def sq(a, b, c):
circ = Circuit(1)
if c != 0:
circ.Rz(c, 0)
if b != 0:
circ.Rx(b, 0)
if a != 0:
circ.Rz(a, 0)
return circ
def U(s, n_qubits):
c = Circuit(n_qubits)
for i in range(len(s)):
if s[i] == "X":
c.H(i)
elif s[i] == "Y":
c.Rx(i, 0.5)
elif s[i] == "Z":
pass
return c
def pauli_evolution(pauli: List[Tuple[int, str]], coeff: complex, circ: Circuit):
"""Appends the evolution circuit corresponding to a given Pauli tensor
Args:
pauli:
coeff (complex):
circ (Circuit):
"""
# set up the correct basis
all_qbs = list(zip(*pauli))[0]
for qb_idx, p in pauli:
if p == 'X':
circ.H(qb_idx)
elif p == 'Y':
# angles in half-turns
circ.Rx(qb_idx, 0.5)
# cnot cascade
cx_qb_pairs = list(zip(sorted(all_qbs)[:-1], sorted(all_qbs)[1:]))
for pair in cx_qb_pairs:
circ.CX(pair[0], pair[1])
# rotation (convert angle from radians to half-turns)
circ.Rz(all_qbs[-1], (2 * coeff.imag) / PI)
# reverse cascade and revert basis
cx_qb_pairs = list(zip(sorted(all_qbs)[:-1], sorted(all_qbs)[1:]))
for pair in reversed(cx_qb_pairs):
circ.CX(pair[0], pair[1])
all_qbs = list(zip(*pauli))[0]
for qb_idx, p in pauli:
if p == 'X':
circ.H(qb_idx)
elif p == 'Y':
circ.Rx(qb_idx, -0.5)
def measurement_circuits(hamiltonian, n_qubits):
all_circs = []
for pauli, _ in hamiltonian.terms.items():
if not pauli:
continue # Ignore the constant term
measure_circ = Circuit(n_qubits, n_qubits)
for qb, p in pauli:
if p == 'I':
continue # Discard I qubits
elif p == 'X':
measure_circ.H(qb)
elif p == 'Y':
measure_circ.Rx(0.5, qb)
measure_circ.Measure(qb, qb)
all_circs.append(measure_circ)
return all_circs
from pytket import Circuit
from pytket.extensions.qiskit import AerBackend
from itertools import combinations
from qiskit.providers.aer.noise import NoiseModel, depolarizing_error
# Quantum teleportation circuit:
c = Circuit()
alice = c.add_q_register("a", 2)
bob = c.add_q_register("b", 1)
data = c.add_c_register("d", 2)
final = c.add_c_register("f", 1)
# Start in an interesting state:
c.Rx(0.3, alice[0])
# Set up a Bell state between Alice and Bob:
c.H(alice[1]).CX(alice[1], bob[0])
# Measure Alice's qubits in the Bell basis:
c.CX(alice[0], alice[1]).H(alice[0])
c.Measure(alice[0], data[0])
c.Measure(alice[1], data[1])
# Correct Bob's qubit:
c.X(bob[0], condition_bits=[data[0], data[1]], condition_value=1)
c.X(bob[0], condition_bits=[data[0], data[1]], condition_value=3)
