Good approximate quantum LDPC codes from spacetime circuit Hamiltonians

2018/11/01 by Thomas C. Bohdanowicz, Elizabeth Crosson, Chinmay Nirkhe +1
Computer Science · Physics and Astronomy · #Algorithm #Computer science #Decoding methods #Low-density parity-check code #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum computer #Quantum mechanics #Quantum-Dot Cellular Automata #Spacetime #Theoretical computer science #quant-ph

paper · pdf · doi:10.1145/3313276.3316384

51 pages, 13 figures

arxiv created 2018/11/01 · openalex publication_date 2019/06/20 · arxiv updated 2020/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

We study approximate quantum low-density parity-check (QLDPC) codes, which are approximate quantum error-correcting codes specified as the ground space of a frustration-free local Hamiltonian, whose terms do not necessarily commute.

Citations

• Topological quantum order: Stability under local perturbations
• Adiabatic Quantum Computation Is Equivalent to Standard Quantum Computation
• Simple Proof of Equivalence between Adiabatic Quantum Computation and the Circuit Model
• Universal Adiabatic Quantum Computation via the Space-Time Circuit-to-Hamiltonian Construction
• A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes
• Good Quantum Error-Correcting Codes Exist
• Fault-tolerant quantum computation by anyons
• Quantum Codes from High-Dimensional Manifolds
• Quantum LDPC Codes With Positive Rate and Minimum Distance Proportional to the Square Root of the Blocklength
• Fault-Tolerant Quantum Computation with Constant Overhead