def test_CMod(): assert apply_operators(CMod(4, 2, 2)*Qubit(0,0,1,0,0,0,0,0)) ==\ Qubit(0,0,1,0,0,0,0,0) assert apply_operators(CMod(5, 5, 7)*Qubit(0,0,1,0,0,0,0,0,0,0)) ==\ Qubit(0,0,1,0,0,0,0,0,1,0) assert apply_operators(CMod(3, 2, 3)*Qubit(0,1,0,0,0,0)) ==\ Qubit(0,1,0,0,0,1)
def period_find(a, N): """Finds the period of a in modulo N arithmetic This is quantum part of Shor's algorithm.It takes two registers, puts first in superposition of states with Hadamards so: |k>|0> with k being all possible choices. It then does a controlled mod and a QFT to determine the order of a. """ epsilon = .5 #picks out t's such that maintains accuracy within epsilon t = int(2 * math.ceil(log(N, 2))) # make the first half of register be 0's |000...000> start = [0 for x in range(t)] #Put second half into superposition of states so we have |1>x|0> + |2>x|0> + ... |k>x>|0> + ... + |2**n-1>x|0> factor = 1 / sqrt(2**t) qubits = 0 for i in range(2**t): qbitArray = arr(i, t) + start qubits = qubits + Qubit(*qbitArray) circuit = (factor * qubits).expand() #Controlled second half of register so that we have: # |1>x|a**1 %N> + |2>x|a**2 %N> + ... + |k>x|a**k %N >+ ... + |2**n-1=k>x|a**k % n> circuit = CMod(t, a, N) * circuit #will measure first half of register giving one of the a**k%N's circuit = apply_operators(circuit) print "controlled Mod'd" for i in range(t): circuit = measure_partial_oneshot(circuit, i) # circuit = measure(i)*circuit # circuit = apply_operators(circuit) print "measured 1" #Now apply Inverse Quantum Fourier Transform on the second half of the register circuit = apply_operators(QFT(t, t * 2).decompose() * circuit, floatingPoint=True) print "QFT'd" for i in range(t): circuit = measure_partial_oneshot(circuit, i + t) # circuit = measure(i+t)*circuit # circuit = apply_operators(circuit) print circuit if isinstance(circuit, Qubit): register = circuit elif isinstance(circuit, Mul): register = circuit.args[-1] else: register = circuit.args[-1].args[-1] print register n = 1 answer = 0 for i in range(len(register) / 2): answer += n * register[i + t] n = n << 1 if answer == 0: raise OrderFindingException( "Order finder returned 0. Happens with chance %f" % epsilon) #turn answer into r using continued fractions g = getr(answer, 2**t, N) print g return g
def period_find(a, N): """Finds the period of a in modulo N arithmetic This is quantum part of Shor's algorithm.It takes two registers, puts first in superposition of states with Hadamards so: |k>|0> with k being all possible choices. It then does a controlled mod and a QFT to determine the order of a. """ epsilon = .5 #picks out t's such that maintains accuracy within epsilon t = int(2*math.ceil(log(N,2))) # make the first half of register be 0's |000...000> start = [0 for x in range(t)] #Put second half into superposition of states so we have |1>x|0> + |2>x|0> + ... |k>x>|0> + ... + |2**n-1>x|0> factor = 1/sqrt(2**t) qubits = 0 for i in range(2**t): qbitArray = arr(i, t) + start qubits = qubits + Qubit(*qbitArray) circuit = (factor*qubits).expand() #Controlled second half of register so that we have: # |1>x|a**1 %N> + |2>x|a**2 %N> + ... + |k>x|a**k %N >+ ... + |2**n-1=k>x|a**k % n> circuit = CMod(t,a,N)*circuit #will measure first half of register giving one of the a**k%N's circuit = apply_operators(circuit) print "controlled Mod'd" for i in range(t): circuit = measure_partial_oneshot(circuit, i) # circuit = measure(i)*circuit # circuit = apply_operators(circuit) print "measured 1" #Now apply Inverse Quantum Fourier Transform on the second half of the register circuit = apply_operators(QFT(t, t*2).decompose()*circuit, floatingPoint = True) print "QFT'd" for i in range(t): circuit = measure_partial_oneshot(circuit, i+t) # circuit = measure(i+t)*circuit # circuit = apply_operators(circuit) print circuit if isinstance(circuit, Qubit): register = circuit elif isinstance(circuit, Mul): register = circuit.args[-1] else: register = circuit.args[-1].args[-1] print register n = 1 answer = 0 for i in range(len(register)/2): answer += n*register[i+t] n = n<<1 if answer == 0: raise OrderFindingException("Order finder returned 0. Happens with chance %f" % epsilon) #turn answer into r using continued fractions g = getr(answer, 2**t, N) print g return g
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 apply_operators(QFT(0,3).decompose()*Qubit(0,0,0)).expand() ==\ apply_operators(HadamardGate(0)*HadamardGate(1)*HadamardGate(2)*Qubit(0,0,0)).expand()
def test_ugate(): """Test the general UGate.""" a,b,c,d = symbols('abcd') uMat = Matrix([[a,b],[c,d]]) # Test basic case where gate exists in 1-qubit space u1 = UGate((0,), uMat) assert represent(u1, nqubits = 1) == uMat assert apply_operators(u1*Qubit('0')) == a*Qubit('0') + c*Qubit('1') assert apply_operators(u1*Qubit('1')) == b*Qubit('0') + d*Qubit('1') # Test case where gate exists in a larger space u2 = UGate((1,), uMat) u2Rep = represent(u2, nqubits=2) for i in range(4): assert u2Rep*qubit_to_matrix(IntQubit(i,2)) ==\ qubit_to_matrix(apply_operators(u2*IntQubit(i,2)))
def test_cnot_gate(): """Test the CNOT gate.""" circuit = CNotGate(1,0) assert represent(circuit, nqubits=2) ==\ Matrix([[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]) circuit = circuit*Qubit('111') assert matrix_to_qubit(represent(circuit, nqubits=3)) ==\ apply_operators(circuit)
def test_ugate(): """Test the general UGate.""" a, b, c, d = symbols('abcd') uMat = Matrix([[a, b], [c, d]]) # Test basic case where gate exists in 1-qubit space u1 = UGate((0, ), uMat) assert represent(u1, nqubits=1) == uMat assert apply_operators(u1 * Qubit('0')) == a * Qubit('0') + c * Qubit('1') assert apply_operators(u1 * Qubit('1')) == b * Qubit('0') + d * Qubit('1') # Test case where gate exists in a larger space u2 = UGate((1, ), uMat) u2Rep = represent(u2, nqubits=2) for i in range(4): assert u2Rep*qubit_to_matrix(IntQubit(i,2)) ==\ qubit_to_matrix(apply_operators(u2*IntQubit(i,2)))
def test_cnot_gate(): """Test the CNOT gate.""" circuit = CNotGate(1, 0) assert represent(circuit, nqubits=2) ==\ Matrix([[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]) circuit = circuit * Qubit('111') assert matrix_to_qubit(represent(circuit, nqubits=3)) ==\ apply_operators(circuit)
def test_swap_gate(): """Test the SWAP gate.""" swap_gate_matrix = Matrix(((1,0,0,0),(0,0,1,0),(0,1,0,0),(0,0,0,1))) assert represent(SwapGate(1,0).decompose(), nqubits=2) == swap_gate_matrix assert apply_operators(SwapGate(1,3)*Qubit('0010')) == Qubit('1000') nqubits = 4 for i in range(nqubits): for j in range(i): assert represent(SwapGate(i,j), nqubits=nqubits) ==\ represent(SwapGate(i,j).decompose(), nqubits=nqubits)
def test_swap_gate(): """Test the SWAP gate.""" swap_gate_matrix = Matrix( ((1, 0, 0, 0), (0, 0, 1, 0), (0, 1, 0, 0), (0, 0, 0, 1))) assert represent(SwapGate(1, 0).decompose(), nqubits=2) == swap_gate_matrix assert apply_operators(SwapGate(1, 3) * Qubit('0010')) == Qubit('1000') nqubits = 4 for i in range(nqubits): for j in range(i): assert represent(SwapGate(i,j), nqubits=nqubits) ==\ represent(SwapGate(i,j).decompose(), nqubits=nqubits)
def test_ugate_cgate_combo(): """Test a UGate/CGate combination.""" a,b,c,d = symbols('abcd') uMat = Matrix([[a,b],[c,d]]) cMat = Matrix([[1,0,0,0],[0,1,0,0],[0,0,a,b],[0,0,c,d]]) # Test basic case where gate exists in 1-qubit space. u1 = UGate((0,), uMat) cu1 = CGate(1, u1) assert represent(cu1, nqubits = 2) == cMat assert apply_operators(cu1*Qubit('10')) == a*Qubit('10') + c*Qubit('11') assert apply_operators(cu1*Qubit('11')) == b*Qubit('10') + d*Qubit('11') assert apply_operators(cu1*Qubit('01')) == Qubit('01') assert apply_operators(cu1*Qubit('00')) == Qubit('00') # Test case where gate exists in a larger space. u2 = UGate((1,), uMat) u2Rep = represent(u2, nqubits=2) for i in range(4): assert u2Rep*qubit_to_matrix(IntQubit(i,2)) ==\ qubit_to_matrix(apply_operators(u2*IntQubit(i,2)))
def test_cgate(): """Test the general CGate.""" # Test single control functionality CNOTMatrix = Matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]]) assert represent(CGate(1, XGate(0)), nqubits=2) == CNOTMatrix # Test multiple control bit functionality ToffoliGate = CGate((1, 2), XGate(0)) assert represent(ToffoliGate, nqubits=3) == \ Matrix([[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],\ [0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1],\ [0,0,0,0,0,0,1,0]]) ToffoliGate = CGate((3, 0), XGate(1)) assert apply_operators(ToffoliGate*Qubit('1001')) == \ matrix_to_qubit(represent(ToffoliGate*Qubit('1001'), nqubits=4)) assert apply_operators(ToffoliGate*Qubit('0000')) == \ matrix_to_qubit(represent(ToffoliGate*Qubit('0000'), nqubits=4)) CYGate = CGate(1, YGate(0)) CYGate_matrix = Matrix( ((1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 0, -I), (0, 0, I, 0))) # Test 2 qubit controlled-Y gate decompose method. assert represent(CYGate.decompose(), nqubits=2) == CYGate_matrix CZGate = CGate(0, ZGate(1)) CZGate_matrix = Matrix( ((1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 1, 0), (0, 0, 0, -1))) assert apply_operators(CZGate * Qubit('11')) == -Qubit('11') assert matrix_to_qubit(represent(CZGate*Qubit('11'),nqubits=2)) ==\ -Qubit('11') # Test 2 qubit controlled-Z gate decompose method. assert represent(CZGate.decompose(), nqubits=2) == CZGate_matrix CPhaseGate = CGate(0, PhaseGate(1)) assert apply_operators(CPhaseGate*Qubit('11')) ==\ I*Qubit('11') assert matrix_to_qubit(represent(CPhaseGate*Qubit('11'), nqubits=2)) == \ I*Qubit('11')
def test_ugate_cgate_combo(): """Test a UGate/CGate combination.""" a, b, c, d = symbols('abcd') uMat = Matrix([[a, b], [c, d]]) cMat = Matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, a, b], [0, 0, c, d]]) # Test basic case where gate exists in 1-qubit space. u1 = UGate((0, ), uMat) cu1 = CGate(1, u1) assert represent(cu1, nqubits=2) == cMat assert apply_operators(cu1 * Qubit('10')) == a * Qubit('10') + c * Qubit('11') assert apply_operators(cu1 * Qubit('11')) == b * Qubit('10') + d * Qubit('11') assert apply_operators(cu1 * Qubit('01')) == Qubit('01') assert apply_operators(cu1 * Qubit('00')) == Qubit('00') # Test case where gate exists in a larger space. u2 = UGate((1, ), uMat) u2Rep = represent(u2, nqubits=2) for i in range(4): assert u2Rep*qubit_to_matrix(IntQubit(i,2)) ==\ qubit_to_matrix(apply_operators(u2*IntQubit(i,2)))
def test_cgate(): """Test the general CGate.""" # Test single control functionality CNOTMatrix = Matrix([[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]) assert represent(CGate(1, XGate(0)), nqubits=2) == CNOTMatrix # Test multiple control bit functionality ToffoliGate = CGate((1,2), XGate(0)) assert represent(ToffoliGate, nqubits=3) == \ Matrix([[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],\ [0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1],\ [0,0,0,0,0,0,1,0]]) ToffoliGate = CGate((3,0), XGate(1)) assert apply_operators(ToffoliGate*Qubit('1001')) == \ matrix_to_qubit(represent(ToffoliGate*Qubit('1001'), nqubits=4)) assert apply_operators(ToffoliGate*Qubit('0000')) == \ matrix_to_qubit(represent(ToffoliGate*Qubit('0000'), nqubits=4)) CYGate = CGate(1, YGate(0)) CYGate_matrix = Matrix(((1,0,0,0),(0,1,0,0),(0,0,0,-I),(0,0,I,0))) # Test 2 qubit controlled-Y gate decompose method. assert represent(CYGate.decompose(), nqubits=2) == CYGate_matrix CZGate = CGate(0, ZGate(1)) CZGate_matrix = Matrix(((1,0,0,0),(0,1,0,0),(0,0,1,0),(0,0,0,-1))) assert apply_operators(CZGate*Qubit('11')) == -Qubit('11') assert matrix_to_qubit(represent(CZGate*Qubit('11'),nqubits=2)) ==\ -Qubit('11') # Test 2 qubit controlled-Z gate decompose method. assert represent(CZGate.decompose(), nqubits=2) == CZGate_matrix CPhaseGate = CGate(0, PhaseGate(1)) assert apply_operators(CPhaseGate*Qubit('11')) ==\ I*Qubit('11') assert matrix_to_qubit(represent(CPhaseGate*Qubit('11'), nqubits=2)) == \ I*Qubit('11')
def _apply_operator_Qubit(self, qubits, **options): return apply_operators(self.decompose() * qubits)
def _apply_operator_Qubit(self, qubits, **options): return apply_operators(self.decompose()*qubits)