Investigate the performance of distance 2 heavy hexagon codes on IBM devices.

[SpiroGicev]

Abstract

Investigate the performance of distance 2 heavy hexagon codes on IBM devices. This involves writing up qiskit circuits to encode states, performing syndrome measurements, and analyzing measurement results to decide which of the results obtained are reliable.

Description

Quantum error correction is expected to be necessary to successfully run large depth quantum algorithms which are useful for fields such as simulation and optimization. Heavy-hexagon codes have achieved attention due to their high noise tolerance and ability to be implemented on a heavy hexagon topology. However, current devices have noise levels above threshold and as a result do not correct more errors than they generate when using bigger codes. We will investigate the properties of the smallest heavy-hexagon code capable of detecting a single error, the distance 2 code, and compare different approaches to state preparation, logical operations, and readout.

Ideas to try:

• Fault-tolerant preparation of specific encoded states. • Encoding general states. • Choice of qubits and error detection code. • Detecting leakage. • Applying logical operations.

Useful resources:

https://arxiv.org/abs/1907.09528 https://arxiv.org/abs/1912.09410 https://arxiv.org/abs/2110.04285 https://qiskit.org/textbook/ch-quantum-hardware/error-correction-repetition-code.html

Members

Qiskit Coach: @SpiroGicev - email: sgicev@student.unimelb.edu.au

Deliverable

A Jupyter Notebook file showing the results of different approaches and a presentation.

GitHub repo

[ljmensen]

Hi,

I'd like to join this team.

• Lucas Mensen, RMIT University

[Lucky-Anton]

I'll join in tomorrow! Project sounds great :)

[SpiroGicev]

Investigating the performance of distance 2 heavy-hexagon codes.pdf