示例#1
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def test_superposition_basis():
    nbits = 2
    first_half_state = IntQubit(0, nbits)/2 + IntQubit(1, 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, nbits) + (1/sqrt(8))*IntQubit(1, 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)
示例#2
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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)
示例#3
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def main():
    print()
    print('Demonstration of Grover\'s Algorithm')
    print('The OracleGate or V Gate carries the unknown function f(x)')
    print(
        '> V|x> = ((-1)^f(x))|x> where f(x) = 1 when x = a (True in our case)')
    print('> and 0 (False in our case) otherwise')
    print()

    nqubits = 2
    print('nqubits = ', nqubits)

    v = OracleGate(nqubits, black_box)
    print('Oracle or v = OracleGate(%r, black_box)' % nqubits)
    print()

    psi = superposition_basis(nqubits)
    print('psi:')
    pprint(psi)
    demo_vgate_app(v)
    print('qapply(v*psi)')
    pprint(qapply(v * psi))
    print()

    w = WGate(nqubits)
    print('WGate or w = WGate(%r)' % nqubits)
    print('On a 2 Qubit system like psi, 1 iteration is enough to yield |1>')
    print('qapply(w*v*psi)')
    pprint(qapply(w * v * psi))
    print()

    nqubits = 3
    print('On a 3 Qubit system, it requires 2 iterations to achieve')
    print('|1> with high enough probability')
    psi = superposition_basis(nqubits)
    print('psi:')
    pprint(psi)

    v = OracleGate(nqubits, black_box)
    print('Oracle or v = OracleGate(%r, black_box)' % nqubits)
    print()

    print('iter1 = grover.grover_iteration(psi, v)')
    iter1 = qapply(grover_iteration(psi, v))
    pprint(iter1)
    print()

    print('iter2 = grover.grover_iteration(iter1, v)')
    iter2 = qapply(grover_iteration(iter1, v))
    pprint(iter2)
    print()
示例#4
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def main():
    print()
    print("Demonstration of Grover's Algorithm")
    print("The OracleGate or V Gate carries the unknown function f(x)")
    print(
        "> V|x> = ((-1)^f(x))|x> where f(x) = 1 when x = a (True in our case)")
    print("> and 0 (False in our case) otherwise")
    print()

    nqubits = 2
    print("nqubits = ", nqubits)

    v = OracleGate(nqubits, black_box)
    print("Oracle or v = OracleGate(%r, black_box)" % nqubits)
    print()

    psi = superposition_basis(nqubits)
    print("psi:")
    pprint(psi)
    demo_vgate_app(v)
    print("qapply(v*psi)")
    pprint(qapply(v * psi))
    print()

    w = WGate(nqubits)
    print("WGate or w = WGate(%r)" % nqubits)
    print("On a 2 Qubit system like psi, 1 iteration is enough to yield |1>")
    print("qapply(w*v*psi)")
    pprint(qapply(w * v * psi))
    print()

    nqubits = 3
    print("On a 3 Qubit system, it requires 2 iterations to achieve")
    print("|1> with high enough probability")
    psi = superposition_basis(nqubits)
    print("psi:")
    pprint(psi)

    v = OracleGate(nqubits, black_box)
    print("Oracle or v = OracleGate(%r, black_box)" % nqubits)
    print()

    print("iter1 = grover.grover_iteration(psi, v)")
    iter1 = qapply(grover_iteration(psi, v))
    pprint(iter1)
    print()

    print("iter2 = grover.grover_iteration(iter1, v)")
    iter2 = qapply(grover_iteration(iter1, v))
    pprint(iter2)
    print()
示例#5
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def main():
    print
    print "Demonstration of Grover's Algorithm"
    print "The OracleGate or V Gate carries the unknown function f(x)"
    print "> V|x> = ((-1)^f(x))|x> where f(x) = 1 when x = a (True in our case)"
    print "> and 0 (False in our case) otherwise"
    print

    nqubits = 2
    print "nqubits = ", nqubits

    v = OracleGate(nqubits, black_box)
    print "Oracle or v = OracleGate(%r, black_box)" % nqubits
    print

    psi = superposition_basis(nqubits)
    print "psi:"
    pprint(psi)
    demo_vgate_app(v)
    print "qapply(v*psi)"
    pprint(qapply(v * psi))
    print

    w = WGate(nqubits)
    print "WGate or w = WGate(%r)" % nqubits
    print "On a 2 Qubit system like psi, 1 iteration is enough to yield |1>"
    print "qapply(w*v*psi)"
    pprint(qapply(w * v * psi))
    print

    nqubits = 3
    print "On a 3 Qubit system, it requires 2 iterations to achieve"
    print "|1> with high enough probability"
    psi = superposition_basis(nqubits)
    print "psi:"
    pprint(psi)

    v = OracleGate(nqubits, black_box)
    print "Oracle or v = OracleGate(%r, black_box)" % nqubits
    print

    print "iter1 = grover.grover_iteration(psi, v)"
    iter1 = qapply(grover_iteration(psi, v))
    pprint(iter1)
    print

    print "iter2 = grover.grover_iteration(iter1, v)"
    iter2 = qapply(grover_iteration(iter1, v))
    pprint(iter2)
    print
示例#6
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def main():
    print()
    print('Demonstration of Grover\'s Algorithm')
    print('The OracleGate or V Gate carries the unknown function f(x)')
    print('> V|x> = ((-1)^f(x))|x> where f(x) = 1 when x = a (True in our case)')
    print('> and 0 (False in our case) otherwise')
    print()

    nqubits = 2
    print('nqubits = ', nqubits)

    v = OracleGate(nqubits, black_box)
    print('Oracle or v = OracleGate(%r, black_box)' % nqubits)
    print()

    psi = superposition_basis(nqubits)
    print('psi:')
    pprint(psi)
    demo_vgate_app(v)
    print('qapply(v*psi)')
    pprint(qapply(v*psi))
    print()

    w = WGate(nqubits)
    print('WGate or w = WGate(%r)' % nqubits)
    print('On a 2 Qubit system like psi, 1 iteration is enough to yield |1>')
    print('qapply(w*v*psi)')
    pprint(qapply(w*v*psi))
    print()

    nqubits = 3
    print('On a 3 Qubit system, it requires 2 iterations to achieve')
    print('|1> with high enough probability')
    psi = superposition_basis(nqubits)
    print('psi:')
    pprint(psi)

    v = OracleGate(nqubits, black_box)
    print('Oracle or v = OracleGate(%r, black_box)' % nqubits)
    print()

    print('iter1 = grover.grover_iteration(psi, v)')
    iter1 = qapply(grover_iteration(psi, v))
    pprint(iter1)
    print()

    print('iter2 = grover.grover_iteration(iter1, v)')
    iter2 = qapply(grover_iteration(iter1, v))
    pprint(iter2)
    print()
示例#7
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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
示例#8
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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)
    assert qapply(WGate(nqubits)*IntQubit(1, nqubits)) == expected
示例#9
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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)
示例#10
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def test_grover():
    nqubits = 2
    assert apply_grover(return_one_on_one, nqubits) == IntQubit(1, 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)
示例#11
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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
示例#12
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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
示例#13
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def main():
    psi = superposition_basis(2)
    psi

    # Dense coding demo:

    # Assume Alice has the left QBit in psi
    print(
        "An even superposition of 2 qubits.  Assume Alice has the left QBit.")
    pprint(psi)

    # The corresponding gates applied to Alice's QBit are:
    # Identity Gate (1), Not Gate (X), Z Gate (Z), Z Gate and Not Gate (ZX)
    # Then there's the controlled not gate (with Alice's as control):CNOT(1, 0)
    # And the Hadamard gate applied to Alice's Qbit: H(1)

    # To Send Bob the message |0>|0>
    print("To Send Bob the message |00>.")
    circuit = H(1) * CNOT(1, 0)
    result = qapply(circuit * psi)
    result
    pprint(result)

    # To send Bob the message |0>|1>
    print("To Send Bob the message |01>.")
    circuit = H(1) * CNOT(1, 0) * X(1)
    result = qapply(circuit * psi)
    result
    pprint(result)

    # To send Bob the message |1>|0>
    print("To Send Bob the message |10>.")
    circuit = H(1) * CNOT(1, 0) * Z(1)
    result = qapply(circuit * psi)
    result
    pprint(result)

    # To send Bob the message |1>|1>
    print("To Send Bob the message |11>.")
    circuit = H(1) * CNOT(1, 0) * Z(1) * X(1)
    result = qapply(circuit * psi)
    result
    pprint(result)
示例#14
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def main():
    psi = superposition_basis(2)
    psi

    # Dense coding demo:

    # Assume Alice has the left QBit in psi
    print "An even superposition of 2 qubits.  Assume Alice has the left QBit."
    pprint(psi)

    # The corresponding gates applied to Alice's QBit are:
    # Identity Gate (1), Not Gate (X), Z Gate (Z), Z Gate and Not Gate (ZX)
    # Then there's the controlled not gate (with Alice's as control):CNOT(1, 0)
    # And the Hadamard gate applied to Alice's Qbit: H(1)

    # To Send Bob the message |0>|0>
    print "To Send Bob the message |00>."
    circuit = H(1)*CNOT(1, 0)
    result = qapply(circuit*psi)
    result
    pprint(result)

    # To send Bob the message |0>|1>
    print "To Send Bob the message |01>."
    circuit = H(1)*CNOT(1, 0)*X(1)
    result = qapply(circuit*psi)
    result
    pprint(result)

    # To send Bob the message |1>|0>
    print "To Send Bob the message |10>."
    circuit = H(1)*CNOT(1, 0)*Z(1)
    result = qapply(circuit*psi)
    result
    pprint(result)

    # To send Bob the message |1>|1>
    print "To Send Bob the message |11>."
    circuit = H(1)*CNOT(1, 0)*Z(1)*X(1)
    result = qapply(circuit*psi)
    result
    pprint(result)
示例#15
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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
示例#16
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def test_g_bbht_search(nqubits=5):
    basis_states = superposition_basis(nqubits)
    oracle = random_oracle(nqubits, min_img=5, max_img=15, q_type="bin")
    x = g_bbht_search(basis_states, oracle)[0]
    assert oracle.search_function(x) == 1
示例#17
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 def superposition(self):
     return superposition_basis(self.qubit.nqubits)
示例#18
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def test_grover_iteration_1():
    numqubits = 2
    basis_states = superposition_basis(numqubits)
    v = OracleGate(numqubits, return_one_on_one)
    expected = IntQubit(1, numqubits)
    assert qapply(grover_iteration(basis_states, v)) == expected