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Quantum Error Correction Using Low-Density Parity-Check Codes and Erasure Qubits


Gu, Shouzhen (2024) Quantum Error Correction Using Low-Density Parity-Check Codes and Erasure Qubits. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/5pj8-wv34.


Quantum error correction is a method to reduce the effective error rate on quantum computers so that they can be used to carry out useful computation. In this thesis, we study two main problems: decoding quantum low-density parity-check codes and using erasure qubits to implement error correction protocols.

In the first part of this thesis, we focus on quantum low-density parity-check codes, which are a promising approach to reducing the spacetime overhead associated with error correction. We show that certain families of codes with constant rate and linear distance can be decoded efficiently. In particular, we propose a linear-time algorithm that will correct any error affecting at most a constant fraction of the qubits.

We also analyze the setting where the measurement outcomes given to the decoder can be corrupted. In this more realistic scenario, the decoder is shown to have the single-shot property. Using one round of noisy syndrome data, it can output a correction that is close to the data error as long as at most a constant fraction of the data qubits and syndrome bits are flipped. As a consequence, the decoder can operate under a stochastic noise model where errors occur with sufficiently small but constant probability.

In the second part of the thesis, we analyze quantum error-correcting codes implemented using erasure qubits. The idea behind erasure qubits is to bias the noise into a form where likely locations of errors are known, for example, by converting the dominant noise source into detectable leakage from the computational subspace. We provide a formalism for simulating and decoding stabilizer circuits with erasures, erasure checks, and resets. Using this formalism, we study the performance of Floquet codes and show that the benefits of knowing error locations outweigh the cost of extra noise due to erasure checks.

Lastly, we optimize erasure check schedules in the context of the surface code. By performing simulations with one, two, or four erasure checks per syndrome extraction round, we find different error parameter regimes where it is optimal to use each schedule. Additionally, we provide a simplified way of decoding erasure circuits suitable for circuits with infrequent erasure checks.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Quantum information; quantum error correction; decoding algorithm; erasure qubit; low-density parity-check code; surface code; Floquet code
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Awards:Robert F. Christy Prize for an Outstanding Doctoral Thesis in Theoretical Physics , 2024.
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Preskill, John P.
Group:Institute for Quantum Information and Matter
Thesis Committee:
  • Kitaev, Alexei (chair)
  • Alicea, Jason F.
  • Chen, Xie
  • Preskill, John P.
Defense Date:14 May 2024
Funding AgencyGrant Number
Air Force Office of Scientific ResearchFA9550-19-1-0360
Department of EnergyDE-SC0018407
Department of EnergyDE-AC02-07CH11359
National Science FoundationPHY-1733907
National Science FoundationPHY-2317110
Record Number:CaltechTHESIS:05172024-212658426
Persistent URL:
Related URLs:
URLURL TypeDescription adapted for Ch. 2 version of Ch. 2 adapted for Ch. 3 adapted for Ch. 4
Gu, Shouzhen0000-0003-2560-4209
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:16388
Deposited By: Shouzhen Gu
Deposited On:31 May 2024 23:46
Last Modified:03 Jun 2024 17:00

Thesis Files

[img] PDF (Redacted thesis (ch. 5 omitted)) - Final Version
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