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| from sympy.functions.elementary.miscellaneous import sqrt | |
| from sympy.matrices.dense import Matrix | |
| from sympy.physics.quantum.represent import represent | |
| from sympy.physics.quantum.qapply import qapply | |
| from sympy.physics.quantum.qubit import IntQubit | |
| from sympy.physics.quantum.grover import (apply_grover, superposition_basis, | |
| OracleGate, grover_iteration, WGate) | |
| def return_one_on_two(qubits): | |
| return qubits == IntQubit(2, qubits.nqubits) | |
| def return_one_on_one(qubits): | |
| return qubits == IntQubit(1, nqubits=qubits.nqubits) | |
| def test_superposition_basis(): | |
| nbits = 2 | |
| first_half_state = IntQubit(0, nqubits=nbits)/2 + IntQubit(1, nqubits=nbits)/2 | |
| second_half_state = IntQubit(2, nbits)/2 + IntQubit(3, nbits)/2 | |
| assert first_half_state + second_half_state == superposition_basis(nbits) | |
| nbits = 3 | |
| firstq = (1/sqrt(8))*IntQubit(0, nqubits=nbits) + (1/sqrt(8))*IntQubit(1, nqubits=nbits) | |
| secondq = (1/sqrt(8))*IntQubit(2, nbits) + (1/sqrt(8))*IntQubit(3, nbits) | |
| thirdq = (1/sqrt(8))*IntQubit(4, nbits) + (1/sqrt(8))*IntQubit(5, nbits) | |
| fourthq = (1/sqrt(8))*IntQubit(6, nbits) + (1/sqrt(8))*IntQubit(7, nbits) | |
| assert firstq + secondq + thirdq + fourthq == superposition_basis(nbits) | |
| def test_OracleGate(): | |
| v = OracleGate(1, lambda qubits: qubits == IntQubit(0)) | |
| assert qapply(v*IntQubit(0)) == -IntQubit(0) | |
| assert qapply(v*IntQubit(1)) == IntQubit(1) | |
| nbits = 2 | |
| v = OracleGate(2, return_one_on_two) | |
| assert qapply(v*IntQubit(0, nbits)) == IntQubit(0, nqubits=nbits) | |
| assert qapply(v*IntQubit(1, nbits)) == IntQubit(1, nqubits=nbits) | |
| assert qapply(v*IntQubit(2, nbits)) == -IntQubit(2, nbits) | |
| assert qapply(v*IntQubit(3, nbits)) == IntQubit(3, nbits) | |
| assert represent(OracleGate(1, lambda qubits: qubits == IntQubit(0)), nqubits=1) == \ | |
| Matrix([[-1, 0], [0, 1]]) | |
| assert represent(v, nqubits=2) == Matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, -1, 0], [0, 0, 0, 1]]) | |
| def test_WGate(): | |
| nqubits = 2 | |
| basis_states = superposition_basis(nqubits) | |
| assert qapply(WGate(nqubits)*basis_states) == basis_states | |
| expected = ((2/sqrt(pow(2, nqubits)))*basis_states) - IntQubit(1, nqubits=nqubits) | |
| assert qapply(WGate(nqubits)*IntQubit(1, nqubits=nqubits)) == expected | |
| def test_grover_iteration_1(): | |
| numqubits = 2 | |
| basis_states = superposition_basis(numqubits) | |
| v = OracleGate(numqubits, return_one_on_one) | |
| expected = IntQubit(1, nqubits=numqubits) | |
| assert qapply(grover_iteration(basis_states, v)) == expected | |
| def test_grover_iteration_2(): | |
| numqubits = 4 | |
| basis_states = superposition_basis(numqubits) | |
| v = OracleGate(numqubits, return_one_on_two) | |
| # After (pi/4)sqrt(pow(2, n)), IntQubit(2) should have highest prob | |
| # In this case, after around pi times (3 or 4) | |
| iterated = grover_iteration(basis_states, v) | |
| iterated = qapply(iterated) | |
| iterated = grover_iteration(iterated, v) | |
| iterated = qapply(iterated) | |
| iterated = grover_iteration(iterated, v) | |
| iterated = qapply(iterated) | |
| # In this case, probability was highest after 3 iterations | |
| # Probability of Qubit('0010') was 251/256 (3) vs 781/1024 (4) | |
| # Ask about measurement | |
| expected = (-13*basis_states)/64 + 264*IntQubit(2, numqubits)/256 | |
| assert qapply(expected) == iterated | |
| def test_grover(): | |
| nqubits = 2 | |
| assert apply_grover(return_one_on_one, nqubits) == IntQubit(1, nqubits=nqubits) | |
| nqubits = 4 | |
| basis_states = superposition_basis(nqubits) | |
| expected = (-13*basis_states)/64 + 264*IntQubit(2, nqubits)/256 | |
| assert apply_grover(return_one_on_two, 4) == qapply(expected) | |