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shors_code.py
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shors_code.py
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""" Shor's code is a stabilizer code for quantum error correction.
It uses 9 qubits to encode 1 logic qubit and is able to correct
at most one bit flip and one sign flip or their combination.
(0, 0): ───@───@───H───@───@───@───@───X───H───@───@───X───M───
│ │ │ │ │ │ │ │ │ │
(0, 1): ───┼───┼───────X───┼───X───┼───@───────┼───┼───┼───M───
│ │ │ │ │ │ │ │
(0, 2): ───┼───┼───────────X───────X───@───────┼───┼───┼───M───
│ │ │ │ │
(0, 3): ───X───┼───H───@───@───@───@───X───H───X───┼───@───M───
│ │ │ │ │ │ │ │
(0, 4): ───────┼───────X───┼───X───┼───@───────────┼───┼───M───
│ │ │ │ │ │
(0, 5): ───────┼───────────X───────X───@───────────┼───┼───M───
│ │ │
(0, 6): ───────X───H───@───@───@───@───X───H───────X───@───M───
│ │ │ │ │
(0, 7): ───────────────X───┼───X───┼───@───────────────────M───
│ │ │
(0, 8): ───────────────────X───────X───@───────────────────M───
reference: P. W. Shor, Phys. Rev. A, 52, R2493 (1995).
"""
import random
import cirq
class OneQubitShorsCode:
def __init__(self):
self.num_physical_qubits = 9
self.physical_qubits = cirq.LineQubit.range(self.num_physical_qubits)
def encode(self):
yield cirq.ops.Moment(
[cirq.CNOT(self.physical_qubits[0], self.physical_qubits[3])])
yield cirq.ops.Moment(
[cirq.CNOT(self.physical_qubits[0], self.physical_qubits[6])])
yield cirq.ops.Moment([
cirq.H(self.physical_qubits[0]),
cirq.H(self.physical_qubits[3]),
cirq.H(self.physical_qubits[6])
])
yield cirq.ops.Moment([
cirq.CNOT(self.physical_qubits[0], self.physical_qubits[1]),
cirq.CNOT(self.physical_qubits[3], self.physical_qubits[4]),
cirq.CNOT(self.physical_qubits[6], self.physical_qubits[7])
])
yield cirq.ops.Moment([
cirq.CNOT(self.physical_qubits[0], self.physical_qubits[2]),
cirq.CNOT(self.physical_qubits[3], self.physical_qubits[5]),
cirq.CNOT(self.physical_qubits[6], self.physical_qubits[8])
])
def apply_gate(self, gate: cirq.Gate, pos: int):
if pos > self.num_physical_qubits:
raise IndexError
else:
return gate(self.physical_qubits[pos])
def correct(self):
yield cirq.ops.Moment([
cirq.CNOT(self.physical_qubits[0], self.physical_qubits[1]),
cirq.CNOT(self.physical_qubits[3], self.physical_qubits[4]),
cirq.CNOT(self.physical_qubits[6], self.physical_qubits[7])
])
yield cirq.ops.Moment([
cirq.CNOT(self.physical_qubits[0], self.physical_qubits[2]),
cirq.CNOT(self.physical_qubits[3], self.physical_qubits[5]),
cirq.CNOT(self.physical_qubits[6], self.physical_qubits[8])
])
yield cirq.ops.Moment([
cirq.CCNOT(self.physical_qubits[1], self.physical_qubits[2],
self.physical_qubits[0]),
cirq.CCNOT(self.physical_qubits[4], self.physical_qubits[5],
self.physical_qubits[3]),
cirq.CCNOT(self.physical_qubits[7], self.physical_qubits[8],
self.physical_qubits[6])
])
yield cirq.ops.Moment([
cirq.H(self.physical_qubits[0]),
cirq.H(self.physical_qubits[3]),
cirq.H(self.physical_qubits[6])
])
yield cirq.ops.Moment(
[cirq.CNOT(self.physical_qubits[0], self.physical_qubits[3])])
yield cirq.ops.Moment(
[cirq.CNOT(self.physical_qubits[0], self.physical_qubits[6])])
yield cirq.ops.Moment([
cirq.CCNOT(self.physical_qubits[3], self.physical_qubits[6],
self.physical_qubits[0])
])
if __name__ == '__main__':
# coverage: ignore
# create circuit with 9 physical qubits
code = OneQubitShorsCode()
circuit = cirq.Circuit(code.apply_gate(cirq.X**(1 / 4), 0))
print(cirq.dirac_notation(circuit.final_state_vector(initial_state=0)))
circuit += cirq.Circuit(code.encode())
print(cirq.dirac_notation(circuit.final_state_vector(initial_state=0)))
# create error
circuit += cirq.Circuit(
code.apply_gate(cirq.X, random.randint(0,
code.num_physical_qubits - 1)))
print(cirq.dirac_notation(circuit.final_state_vector(initial_state=0)))
# correct error and decode
circuit += cirq.Circuit(code.correct())
print(cirq.dirac_notation(circuit.final_state_vector(initial_state=0)))