|
1 |
| -import numpy as np |
2 |
| -from qutip import Qobj, tensor, basis, sigmax, sigmay, sigmaz |
3 |
| -from qutip_qip.operations import Gate |
4 | 1 | from qutip_qip.circuit import QubitCircuit
|
5 |
| - |
6 |
| -__all__ = ["ShorCode"] |
7 |
| - |
| 2 | +from qutip_qip.algorithms import BitFlipCode |
| 3 | +from qutip_qip.algorithms import PhaseFlipCode |
8 | 4 |
|
9 | 5 | class ShorCode:
|
10 | 6 | """
|
11 |
| - Implementation of the 9-qubit Shor code. |
12 |
| -
|
13 |
| - The Shor code protects against arbitrary single-qubit errors by combining |
14 |
| - the 3-qubit phase-flip code with the 3-qubit bit-flip code. |
15 |
| -
|
16 |
| - The logical states are encoded as: |
17 |
| - |0⟩ → (|000⟩ + |111⟩)(|000⟩ + |111⟩)(|000⟩ + |111⟩) / 2√2 |
18 |
| - |1⟩ → (|000⟩ - |111⟩)(|000⟩ - |111⟩)(|000⟩ - |111⟩) / 2√2 |
19 |
| -
|
20 |
| - This encoding allows correction of any single-qubit error (bit-flip, phase-flip, |
21 |
| - or both) on any of the 9 physical qubits. |
| 7 | + Constructs the 9-qubit Shor code encoding circuit using BitFlipCode and PhaseFlipCode. |
22 | 8 | """
|
23 | 9 |
|
24 |
| - @staticmethod |
25 |
| - def encode_circuit(): |
| 10 | + def __init__(self): |
| 11 | + # Logical qubit -> Phase protection: [0, 3, 6] (1 qubit to 3) |
| 12 | + # Each → BitFlipCode: [0,1,2], [3,4,5], [6,7,8] |
| 13 | + self.data_qubits = list(range(9)) |
| 14 | + self.phase_code = PhaseFlipCode(data_qubits=[0, 3, 6], syndrome_qubits=[]) # No ancillas for encoding |
| 15 | + self.bit_blocks = [ |
| 16 | + BitFlipCode(data_qubits=[0, 1, 2], syndrome_qubits=[]), |
| 17 | + BitFlipCode(data_qubits=[3, 4, 5], syndrome_qubits=[]), |
| 18 | + BitFlipCode(data_qubits=[6, 7, 8], syndrome_qubits=[]) |
| 19 | + ] |
| 20 | + self.n_qubits = 9 # Encoding only requires 9 qubits |
| 21 | + |
| 22 | + def encode_circuit(self): |
26 | 23 | """
|
27 |
| - Create a circuit for encoding a single qubit into the 9-qubit Shor code. |
28 |
| -
|
29 |
| - The encoding process: |
30 |
| - 1. Apply phase-flip encoding to the input (creating |+++⟩ or |---⟩) |
31 |
| - 2. Apply bit-flip encoding to each of the three qubits |
| 24 | + Construct the 9-qubit Shor code encoding circuit. |
32 | 25 |
|
33 | 26 | Returns
|
34 | 27 | -------
|
35 |
| - qc : instance of QubitCircuit |
36 |
| - Encoding circuit for the Shor code. |
| 28 | + QubitCircuit |
| 29 | + Circuit that encodes one logical qubit into the Shor code. |
37 | 30 | """
|
38 |
| - qc = QubitCircuit(9) |
39 |
| - |
40 |
| - # Step 1: Phase-flip encoding on the first qubit |
41 |
| - # Apply Hadamard to the input qubit |
42 |
| - qc.add_gate("SNOT", targets=0) |
43 |
| - |
44 |
| - # Create the GHZ-like state by using CNOTs |
45 |
| - qc.add_gate("CNOT", controls=0, targets=3) |
46 |
| - qc.add_gate("CNOT", controls=0, targets=6) |
47 |
| - |
48 |
| - # Apply Hadamard to all three qubits |
49 |
| - qc.add_gate("SNOT", targets=0) |
50 |
| - qc.add_gate("SNOT", targets=3) |
51 |
| - qc.add_gate("SNOT", targets=6) |
52 |
| - |
53 |
| - # Step 2: Bit-flip encoding for each of the three blocks |
54 |
| - # First block: qubits 0,1,2 |
55 |
| - qc.add_gate("CNOT", controls=0, targets=1) |
56 |
| - qc.add_gate("CNOT", controls=0, targets=2) |
| 31 | + qc = QubitCircuit(self.n_qubits) |
57 | 32 |
|
58 |
| - # Second block: qubits 3,4,5 |
59 |
| - qc.add_gate("CNOT", controls=3, targets=4) |
60 |
| - qc.add_gate("CNOT", controls=3, targets=5) |
| 33 | + phase_encode = self.phase_code.encode_circuit() |
| 34 | + qc.gates.extend(phase_encode.gates) |
61 | 35 |
|
62 |
| - # Third block: qubits 6,7,8 |
63 |
| - qc.add_gate("CNOT", controls=6, targets=7) |
64 |
| - qc.add_gate("CNOT", controls=6, targets=8) |
| 36 | + for bit_code in self.bit_blocks: |
| 37 | + bit_encode = bit_code.encode_circuit() |
| 38 | + qc.gates.extend(bit_encode.gates) |
65 | 39 |
|
66 | 40 | return qc
|
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