New!! 量子ゲートで７セグメントLEDを作る（②単一セグメント編）

𝑎(𝐴, 𝐵, 𝐶, 𝐷) = 𝐵𝐶'𝐷 + 𝐴'𝐶 + 𝐵'𝐶 + 𝐴𝐷' + 𝐵'𝐷'

segment a　=　C(B + A') + D'(A + B') + A'BD + AB'C'

#初期化
qc = QuantumCircuit(19)

#同時計算のため入力ビットを重ね合わせにする
qc.h(0)
qc.h(2)
qc.h(4)
qc.h(6)

#入力ビットの反転を用意しておく
NOT(0, 1) # A, A'
NOT(2, 3) # B, B'
NOT(4, 5) # C, C'
NOT(6, 7) # D, D'

#segment a　=　C(B + A') + D'(A + B') + A'BD + AB'C'
OR(2, 1, 8)
AND(4, 8, 9)

OR(0, 3, 10)
AND(7, 10, 11)

AND(1, 2, 12)
AND(12, 6, 13)

AND(0, 3, 14)
AND(14, 5, 15)

OR(9, 11, 16)
OR(16, 13, 17)
OR(17, 15, 18)

#計算
qc.measure_all()
backend = AerSimulator(method='matrix_product_state')
result = backend.run(qc, shots=500).result().get_counts()

#解の確認
pos = (0, 2, 4, 6, 18)
for i in range(2):
    for j in range(2):
        for k in range(2):
            for l in range(2):
                for r in result:
                    sel = ''.join(r[::-1][p] for p in pos)
                    if f'{i}{j}{k}{l}' == sel[:4]:
                        print(f'{sel} | {result[r]}/500')

segment b = A'B' + B'D' + A'C'D' + D(A ⊕ C)

#初期化
qc = QuantumCircuit(17)

#同時計算のため入力ビットを重ね合わせにする
qc.h(0)
qc.h(2)
qc.h(4)
qc.h(6)

#入力ビットの反転を用意しておく
NOT(0, 1) # A, A'
NOT(2, 3) # B, B'
NOT(4, 5) # C, C'
NOT(6, 7) # D, D'

#segment b = A'B' + B'D' + A'C'D' + D(A ⊕ C)
AND(1, 3, 8)

AND(3, 7, 9)

AND(1, 5, 10)
AND(10, 7, 11)

XOR(0, 4, 12)
AND(6, 12, 13)

OR(8, 9, 14)
OR(14, 11, 15)
OR(15, 13, 16)

#計算
qc.measure_all()
backend = AerSimulator(method='matrix_product_state')
result = backend.run(qc, shots=500).result().get_counts()

#解の確認
pos = (0, 2, 4, 6, 16)
for i in range(2):
    for j in range(2):
        for k in range(2):
            for l in range(2):
                for r in result:
                    sel = ''.join(r[::-1][p] for p in pos)
                    if f'{i}{j}{k}{l}' == sel[:4]:
                        print(f'{sel} | {result[r]}/500')

#初期化
qc = QuantumCircuit(15)

#segment c = (A ⊕ B) + A'C' + A'D + C'D
XOR(0, 2, 8)

AND(1, 5, 9)

AND(1, 6, 10)

AND(5, 6, 11)

OR(8, 9, 12)
OR(12, 10, 13)
OR(13, 11, 14)

#解の確認
pos = (0, 2, 4, 6, 14)

#初期化
qc = QuantumCircuit(20)

#segment d = AC' + A'B'D' + B(C ⊕ D) + C(B'D + A'D')
AND(0, 5, 8)

AND(1, 3, 9)
AND(9, 7, 10)

XOR(4, 6, 11)
AND(2, 11, 12)

AND(3, 6, 13)
AND(1, 7, 14)
OR(13, 14, 15)
AND(4, 15, 16)

OR(8, 10, 17)
OR(17, 12, 18)
OR(18, 16, 19)

#解の確認
pos = (0, 2, 4, 6, 19)

#初期化
qc = QuantumCircuit(13)

#segment e = A(B + C) + D'(B' + C)​
OR(2, 4, 8)
AND(0, 8, 9)

OR(3, 4, 10)
AND(7, 10, 11)

OR(9, 11, 12)

#解の確認
pos = (0, 2, 4, 6, 12)

#初期化
qc = QuantumCircuit(19)

#segment f = D'(A + B + C') + AD(B' + C) + A'BC'D
OR(0, 2, 8)
OR(8, 5, 9)
AND(7, 9, 10)

OR(3, 4, 11)
AND(0, 6, 12)
AND(11, 12, 13)

AND(1, 2, 14)
AND(14, 5, 15)
AND(15, 6, 16)

OR(10, 13, 17)
OR(17, 16, 18)

#解の確認
pos = (0, 2, 4, 6, 18)

#初期化
qc = QuantumCircuit(16)

#segment g = A(B' + D) + C(B' + D') + A'BC'
OR(3, 6, 8)
AND(0, 8, 9)

OR(3, 7, 10)
AND(4, 10, 11)

AND(1, 2, 12)
AND(12, 5, 13)

OR(9, 11, 14)
OR(14, 13, 15)

#解の確認
pos = (0, 2, 4, 6, 15)