def _double_controlled_modular_adder(constant: int, N: int, n: int, qft: Gate,
iqft: Gate) -> Gate:
ctrl_qreg = QuantumRegister(2, name='ctrl')
x_qreg = QuantumRegister(n, name='x')
g_qreg = QuantumRegister(n - 1 if n >= 2 else 1, name='g')
flag_qreg = QuantumRegister(1, name='flag')
circuit = QuantumCircuit(ctrl_qreg,
x_qreg,
g_qreg,
flag_qreg,
name=f'CC-MA_({constant})_Mod_{N}')
adder_regs = list(chain(flag_qreg, x_qreg))
circuit.append(double_controlled_comparator(N - constant, n),
circuit.qubits)
circuit.append(qft, x_qreg)
circuit.append(
phi_constant_adder(get_angles(constant, n)).control(1), adder_regs)
circuit.ccx(ctrl_qreg[0], ctrl_qreg[1], flag_qreg[0])
circuit.append(
phi_constant_adder(get_angles(N - constant, n)).control(1).inverse(),
adder_regs)
circuit.append(iqft, x_qreg)
circuit.append(double_controlled_comparator(constant, n), circuit.qubits)
return circuit.to_gate()
def _construct_circuit_with_semiclassical_QFT(self, a: int, N: int,
n: int) -> QuantumCircuit:
self._qft = QFT(n + 1, do_swaps=False).to_gate()
self._iqft = self._qft.inverse()
phi_add_N = phi_constant_adder(get_angles(N, n + 1))
self._iphi_add_N = phi_add_N.inverse()
self._c_phi_add_N = phi_add_N.control(1)
return super()._construct_circuit_with_semiclassical_QFT(a, N, n)
def _double_controlled_phi_add_mod_N(angles: Union[np.ndarray,
ParameterVector],
c_phi_add_N: Gate, iphi_add_N: Gate,
qft: Gate, iqft: Gate) -> QuantumCircuit:
ctrl_qreg = QuantumRegister(2, 'ctrl')
b_qreg = QuantumRegister(len(angles), 'b')
flag_qreg = QuantumRegister(1, 'flag')
circuit = QuantumCircuit(ctrl_qreg,
b_qreg,
flag_qreg,
name='ccphi_add_a_mod_N')
cc_phi_add_a = phi_constant_adder(angles).control(2)
cc_iphi_add_a = cc_phi_add_a.inverse()
circuit.append(cc_phi_add_a, [*ctrl_qreg, *b_qreg])
circuit.append(iphi_add_N, b_qreg)
circuit.append(iqft, b_qreg)
circuit.cx(b_qreg[-1], flag_qreg[0])
circuit.append(qft, b_qreg)
circuit.append(c_phi_add_N, [*flag_qreg, *b_qreg])
circuit.append(cc_iphi_add_a, [*ctrl_qreg, *b_qreg])
circuit.append(iqft, b_qreg)
circuit.x(b_qreg[-1])
circuit.cx(b_qreg[-1], flag_qreg[0])
circuit.x(b_qreg[-1])
circuit.append(qft, b_qreg)
circuit.append(cc_phi_add_a, [*ctrl_qreg, *b_qreg])
return circuit
def modular_exponentiation_gate(constant: int, N: int, n: int) -> Instruction:
up_qreg = QuantumRegister(2 * n, name='up')
down_qreg = QuantumRegister(n, name='down')
aux_qreg = QuantumRegister(n + 2, name='aux')
circuit = QuantumCircuit(up_qreg,
down_qreg,
aux_qreg,
name=f'{constant}^x mod {N}')
qft = QFT(n + 1, do_swaps=False).to_gate()
iqft = qft.inverse()
phi_add_N = phi_constant_adder(get_angles(N, n + 1))
iphi_add_N = phi_add_N.inverse()
c_phi_add_N = phi_add_N.control(1)
for i in range(2 * n):
partial_constant = pow(constant, pow(2, i), mod=N)
modulo_multiplier = controlled_modular_multiplication_gate(
partial_constant, N, n, c_phi_add_N, iphi_add_N, qft, iqft)
circuit.append(modulo_multiplier, [up_qreg[i], *down_qreg, *aux_qreg])
return circuit.to_instruction()