Overview

PyQecc mainly provide quantum error correction code (QECC) simulator.

• Installation (This page)
• Quick start (This page)
• Features
• Source code
• PyPI

Installation

pip install pyqecc

In some cases, installation required setting for --proxy, --user or sudo. PyQecc is written by python3.

Quick start

We explain the tutorial usage. Please prepare the new .py file (e.g. test.py). Next we copy and paste following code;

from pyqecc import FiveCode, dec_sim

my_code = FiveCode(mode="ML")
print(my_code)
dec_sim(my_code)

The steps of evalutation for decoding performance are Import the PyQecc., Create the instance for QECC., Prepare the decoding simulator, Start the decoding simulation, and Confirm the decoding result.

1. Import the PyQecc.

from pyqecc import FiveCode, dec_sim

2. Create the instance for QECC.

For example, we prepare the 5-qubit code.

my_code = FiveCode()

We confirm the information for QECC my_code by

print(my_code)

NAME               : FIVE_CODE
PHYSICAL QUBITS (n): 5
LOGICAL QUBITS (k) : 1
CODE RATE (R = k/n): 0.2
DECODING_MODE      : ML

3. Prepare the decoding simulator.

dec_sim(my_code)

default settings:

• depolarizing channel
• 1000 codeward
• maximum likelihood decoding.

4. Start the decoding simulation.

python test.py

Please wait patiently.

5. Confirm the decoding results.

In /dec_data, PyQecc generates the simulation results.

MONTE: 100 BLOCK_ERROR: 5 p: 0.1 LOGICAL_ERROR_PROB: 0.05
MONTE: 200 BLOCK_ERROR: 19 p: 0.1 LOGICAL_ERROR_PROB: 0.095
MONTE: 300 BLOCK_ERROR: 24 p: 0.1 LOGICAL_ERROR_PROB: 0.08
MONTE: 400 BLOCK_ERROR: 29 p: 0.1 LOGICAL_ERROR_PROB: 0.0725
MONTE: 500 BLOCK_ERROR: 35 p: 0.1 LOGICAL_ERROR_PROB: 0.07
MONTE: 600 BLOCK_ERROR: 44 p: 0.1 LOGICAL_ERROR_PROB: 0.07333333333333333
MONTE: 700 BLOCK_ERROR: 53 p: 0.1 LOGICAL_ERROR_PROB: 0.07571428571428572
MONTE: 800 BLOCK_ERROR: 63 p: 0.1 LOGICAL_ERROR_PROB: 0.07875
MONTE: 900 BLOCK_ERROR: 71 p: 0.1 LOGICAL_ERROR_PROB: 0.07888888888888888
...

directory structure

├── test.py
└── dec_data (Folder)

dec_data/FIVE_CODE_5_1_monte_1000_20220220212203.csv

p,LOGICAL_ERROR_PROB,
0.1,0.08,
0.01,0.0,

Features

See the detail for features

Stabilizer Code

• 5-qubit code
• 7-qubit code (STEANE code)
• bit flip code
• phase flip code
• 9-qubit shor code (concatenated bit and phase flip code.)
• concatenated code

decoder

• syndrome decoding
• maximum likelihood (ML) decoding
• belief propagation decoding (concatenated code only)
• decoding with analog informatuon [3] (GKP qubit only)

Decoding simulation

• block error rate

Channel Model

• depolarizing channel
• pauli channel
• bit flip channel
• quantum gaussian channel

Simulation example

1. Concatenated 5-qubit codes (concatenation for 1, 2, and 3) [2, Fig. 1].

#Source code
from pyqecc import FiveCode, dec_sim, ConcCode, ParaCode, DepolarizingChannel

NUM_OF_CONCATENATE = 3
for num_of_concatenate in range(1, NUM_OF_CONCATENATE + 1):
    conc_code = [FiveCode()]
    for i in range(1, num_of_concatenate):
        conc_code += [ParaCode([FiveCode() for i in range(5**i)])]
    my_code = ConcCode(conc_code)
    print(my_code)
    dec_sim(
        my_code,
        channel_instance=DepolarizingChannel(
            my_code.n, p=[0.13, 0.15, 0.17, 0.18, 0.1885, 0.19]
        ),
        MONTE=5000,
    )

2. Conatenated Gottesman-Kitaev-Preskill (GKP)-bit flip code with analog information [3]

#Source code
import numpy as np
from pyqecc import GKP, BitFlipCode, GaussianQuantumChannel, dec_sim


my_code = BitFlipCode()
my_GKP = GKP(my_code)
my_channel = GaussianQuantumChannel(my_GKP.n,sigma=[0.33,0.35,0.37,0.39],phase_flip=False)
print(my_GKP)
dec_sim(my_GKP,channel_instance=my_channel,MONTE=10000000,ERR_STOP=1000000)

Future works

• surface code
• color code
• quantum LDPC code
• quantum polar code

References

[1] Nielsen, Michael A., and Isaac Chuang. "Quantum computation and quantum information." (2002): 558-559.

[2] Poulin, David. "Optimal and efficient decoding of concatenated quantum block codes." Physical Review A 74.5 (2006): 052333.

[3] Kosuke Fukui, Akihisa Tomita, and Atsushi Okamoto Phys. Rev. Lett. 119, 180507 – Published 3 November 2017