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| from sympy.core.numbers import (I, pi) | |
| from sympy.core.symbol import Symbol | |
| from sympy.functions.elementary.exponential import exp | |
| from sympy.functions.elementary.miscellaneous import sqrt | |
| from sympy.matrices.dense import Matrix | |
| from sympy.physics.quantum.qft import QFT, IQFT, RkGate | |
| from sympy.physics.quantum.gate import (ZGate, SwapGate, HadamardGate, CGate, | |
| PhaseGate, TGate) | |
| from sympy.physics.quantum.qubit import Qubit | |
| from sympy.physics.quantum.qapply import qapply | |
| from sympy.physics.quantum.represent import represent | |
| from sympy.functions.elementary.complexes import sign | |
| def test_RkGate(): | |
| x = Symbol('x') | |
| assert RkGate(1, x).k == x | |
| assert RkGate(1, x).targets == (1,) | |
| assert RkGate(1, 1) == ZGate(1) | |
| assert RkGate(2, 2) == PhaseGate(2) | |
| assert RkGate(3, 3) == TGate(3) | |
| assert represent( | |
| RkGate(0, x), nqubits=1) == Matrix([[1, 0], [0, exp(sign(x)*2*pi*I/(2**abs(x)))]]) | |
| def test_quantum_fourier(): | |
| assert QFT(0, 3).decompose() == \ | |
| SwapGate(0, 2)*HadamardGate(0)*CGate((0,), PhaseGate(1)) * \ | |
| HadamardGate(1)*CGate((0,), TGate(2))*CGate((1,), PhaseGate(2)) * \ | |
| HadamardGate(2) | |
| assert IQFT(0, 3).decompose() == \ | |
| HadamardGate(2)*CGate((1,), RkGate(2, -2))*CGate((0,), RkGate(2, -3)) * \ | |
| HadamardGate(1)*CGate((0,), RkGate(1, -2))*HadamardGate(0)*SwapGate(0, 2) | |
| assert represent(QFT(0, 3), nqubits=3) == \ | |
| Matrix([[exp(2*pi*I/8)**(i*j % 8)/sqrt(8) for i in range(8)] for j in range(8)]) | |
| assert QFT(0, 4).decompose() # non-trivial decomposition | |
| assert qapply(QFT(0, 3).decompose()*Qubit(0, 0, 0)).expand() == qapply( | |
| HadamardGate(0)*HadamardGate(1)*HadamardGate(2)*Qubit(0, 0, 0) | |
| ).expand() | |
| def test_qft_represent(): | |
| c = QFT(0, 3) | |
| a = represent(c, nqubits=3) | |
| b = represent(c.decompose(), nqubits=3) | |
| assert a.evalf(n=10) == b.evalf(n=10) | |