('01'), CX.eval('10'), CX.eval('11'))

print(CX.eval('00').eval('00'), CX.eval('00').eval('01'), CX.eval('00').eval('10'), CX.eval('00').eval('11')) # (1, 1) - (4, 1)成分.

print(CX.eval('01').eval('00'), CX.eval('01').eval('01'), CX.eval('01').eval('10'), CX.eval('01').eval('11')) # (1, 2) - (4, 2)成分.

print(CX.eval('10').eval('00'), CX.eval('10').eval('01'), CX.eval('10').eval('10'), CX.eval('10').eval('11')) # (1, 3) - (4, 3)成分.

print(CX.eval('11').eval('00'), CX.eval('11').eval('01'), CX.eval('11').eval('10'), CX.eval('11').eval('11')) # (1, 4) - (4, 4)成分.

print(CX)

print(CX.to_matrix().real)

# X ^ Z.

XZ = X ^ Z

print(XZ.eval('00'), XZ.eval('01'), XZ.eval('10'), XZ.eval('11'))

print(XZ.eval('00').eval('00'), XZ.eval('00').eval('01'), XZ.eval('00').eval('10'), XZ.eval('00').eval('11')) # (1, 1) - (4, 1)成分.

print(XZ.eval('01').eval('00'), XZ.eval('01').eval('01'), XZ.eval('01').eval('10'), XZ.eval('01').eval('11')) # (1, 2) - (4, 2)成分.

print(XZ.eval('10').eval('00'), XZ.eval('10').eval('01'), XZ.eval('10').eval('10'), XZ.eval('10').eval('11')) # (1, 3) - (4, 3)成分.

print(XZ.eval('11').eval('00'), XZ.eval('11').eval('01'), XZ.eval('11').eval('10'), XZ.eval('11').eval('11')) # (1, 4) - (4, 4)成分.

print(XZ)

print(XZ.to_matrix().real)

[出力結果]
CircuitOp(<qiskit.circuit.quantumcircuit.QuantumCircuit object at 0x7f7b4a4fd150>, coeff=1.0)
VectorStateFn(Statevector([1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],
            dims=(2, 2))) VectorStateFn(Statevector([0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j],
            dims=(2, 2))) VectorStateFn(Statevector([0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],
            dims=(2, 2))) VectorStateFn(Statevector([0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j],
            dims=(2, 2)))
(1+0j) 0j 0j 0j
0j 0j 0j (1+0j)
0j 0j (1+0j) 0j
0j (1+0j) 0j 0j
          
q_0: ──■──
     ┌─┴─┐
q_1: ┤ X ├
     └───┘
[[1. 0. 0. 0.]
 [0. 0. 0. 1.]
 [0. 0. 1. 0.]
 [0. 1. 0. 0.]]
PauliOp(Pauli('XZ'), coeff=1.0)
DictStateFn({'10': (1+0j)}) DictStateFn({'11': (-1+0j)}) DictStateFn({'00': (1+0j)}) DictStateFn({'01': (-1+0j)})
0j 0j (1+0j) 0j
0j 0j 0j (-1+0j)
(1+0j) 0j 0j 0j
0j (-1+0j) 0j 0j
XZ
[[ 0.  0.  1.  0.]
 [ 0.  0.  0. -1.]
 [ 1.  0.  0.  0.]
 [ 0. -1.  0.  0.]]

[出力結果]

CircuitOp(<qiskit.circuit.quantumcircuit.QuantumCircuit object at 0x7f7b4a4fd150>, coeff=1.0)

VectorStateFn(Statevector([1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],

dims=(2, 2))) VectorStateFn(Statevector([0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j],

dims=(2, 2))) VectorStateFn(Statevector([0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],

dims=(2, 2))) VectorStateFn(Statevector([0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j],

dims=(2, 2)))

(1+0j) 0j 0j 0j

0j 0j 0j (1+0j)

0j 0j (1+0j) 0j

0j (1+0j) 0j 0j

q_0: ──■──

┌─┴─┐

q_1: ┤ X ├

└───┘

[[1. 0. 0. 0.]

[0. 0. 0. 1.]

[0. 0. 1. 0.]

[0. 1. 0. 0.]]

PauliOp(Pauli('XZ'), coeff=1.0)

DictStateFn({'10': (1+0j)}) DictStateFn({'11': (-1+0j)}) DictStateFn({'00': (1+0j)}) DictStateFn({'01': (-1+0j)})

0j 0j (1+0j) 0j

0j 0j 0j (-1+0j)

(1+0j) 0j 0j 0j

0j (-1+0j) 0j 0j

[[ 0. 0. 1. 0.]

[ 0. 0. 0. -1.]

[ 1. 0. 0. 0.]

[ 0. -1. 0. 0.]]

参照サイト

qiskit-tutorials/tutorials/operators/01_operator_flow.ipynb

2021年4月7日

Python（Qiskit）について（６）

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.

Algebraic operations and predicates

StateFns

[編集内容(StateFns)]
from qiskit.aqua.operators import (StateFn, Zero, One, Plus, Minus, X, H,
                                   DictStateFn, VectorStateFn, CircuitStateFn, OperatorStateFn)
import math

# Check the output by changing the comment out for each.
# (1.2 + 3.4i)|0>
# (1.2 + 3.4i) * Zero # SyntaxError: invalid syntax
(1.2 + 3.4j) * Zero

# (4.3 + 2.1i)|1>
(4.3 + 2.1j) * One

# (1.2 + 3.4i)|0> + (5.6 + 7.8i)|1>
(1.2 + 3.4j) * Zero + (5.6 + 7.8j) * One

# (|0> + |1>) / (1/√2)
cPlus = (Zero + One) / math.sqrt(2)
print(cPlus)

# (|0> - |1>) / (1/√2)
cMinus = (Zero - One) / math.sqrt(2)
print(cMinus)

# |+> + |->
print(Plus + Minus)

# cPlus + cMinus
print(cPlus + cMinus) # display contents are different from (|+> + |->).

# |+> - |->
print(Plus - Minus)

# cPlus - cMinus
print(cPlus - cMinus) # display contents are different from (|+> - |->).

# <0|0>
print(~Zero @ Zero)

# <1|1>
print(~One @ One)

[編集内容(StateFns)]

from qiskit.aqua.operators import (StateFn, Zero, One, Plus, Minus, X, H,

DictStateFn, VectorStateFn, CircuitStateFn, OperatorStateFn)

import math

# Check the output by changing the comment out for each.

# (1.2 + 3.4i)|0>

# (1.2 + 3.4i) * Zero # SyntaxError: invalid syntax

(1.2 + 3.4j) * Zero

# (4.3 + 2.1i)|1>

(4.3 + 2.1j) * One

# (1.2 + 3.4i)|0> + (5.6 + 7.8i)|1>

(1.2 + 3.4j) * Zero + (5.6 + 7.8j) * One

# (|0> + |1>) / (1/√2)

cPlus = (Zero + One) / math.sqrt(2)

print(cPlus)

# (|0> - |1>) / (1/√2)

cMinus = (Zero - One) / math.sqrt(2)

print(cMinus)

# |+> + |->

print(Plus + Minus)

# cPlus + cMinus

print(cPlus + cMinus) # display contents are different from (|+> + |->).

# |+> - |->

print(Plus - Minus)

# cPlus - cMinus

print(cPlus - cMinus) # display contents are different from (|+> - |->).

# <0|0>

print(~Zero @ Zero)

# <1|1>

print(~One @ One)

[出力結果]
DictStateFn({'0': 1}, coeff=(1.2+3.4j), is_measurement=False)
DictStateFn({'1': 1}, coeff=(4.3+2.1j), is_measurement=False)
DictStateFn({'0': (1.2+3.4j), '1': (5.6+7.8j)}, coeff=1.0, is_measurement=False)
DictStateFn({'0': 1.0, '1': 1.0}) * 0.7071067811865475
DictStateFn({'0': 1.0, '1': -1.0}) * 0.7071067811865475
SummedOp([
  CircuitStateFn(
       ┌───┐
  q_0: ┤ H ├
       └───┘
  ),
  CircuitStateFn(
       ┌───┐┌───┐
  q_0: ┤ X ├┤ H ├
       └───┘└───┘
  )
])
DictStateFn({'0': 1.414213562373095, '1': 0.0})
SummedOp([
  CircuitStateFn(
       ┌───┐
  q_0: ┤ H ├
       └───┘
  ),
  CircuitStateFn(
       ┌───┐┌───┐
  q_0: ┤ X ├┤ H ├
       └───┘└───┘
  ) * -1.0
])
DictStateFn({'0': 0.0, '1': 1.414213562373095})
ComposedOp([
  DictMeasurement({'0': 1}),
  DictStateFn({'0': 1})
])
ComposedOp([
  DictMeasurement({'1': 1}),
  DictStateFn({'1': 1})
])

[出力結果]

DictStateFn({'0': 1}, coeff=(1.2+3.4j), is_measurement=False)

DictStateFn({'1': 1}, coeff=(4.3+2.1j), is_measurement=False)

DictStateFn({'0': (1.2+3.4j), '1': (5.6+7.8j)}, coeff=1.0, is_measurement=False)

DictStateFn({'0': 1.0, '1': 1.0}) * 0.7071067811865475

DictStateFn({'0': 1.0, '1': -1.0}) * 0.7071067811865475

SummedOp([

CircuitStateFn(

┌───┐

q_0: ┤ H ├

└───┘

CircuitStateFn(

┌───┐┌───┐

q_0: ┤ X ├┤ H ├

└───┘└───┘

)

])

DictStateFn({'0': 1.414213562373095, '1': 0.0})

SummedOp([

CircuitStateFn(

┌───┐

q_0: ┤ H ├

└───┘

CircuitStateFn(

┌───┐┌───┐

q_0: ┤ X ├┤ H ├

└───┘└───┘

) * -1.0

])

DictStateFn({'0': 0.0, '1': 1.414213562373095})

ComposedOp([

DictMeasurement({'0': 1}),

DictStateFn({'0': 1})

])

ComposedOp([

DictMeasurement({'1': 1}),

DictStateFn({'1': 1})

])

eval etc

[編集内容(eval etc)]
from qiskit.aqua.operators import (StateFn, Zero, One, Plus, Minus, X, H,
                                   DictStateFn, VectorStateFn, CircuitStateFn, OperatorStateFn)
import math

# (|0> + |1>) / (1/√2)
cPlus = (Zero + One) / math.sqrt(2)
print((~cPlus @ cPlus).eval())

# (|0> - |1>) / (1/√2)
cMinus = (Zero - One) / math.sqrt(2)
print((~cMinus @ cMinus).eval())

# <0|0>
print((~Zero @ Zero).eval())

# <1|1>
print((~One @ One).eval())

# @ is equivalent to compose.
print(~One @ One)
print((~One).compose(One))

# |0> tensor |+>
print(Zero ^ Plus)

# |0> tensor |->
print(Zero ^ Minus)

# |1> tensor |+>
print(One ^ Plus)

# |1> tensor |->
print(One ^ Minus)

[編集内容(eval etc)]

from qiskit.aqua.operators import (StateFn, Zero, One, Plus, Minus, X, H,

DictStateFn, VectorStateFn, CircuitStateFn, OperatorStateFn)

import math

# (|0> + |1>) / (1/√2)

cPlus = (Zero + One) / math.sqrt(2)

print((~cPlus @ cPlus).eval())

# (|0> - |1>) / (1/√2)

cMinus = (Zero - One) / math.sqrt(2)

print((~cMinus @ cMinus).eval())

# <0|0>

print((~Zero @ Zero).eval())

# <1|1>

print((~One @ One).eval())

# @ is equivalent to compose.

print(~One @ One)

print((~One).compose(One))

# |0> tensor |+>

print(Zero ^ Plus)

# |0> tensor |->

print(Zero ^ Minus)

# |1> tensor |+>

print(One ^ Plus)

# |1> tensor |->

print(One ^ Minus)

[出力結果]
0.9999999999999998
0.9999999999999998
1.0
1.0
ComposedOp([
  DictMeasurement({'1': 1}),
  DictStateFn({'1': 1})
])
ComposedOp([
  DictMeasurement({'1': 1}),
  DictStateFn({'1': 1})
])
TensoredOp([
  DictStateFn({'0': 1}),
  CircuitStateFn(
       ┌───┐
  q_0: ┤ H ├
       └───┘
  )
])
TensoredOp([
  DictStateFn({'0': 1}),
  CircuitStateFn(
       ┌───┐┌───┐
  q_0: ┤ X ├┤ H ├
       └───┘└───┘
  )
])
TensoredOp([
  DictStateFn({'1': 1}),
  CircuitStateFn(
       ┌───┐
  q_0: ┤ H ├
       └───┘
  )
])
TensoredOp([
  DictStateFn({'1': 1}),
  CircuitStateFn(
       ┌───┐┌───┐
  q_0: ┤ X ├┤ H ├
       └───┘└───┘
  )
])

[出力結果]

0.9999999999999998

1.0

ComposedOp([

DictMeasurement({'1': 1}),

DictStateFn({'1': 1})

])

ComposedOp([

DictMeasurement({'1': 1}),

DictStateFn({'1': 1})

])

TensoredOp([

DictStateFn({'0': 1}),

CircuitStateFn(

┌───┐

q_0: ┤ H ├

└───┘

)

])

TensoredOp([

DictStateFn({'0': 1}),

CircuitStateFn(

┌───┐┌───┐

q_0: ┤ X ├┤ H ├

└───┘└───┘

)

])

TensoredOp([

DictStateFn({'1': 1}),

CircuitStateFn(

┌───┐

q_0: ┤ H ├

└───┘

)

])

TensoredOp([

DictStateFn({'1': 1}),

CircuitStateFn(

┌───┐┌───┐

q_0: ┤ X ├┤ H ├

└───┘└───┘

)

])

to_circuit_op etc

[編集内容(to_circuit_op etc)]
from qiskit.aqua.operators import (StateFn, Zero, One, Plus, Minus, X, H,
                                   DictStateFn, VectorStateFn, CircuitStateFn, OperatorStateFn)
import math

# to_circuit_op
print((Zero ^ Zero).to_circuit_op())
print((One ^ One).to_circuit_op())
print((Plus ^ Plus).to_circuit_op())
print((Minus ^ Minus).to_circuit_op())

# to_circuit_op
print((Zero ^ One).to_circuit_op())
print((Zero ^ Plus).to_circuit_op())
print((Zero ^ Minus).to_circuit_op())

# tensor powers
# ValueError: Sum over statefns with different numbers of qubits, 2 and 3, is not well defined
# print(1.2 * ((One ^ 2) + (Zero ^ 3))) # error.
print((One ^ 3) + (Zero ^ 3))
print((Zero ^ Zero ^ One) + (Zero ^ One ^ Zero) + (One ^ Zero ^ Zero))
print(2 * ((Plus ^ 3) + (Minus ^ 3)))
print((One ^ Zero) ^ 5)

[編集内容(to_circuit_op etc)]

from qiskit.aqua.operators import (StateFn, Zero, One, Plus, Minus, X, H,

DictStateFn, VectorStateFn, CircuitStateFn, OperatorStateFn)

import math

# to_circuit_op

print((Zero ^ Zero).to_circuit_op())

print((One ^ One).to_circuit_op())

print((Plus ^ Plus).to_circuit_op())

print((Minus ^ Minus).to_circuit_op())

# to_circuit_op

print((Zero ^ One).to_circuit_op())

print((Zero ^ Plus).to_circuit_op())

print((Zero ^ Minus).to_circuit_op())

# tensor powers

# ValueError: Sum over statefns with different numbers of qubits, 2 and 3, is not well defined

# print(1.2 * ((One ^ 2) + (Zero ^ 3))) # error.

print((One ^ 3) + (Zero ^ 3))

print((Zero ^ Zero ^ One) + (Zero ^ One ^ Zero) + (One ^ Zero ^ Zero))

print(2 * ((Plus ^ 3) + (Minus ^ 3)))

print((One ^ Zero) ^ 5)

[出力結果]
CircuitStateFn(
     
q_0: 
     
q_1: 
     
)
CircuitStateFn(
     ┌───┐
q_0: ┤ X ├
     ├───┤
q_1: ┤ X ├
     └───┘
)
CircuitStateFn(
     ┌───┐
q_0: ┤ H ├
     ├───┤
q_1: ┤ H ├
     └───┘
)
CircuitStateFn(
     ┌───┐┌───┐
q_0: ┤ X ├┤ H ├
     ├───┤├───┤
q_1: ┤ X ├┤ H ├
     └───┘└───┘
)
CircuitStateFn(
     ┌───┐
q_0: ┤ X ├
     └───┘
q_1: ─────
          
)
CircuitStateFn(
     ┌───┐
q_0: ┤ H ├
     └───┘
q_1: ─────
          
)
CircuitStateFn(
     ┌───┐┌───┐
q_0: ┤ X ├┤ H ├
     └───┘└───┘
q_1: ──────────
               
)
DictStateFn({'111': 1.0, '000': 1.0})
DictStateFn({'001': 1.0, '010': 1.0, '100': 1.0})
2.0 * SummedOp([
  CircuitStateFn(
       ┌───┐
  q_0: ┤ H ├
       ├───┤
  q_1: ┤ H ├
       ├───┤
  q_2: ┤ H ├
       └───┘
  ),
  CircuitStateFn(
       ┌───┐┌───┐
  q_0: ┤ X ├┤ H ├
       ├───┤├───┤
  q_1: ┤ X ├┤ H ├
       ├───┤├───┤
  q_2: ┤ X ├┤ H ├
       └───┘└───┘
  )
])
DictStateFn({'1010101010': 1})

[出力結果]

CircuitStateFn(

q_0:

q_1:

)

CircuitStateFn(

┌───┐

q_0: ┤ X ├

├───┤

q_1: ┤ X ├

└───┘

)

CircuitStateFn(

┌───┐

q_0: ┤ H ├

├───┤

q_1: ┤ H ├

└───┘

)

CircuitStateFn(

┌───┐┌───┐

q_0: ┤ X ├┤ H ├

├───┤├───┤

q_1: ┤ X ├┤ H ├

└───┘└───┘

)

CircuitStateFn(

┌───┐

q_0: ┤ X ├

└───┘

q_1: ─────

)

CircuitStateFn(

┌───┐

q_0: ┤ H ├

└───┘

q_1: ─────

)

CircuitStateFn(

┌───┐┌───┐

q_0: ┤ X ├┤ H ├

└───┘└───┘

q_1: ──────────

)

DictStateFn({'111': 1.0, '000': 1.0})

DictStateFn({'001': 1.0, '010': 1.0, '100': 1.0})

2.0 * SummedOp([

CircuitStateFn(

┌───┐

q_0: ┤ H ├

├───┤

q_1: ┤ H ├

├───┤

q_2: ┤ H ├

└───┘

CircuitStateFn(

┌───┐┌───┐

q_0: ┤ X ├┤ H ├

├───┤├───┤

q_1: ┤ X ├┤ H ├

├───┤├───┤

q_2: ┤ X ├┤ H ├

└───┘└───┘

)

])

DictStateFn({'1010101010': 1})

参照サイト

qiskit-tutorials/tutorials/operators/01_operator_flow.ipynb

2021年4月5日

Python（Qiskit）について（５）

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.

Operators

operators

[編集内容(operators)]
from qiskit.aqua.operators import I, X, Y, Z
from qiskit.aqua.operators import CX, S, H, T, Swap, CZ
from qiskit.aqua.operators import Zero, One, Plus, Minus

# One qubit Pauli operators.
print(I, X, Y, Z)

# Clifford + T etc.
print(CX)
print(S)
print(H)
print(T)
print(Swap)
print(CZ)

# One qubit states.
print(Zero)
print(One)
print(Plus)
print(Minus)

[編集内容(operators)]

from qiskit.aqua.operators import I, X, Y, Z

from qiskit.aqua.operators import CX, S, H, T, Swap, CZ

from qiskit.aqua.operators import Zero, One, Plus, Minus

# One qubit Pauli operators.

print(I, X, Y, Z)

# Clifford + T etc.

print(CX)

print(S)

print(H)

print(T)

print(Swap)

print(CZ)

# One qubit states.

print(Zero)

print(One)

print(Plus)

print(Minus)

[出力結果]
I X Y Z
          
q_0: ──■──
     ┌─┴─┐
q_1: ┤ X ├
     └───┘
     ┌───┐
q_0: ┤ S ├
     └───┘
     ┌───┐
q_0: ┤ H ├
     └───┘
     ┌───┐
q_0: ┤ T ├
     └───┘
        
q_0: ─X─
      │ 
q_1: ─X─
        
        
q_0: ─■─
      │ 
q_1: ─■─
        
DictStateFn({'0': 1})
DictStateFn({'1': 1})
CircuitStateFn(
     ┌───┐
q_0: ┤ H ├
     └───┘
)
CircuitStateFn(
     ┌───┐┌───┐
q_0: ┤ X ├┤ H ├
     └───┘└───┘
)

[出力結果]

I X Y Z

q_0: ──■──

┌─┴─┐

q_1: ┤ X ├

└───┘

┌───┐

q_0: ┤ S ├

└───┘

┌───┐

q_0: ┤ H ├

└───┘

┌───┐

q_0: ┤ T ├

└───┘

q_0: ─X─

│

q_1: ─X─

q_0: ─■─

│

q_1: ─■─

DictStateFn({'0': 1})

DictStateFn({'1': 1})

CircuitStateFn(

┌───┐

q_0: ┤ H ├

└───┘

)

CircuitStateFn(

┌───┐┌───┐

q_0: ┤ X ├┤ H ├

└───┘└───┘

)

operators addition and subtraction etc

[編集内容(operators addition and subtraction etc)]
from qiskit.aqua.operators import I, X, Y, Z

# addition.
print(X + Y)

# subtraction.
print(X - Y)

# multiply.
# ValueError: Operators can only be scalar multiplied by float or complex, 
# not Y of type <class 'qiskit.aqua.operators.primitive_ops.pauli_op.PauliOp'>.
# print(X * Y)

# division.
# TypeError: unsupported operand type(s) for /: 'int' and 'PauliOp'
# print(X / Y)

# tensor products
print(X ^ Y)

# composition
print(X @ Y)

# other
print(2 * (3 * X) @ (4 * Y) ^ (5 * Z))
print(I @ I @ I)
print(I ^ I ^ I)
print((X + Y - Z) @ (Y + Z - X) ^ (Z + X - Y))

[編集内容(operators addition and subtraction etc)]

from qiskit.aqua.operators import I, X, Y, Z

# addition.

print(X + Y)

# subtraction.

print(X - Y)

# multiply.

# ValueError: Operators can only be scalar multiplied by float or complex,

# not Y of type <class 'qiskit.aqua.operators.primitive_ops.pauli_op.PauliOp'>.

# print(X * Y)

# division.

# TypeError: unsupported operand type(s) for /: 'int' and 'PauliOp'

# print(X / Y)

# tensor products

print(X ^ Y)

# composition

print(X @ Y)

# other

print(2 * (3 * X) @ (4 * Y) ^ (5 * Z))

print(I @ I @ I)

print(I ^ I ^ I)

print((X + Y - Z) @ (Y + Z - X) ^ (Z + X - Y))

[出力結果]
SummedOp([
  X,
  Y
])
SummedOp([
  X,
  -1.0 * Y
])
XY
1j * Z
120j * ZZ
I
III
TensoredOp([
  ComposedOp([
    SummedOp([
      X,
      Y,
      -1.0 * Z
    ]),
    SummedOp([
      Y,
      Z,
      -1.0 * X
    ])
  ]),
  SummedOp([
    Z,
    X,
    -1.0 * Y
  ])
])

[出力結果]

SummedOp([

])

SummedOp([

-1.0 * Y

])

1j * Z

120j * ZZ

III

TensoredOp([

ComposedOp([

SummedOp([

-1.0 * Z

]),

SummedOp([

-1.0 * X

])

]),

SummedOp([

-1.0 * Y

])

closer look

[編集内容(closer look)]
from qiskit.aqua.operators import I, X, Y, Z

# コメントアウトの箇所を変えながら確認.
# (1 * I, 2 * X, 3 * Y, 4 * Z)
# (X + Y, Y @ Z, Z ^ X)
# (2 * I + 3 * X - 4 * Y - 5 * Z, X ^ Y @ Z)

[編集内容(closer look)]

from qiskit.aqua.operators import I, X, Y, Z

# コメントアウトの箇所を変えながら確認.

# (1 * I, 2 * X, 3 * Y, 4 * Z)

# (X + Y, Y @ Z, Z ^ X)

# (2 * I + 3 * X - 4 * Y - 5 * Z, X ^ Y @ Z)

[出力結果]
(PauliOp(Pauli('I'), coeff=1.0),
 PauliOp(Pauli('X'), coeff=2.0),
 PauliOp(Pauli('Y'), coeff=3.0),
 PauliOp(Pauli('Z'), coeff=4.0))
(SummedOp([PauliOp(Pauli('X'), coeff=1.0), PauliOp(Pauli('Y'), coeff=1.0)], coeff=1.0, abelian=False),
 PauliOp(Pauli('X'), coeff=1j),
 PauliOp(Pauli('ZX'), coeff=1.0))
(SummedOp([PauliOp(Pauli('I'), coeff=2.0), PauliOp(Pauli('X'), coeff=3.0), PauliOp(Pauli('Y'), coeff=-4.0), PauliOp(Pauli('Z'), coeff=-5.0)], coeff=1.0, abelian=False),
 PauliOp(Pauli('XX'), coeff=1j))

[出力結果]

(PauliOp(Pauli('I'), coeff=1.0),

PauliOp(Pauli('X'), coeff=2.0),

PauliOp(Pauli('Y'), coeff=3.0),

PauliOp(Pauli('Z'), coeff=4.0))

(SummedOp([PauliOp(Pauli('X'), coeff=1.0), PauliOp(Pauli('Y'), coeff=1.0)], coeff=1.0, abelian=False),

PauliOp(Pauli('X'), coeff=1j),

PauliOp(Pauli('ZX'), coeff=1.0))

(SummedOp([PauliOp(Pauli('I'), coeff=2.0), PauliOp(Pauli('X'), coeff=3.0), PauliOp(Pauli('Y'), coeff=-4.0), PauliOp(Pauli('Z'), coeff=-5.0)], coeff=1.0, abelian=False),

PauliOp(Pauli('XX'), coeff=1j))

State Functions and Measurements

StateFn etc

[編集内容(StateFn etc)]
from qiskit.aqua.operators import (StateFn, Zero, One, Plus, Minus, H,
                                   DictStateFn, VectorStateFn, CircuitStateFn, OperatorStateFn)

# One qubit states.
print(Zero)
print(One)
print(Plus)
print(Minus)

# eval.
print(Zero.eval('0'))
print(Zero.eval('1'))
print(Zero.eval('2'))
print(One.eval('0'))
print(One.eval('1'))
print(One.eval('2'))
print(Plus.eval('0'))
print(Plus.eval('1'))
# print(Plus.eval('2')) # ValueError: invalid literal for int() with base 2: '2'
print(Minus.eval('0'))
print(Minus.eval('1'))
# print(Minus.eval('2')) # ValueError: invalid literal for int() with base 2: '2'

# adjoint.
# コメントアウトの箇所を変えながら確認.
# Zero.adjoint()  # equal to ~Zero
# One.adjoint()   # equal to ~One
# Plus.adjoint()
# Minus.adjoint()

[編集内容(StateFn etc)]

from qiskit.aqua.operators import (StateFn, Zero, One, Plus, Minus, H,

DictStateFn, VectorStateFn, CircuitStateFn, OperatorStateFn)

# One qubit states.

print(Zero)

print(One)

print(Plus)

print(Minus)

# eval.

print(Zero.eval('0'))

print(Zero.eval('1'))

print(Zero.eval('2'))

print(One.eval('0'))

print(One.eval('1'))

print(One.eval('2'))

print(Plus.eval('0'))

print(Plus.eval('1'))

# print(Plus.eval('2')) # ValueError: invalid literal for int() with base 2: '2'

print(Minus.eval('0'))

print(Minus.eval('1'))

# print(Minus.eval('2')) # ValueError: invalid literal for int() with base 2: '2'

# adjoint.

# コメントアウトの箇所を変えながら確認.

# Zero.adjoint() # equal to ~Zero

# One.adjoint() # equal to ~One

# Plus.adjoint()

# Minus.adjoint()

[出力結果]
DictStateFn({'0': 1})
DictStateFn({'1': 1})
CircuitStateFn(
     ┌───┐
q_0: ┤ H ├
     └───┘
)
CircuitStateFn(
     ┌───┐┌───┐
q_0: ┤ X ├┤ H ├
     └───┘└───┘
)
1.0
0.0
0.0
0.0
1.0
0.0
(0.7071067811865475+0j)
(0.7071067811865475+0j)
(0.7071067811865475-8.7e-17j)
(-0.7071067811865475+8.7e-17j)
DictStateFn({'0': 1}, coeff=1.0, is_measurement=True)
DictStateFn({'1': 1}, coeff=1.0, is_measurement=True)
CircuitStateFn(<qiskit.circuit.quantumcircuit.QuantumCircuit object at 0x7fc0b997f8d0>, coeff=1.0, is_measurement=True)
CircuitStateFn(<qiskit.circuit.quantumcircuit.QuantumCircuit object at 0x7fc0b9990690>, coeff=1.0, is_measurement=True)

[出力結果]

DictStateFn({'0': 1})

DictStateFn({'1': 1})

CircuitStateFn(

┌───┐

q_0: ┤ H ├

└───┘

)

CircuitStateFn(

┌───┐┌───┐

q_0: ┤ X ├┤ H ├

└───┘└───┘

)

1.0

0.0

1.0

0.0

(0.7071067811865475+0j)

(0.7071067811865475-8.7e-17j)

(-0.7071067811865475+8.7e-17j)

DictStateFn({'0': 1}, coeff=1.0, is_measurement=True)

DictStateFn({'1': 1}, coeff=1.0, is_measurement=True)

CircuitStateFn(<qiskit.circuit.quantumcircuit.QuantumCircuit object at 0x7fc0b997f8d0>, coeff=1.0, is_measurement=True)

CircuitStateFn(<qiskit.circuit.quantumcircuit.QuantumCircuit object at 0x7fc0b9990690>, coeff=1.0, is_measurement=True)

参照サイト

2021年4月3日

/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:17: DeprecationWarning: The QuantumCircuit.cu1 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.cp method instead, which acts identically.

/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:18: DeprecationWarning: The QuantumCircuit.cu3 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.cu method instead, where cu3(ϴ,φ,λ) = cu(ϴ,φ,λ,0).

q0_0: ─────■──────■─────────────────■──────────X─

┌────┴────┐ │U1(π/2) ┌────────┴────────┐ │

q0_1: ┤ RZ(π/2) ├─■────────┤ U3(π/2,π/2,π/2) ├─X─

└─────────┘ └─────────────────┘

Three-qubit gates

[編集内容(Three-qubit gates)]
q = QuantumRegister(3)
qc = QuantumCircuit(q)
qc.ccx(q[0], q[1], q[2])
qc.cswap(q[0], q[1], q[2])
qc.draw()

[編集内容(Three-qubit gates)]

q = QuantumRegister(3)

qc = QuantumCircuit(q)

qc.ccx(q[0], q[1], q[2])

qc.cswap(q[0], q[1], q[2])

qc.draw()

[出力結果]
q1_0: ──■───■─
        │   │ 
q1_1: ──■───X─
      ┌─┴─┐ │ 
q1_2: ┤ X ├─X─
      └───┘

[出力結果]

q1_0: ──■───■─

│ │

q1_1: ──■───X─

┌─┴─┐ │

q1_2: ┤ X ├─X─

└───┘

Non-unitary operations

Measurements

[編集内容(Measurements)]
q, c = QuantumRegister(1), ClassicalRegister(1)
qc = QuantumCircuit(q, c)
qc.x(q)
qc.y(q)
qc.z(q)
qc.h(q)
qc.measure(q, c)
qc.draw()

backend = BasicAer.get_backend('qasm_simulator')
job = execute(qc, backend, shots=1024)
job.result().get_counts(qc)

[編集内容(Measurements)]

q, c = QuantumRegister(1), ClassicalRegister(1)

qc = QuantumCircuit(q, c)

qc.x(q)

qc.y(q)

qc.z(q)

qc.h(q)

qc.measure(q, c)

qc.draw()

backend = BasicAer.get_backend('qasm_simulator')

job = execute(qc, backend, shots=1024)

job.result().get_counts(qc)

[出力結果]
※qc.draw() で 表示される出力.
      ┌───┐┌───┐┌───┐┌───┐┌─┐
q7_0: ┤ X ├┤ Y ├┤ Z ├┤ H ├┤M├
      └───┘└───┘└───┘└───┘└╥┘
c6: 1/═════════════════════╩═
                           0 

※job.result().get_counts(qc) で 表示される出力(実行するごとに変化する).
{'0': 520, '1': 504}

[出力結果]

※qc.draw() で表示される出力.

┌───┐┌───┐┌───┐┌───┐┌─┐

q7_0: ┤ X ├┤ Y ├┤ Z ├┤ H ├┤M├

└───┘└───┘└───┘└───┘└╥┘

c6: 1/═════════════════════╩═

※job.result().get_counts(qc) で表示される出力(実行するごとに変化する).

{'0': 520, '1': 504}

Reset

[編集内容(Reset)]
q, c = QuantumRegister(1), ClassicalRegister(1)
qc = QuantumCircuit(q, c)
qc.x(q)
qc.y(q)
qc.z(q)
qc.h(q)
qc.reset(q[0])
qc.measure(q, c)
qc.draw()

backend = BasicAer.get_backend('qasm_simulator')
job = execute(qc, backend, shots=1024)
job.result().get_counts(qc)

[編集内容(Reset)]

q, c = QuantumRegister(1), ClassicalRegister(1)

qc = QuantumCircuit(q, c)

qc.x(q)

qc.y(q)

qc.z(q)

qc.h(q)

qc.reset(q[0])

qc.measure(q, c)

qc.draw()

backend = BasicAer.get_backend('qasm_simulator')

job = execute(qc, backend, shots=1024)

job.result().get_counts(qc)

[出力結果]
※qc.draw() で 表示される出力.
       ┌───┐┌───┐┌───┐┌───┐     ┌─┐
q33_0: ┤ X ├┤ Y ├┤ Z ├┤ H ├─|0>─┤M├
       └───┘└───┘└───┘└───┘     └╥┘
c10: 1/══════════════════════════╩═
                                 0 

※job.result().get_counts(qc) で 表示される出力.
{'0': 1024}

[出力結果]

※qc.draw() で表示される出力.

┌───┐┌───┐┌───┐┌───┐ ┌─┐

q33_0: ┤ X ├┤ Y ├┤ Z ├┤ H ├─|0>─┤M├

└───┘└───┘└───┘└───┘ └╥┘

c10: 1/══════════════════════════╩═

※job.result().get_counts(qc) で表示される出力.

{'0': 1024}

Conditional operations

[編集内容(Conditional operations)]
q, c = QuantumRegister(1), ClassicalRegister(1)
qc = QuantumCircuit(q, c)
# qc.x(q).c_if(c, 0)
qc.x(q).c_if(c, 1)
qc.y(q)
qc.z(q)
qc.s(q)
qc.t(q)
qc.measure(q, c)
qc.draw()

backend = BasicAer.get_backend('qasm_simulator')
job = execute(qc, backend, shots=1024)
job.result().get_counts(qc)

[編集内容(Conditional operations)]

q, c = QuantumRegister(1), ClassicalRegister(1)

qc = QuantumCircuit(q, c)

# qc.x(q).c_if(c, 0)

qc.x(q).c_if(c, 1)

qc.y(q)

qc.z(q)

qc.s(q)

qc.t(q)

qc.measure(q, c)

qc.draw()

backend = BasicAer.get_backend('qasm_simulator')

job = execute(qc, backend, shots=1024)

job.result().get_counts(qc)

[出力結果]
①qc.x(q).c_if(c, 0) の 場合.
※qc.draw() で 表示される出力.
        ┌───┐ ┌───┐┌───┐┌───┐┌───┐┌─┐
q72_0: ─┤ X ├─┤ Y ├┤ Z ├┤ S ├┤ T ├┤M├
        └─╥─┘ └───┘└───┘└───┘└───┘└╥┘
       ┌──╨──┐                     ║ 
c18: 1/╡ = 0 ╞═════════════════════╩═
       └─────┘                     0 

※job.result().get_counts(qc) で 表示される出力.
{'0': 1024}

②qc.x(q).c_if(c, 1) の 場合.
※qc.draw() で 表示される出力.
        ┌───┐ ┌───┐┌───┐┌───┐┌───┐┌─┐
q91_0: ─┤ X ├─┤ Y ├┤ Z ├┤ S ├┤ T ├┤M├
        └─╥─┘ └───┘└───┘└───┘└───┘└╥┘
       ┌──╨──┐                     ║ 
c21: 1/╡ = 1 ╞═════════════════════╩═
       └─────┘                     0 

※job.result().get_counts(qc) で 表示される出力.
{'1': 1024}

[出力結果]

①qc.x(q).c_if(c, 0) の場合.

※qc.draw() で表示される出力.

┌───┐ ┌───┐┌───┐┌───┐┌───┐┌─┐

q72_0: ─┤ X ├─┤ Y ├┤ Z ├┤ S ├┤ T ├┤M├

└─╥─┘ └───┘└───┘└───┘└───┘└╥┘

┌──╨──┐ ║

c18: 1/╡ = 0 ╞═════════════════════╩═

└─────┘ 0

※job.result().get_counts(qc) で表示される出力.

{'0': 1024}

②qc.x(q).c_if(c, 1) の場合.

※qc.draw() で表示される出力.

┌───┐ ┌───┐┌───┐┌───┐┌───┐┌─┐

q91_0: ─┤ X ├─┤ Y ├┤ Z ├┤ S ├┤ T ├┤M├

└─╥─┘ └───┘└───┘└───┘└───┘└╥┘

┌──╨──┐ ║

c21: 1/╡ = 1 ╞═════════════════════╩═

└─────┘ 0

※job.result().get_counts(qc) で表示される出力.

{'1': 1024}

Arbitrary initialization

Initialize

# Initializing a ont-qubit quantum state
import math
desired_vector = [
    1 / math.sqrt(2) * complex(1, 0),
    1 / math.sqrt(2) * complex(0, 1)]

q = QuantumRegister(1)
qc = QuantumCircuit(q)
qc.initialize(desired_vector, [q[0]])
qc.draw()

# qc_state
backend = BasicAer.get_backend('statevector_simulator')
job = execute(qc, backend)
qc_state = job.result().get_statevector(qc)
qc_state

# state_fidelity
state_fidelity(desired_vector, qc_state)

# Initializing a ont-qubit quantum state

import math

desired_vector = [

1 / math.sqrt(2) * complex(1, 0),

1 / math.sqrt(2) * complex(0, 1)]

q = QuantumRegister(1)

qc = QuantumCircuit(q)

qc.initialize(desired_vector, [q[0]])

qc.draw()

# qc_state

backend = BasicAer.get_backend('statevector_simulator')

job = execute(qc, backend)

qc_state = job.result().get_statevector(qc)

qc_state

# state_fidelity

state_fidelity(desired_vector, qc_state)

[出力結果]
※qc.draw() で 表示される出力.
       ┌──────────────────────────────┐
q93_0: ┤ initialize(0.70711,0.70711j) ├
       └──────────────────────────────┘

※qc_state で 表示される出力.
array([7.07106781e-01+0.j        , 4.32978028e-17+0.70710678j])

※state_fidelity で 表示される出力.
0.9999999999999996

[出力結果]

※qc.draw() で表示される出力.

┌──────────────────────────────┐

q93_0: ┤ initialize(0.70711,0.70711j) ├

└──────────────────────────────┘

※qc_state で表示される出力.

array([7.07106781e-01+0.j , 4.32978028e-17+0.70710678j])

※state_fidelity で表示される出力.

0.9999999999999996

Initialize

# Initializing a two-qubit quantum state
import math
desired_vector = [
    1 / math.sqrt(2) * complex(1, 0),
    1 / math.sqrt(3) * complex(0, 1),
    1 / math.sqrt(12) * complex(1, 0),
    1 / math.sqrt(12) * complex(0, 1)]

q = QuantumRegister(2)
qc = QuantumCircuit(q)
qc.initialize(desired_vector, [q[0], q[1]])
qc.draw()

# qc_state
backend = BasicAer.get_backend('statevector_simulator')
job = execute(qc, backend)
qc_state = job.result().get_statevector(qc)
qc_state

# state_fidelity
state_fidelity(desired_vector, qc_state)

# Initializing a two-qubit quantum state

import math

desired_vector = [

1 / math.sqrt(2) * complex(1, 0),

1 / math.sqrt(3) * complex(0, 1),

1 / math.sqrt(12) * complex(1, 0),

1 / math.sqrt(12) * complex(0, 1)]

q = QuantumRegister(2)

qc = QuantumCircuit(q)

qc.initialize(desired_vector, [q[0], q[1]])

qc.draw()

# qc_state

backend = BasicAer.get_backend('statevector_simulator')

job = execute(qc, backend)

qc_state = job.result().get_statevector(qc)

qc_state

# state_fidelity

state_fidelity(desired_vector, qc_state)

[出力結果]
※qc.draw() で 表示される出力.
       ┌────────────────────────────────────────────────┐
q95_0: ┤0                                               ├
       │  initialize(0.70711,0.57735j,0.28868,0.28868j) │
q95_1: ┤1                                               ├
       └────────────────────────────────────────────────┘

※qc_state で 表示される出力.
array([7.07106781e-01+3.77249733e-18j, 3.11797104e-17+5.77350269e-01j,
       2.88675135e-01+1.68711209e-18j, 1.58101222e-17+2.88675135e-01j])

※state_fidelity で 表示される出力.
1.0

[出力結果]

※qc.draw() で表示される出力.

┌────────────────────────────────────────────────┐

q95_0: ┤0 ├

│ initialize(0.70711,0.57735j,0.28868,0.28868j) │

q95_1: ┤1 ├

└────────────────────────────────────────────────┘

※qc_state で表示される出力.

array([7.07106781e-01+3.77249733e-18j, 3.11797104e-17+5.77350269e-01j,

2.88675135e-01+1.68711209e-18j, 1.58101222e-17+2.88675135e-01j])

※state_fidelity で表示される出力.

1.0

参照サイト

Summary of Quantum Operations

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

Collecting qiskit

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Collecting websockets>=8

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Collecting yfinance

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

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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

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Collecting quandl

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

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Collecting cryptography>=1.3

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Collecting ntlm-auth>=1.0.2

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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

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

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 ├

└───┘

概要

感想

量子ビット状態を表現する(練習問題(パターン①))

量子ビット状態を表現する(練習問題(パターン②))

量子ビット状態を表現する(練習問題(パターン③))

量子ビット状態を表現する(練習問題(パターン④))

量子ビット状態を表現する(練習問題(パターン⑤))

参照サイト

概要

感想

QAOA(4頂点)

QAOA(6頂点)

QAOA(8頂点)

参照サイト

概要

感想

PrimitiveOps

参照サイト

概要

感想

Algebraic operations and predicates

PrimitiveOps

参照サイト

概要

感想

Algebraic operations and predicates

参照サイト

概要

感想

Operators

State Functions and Measurements

参照サイト

概要

感想

Summary of Quantum Operations

Non-unitary operations

Arbitrary initialization

参照サイト

概要

感想

量子ゲートのサンプル

参照サイト

概要

感想

Qiskit Visualizations

Single-Qubit Gates

参照サイト

概要

感想

Installing Qiskit

Circuit Basics

参照サイト