Simplified Quantum Weight Reduction with Optimal Bounds

• URL: http://arxiv.org/abs/2510.09601v1
• Date: Fri, 10 Oct 2025 17:58:31 GMT
• Title: Simplified Quantum Weight Reduction with Optimal Bounds
• Authors: Min-Hsiu Hsieh, Xingjian Li, Ting-Chun Lin,
• Abstract summary: Low-weight codes are essential for implementing quantum error correction on physical hardware.<n>Weight reduction also serves as a critical theoretical tool, which may be relevant to the quantum PCP conjecture.<n>We introduce a new procedure for quantum weight reduction that combines geometric insights with coning techniques.
• Score: 9.984974174262328
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum weight reduction is the task of transforming a quantum code with large check weight into one with small check weight. Low-weight codes are essential for implementing quantum error correction on physical hardware, since high-weight measurements cannot be executed reliably. Weight reduction also serves as a critical theoretical tool, which may be relevant to the quantum PCP conjecture. We introduce a new procedure for quantum weight reduction that combines geometric insights with coning techniques, which simplifies Hastings' previous approach while achieving better parameters. Given an arbitrary $[[n,k,d]]$ quantum code with weight $w$, our method produces a code with parameters $[[O(n w^2 \log w), k, \Omega(d w)]]$ with check weight $5$ and qubit weight $6$. When applied to random dense CSS codes, our procedure yields explicit quantum codes that surpass the square-root distance barrier, achieving parameters $[[n, \tilde O(n^{1/3}), \tilde \Omega(n^{2/3})]]$. Furthermore, these codes admit a three-dimensional embedding that saturates the Bravyi-Poulin-Terhal (BPT) bound. As a further application, our weight reduction technique improves fault-tolerant logical operator measurements by reducing the number of ancilla qubits.

Related papers

• Quantum Weight Reduction with Layer Codes [0.0]
  We introduce a simple and general procedure for quantum weight reduction that achieves check weight 6 and total qubit degree 6.<n>Our quantum weight reduction procedure replaces each qubit and check in an arbitrary Calderbank-Shor-Steane code with an ample patch of surface code.<n>This is a quantum analog of the simple classical weight reduction procedure where each bit and check is replaced by a repetition code.
  arXiv  Detail & Related papers  (2026-03-05T07:23:37Z)
• Fine-Grained Unambiguous Measurements [2.5782420501870296]
  We introduce the notion of fine-grained unambiguous measurements.<n>We show that determining the maximal number of parities that a measurement can output can be formulated as a linear program.<n>We discuss the implications of these findings for the Quantum Decoding Problem.
  arXiv  Detail & Related papers  (2025-10-08T17:53:08Z)
• Parallel Logical Measurements via Quantum Code Surgery [42.95092131256421]
  Quantum code surgery is a flexible and low overhead technique for performing logical measurements on quantum error-correcting codes.<n>We present a code surgery scheme, applicable to any qubit stabiliser low-density parity check (LDPC) code, that fault-tolerantly measures many logical Pauli operators in parallel.
  arXiv  Detail & Related papers  (2025-03-06T22:05:52Z)
• Weight Reduced Stabilizer Codes with Lower Overhead [0.0]
  A stabilizer code is defined by a set of parity-check operators, which are measured in order to infer information about errors that may have occurred. Hastings proposed a method for reducing the parity checks of a stabilizer code, though it has previously only been studied in the regime. Here, we focus on the regime of small-to-medium size codes suitable for quantum computing hardware.
  arXiv  Detail & Related papers  (2024-02-07T20:08:38Z)
• Towards large-scale quantum optimization solvers with few qubits [59.63282173947468]
  We introduce a variational quantum solver for optimizations over $m=mathcalO(nk)$ binary variables using only $n$ qubits, with tunable $k>1$. We analytically prove that the specific qubit-efficient encoding brings in a super-polynomial mitigation of barren plateaus as a built-in feature.
  arXiv  Detail & Related papers  (2024-01-17T18:59:38Z)
• Fast Flux-Activated Leakage Reduction for Superconducting Quantum Circuits [84.60542868688235]
  leakage out of the computational subspace arising from the multi-level structure of qubit implementations. We present a resource-efficient universal leakage reduction unit for superconducting qubits using parametric flux modulation. We demonstrate that using the leakage reduction unit in repeated weight-two stabilizer measurements reduces the total number of detected errors in a scalable fashion.
  arXiv  Detail & Related papers  (2023-09-13T16:21:32Z)
• QuIP: 2-Bit Quantization of Large Language Models With Guarantees [44.212441764241]
  This work studies post-training parameter quantization in large language models (LLMs) We introduce quantization with incoherence processing (QuIP), a new method based on the insight that quantization benefits from $textitincoherent$ weight and Hessian matrices.
  arXiv  Detail & Related papers  (2023-07-25T07:44:06Z)
• Performance Analysis of Quantum CSS Error-Correcting Codes via MacWilliams Identities [9.69910104594168]
  We analyze the performance of stabilizer codes, one of the most important classes for practical implementations. We introduce a novel approach that combines the knowledge of WE with a logical operator analysis. For larger codes our bound provides $rho_mathrmL approx 1215 rho4$ and $rho_mathrmL approx 663 rho5$ for the $[85,1,7]]$ and the $[181,1,10]]$ surface codes.
  arXiv  Detail & Related papers  (2023-05-02T10:19:02Z)
• Quantum Worst-Case to Average-Case Reductions for All Linear Problems [66.65497337069792]
  We study the problem of designing worst-case to average-case reductions for quantum algorithms. We provide an explicit and efficient transformation of quantum algorithms that are only correct on a small fraction of their inputs into ones that are correct on all inputs.
  arXiv  Detail & Related papers  (2022-12-06T22:01:49Z)
• On Applying the Lackadaisical Quantum Walk Algorithm to Search for Multiple Solutions on Grids [63.75363908696257]
  The lackadaisical quantum walk is an algorithm developed to search graph structures whose vertices have a self-loop of weight $l$. This paper addresses several issues related to applying the lackadaisical quantum walk to search for multiple solutions on grids successfully.
  arXiv  Detail & Related papers  (2021-06-11T09:43:09Z)
• On Quantum Weight Reduction [0.0]
  We introduce a new technique that we call "coning" to effectively induce high weight stabilizers in an LDPC code. As one application, any LDPC code (with arbitrary $O(1)$ stabilizer weights) may be turned into a code where all stabilizers have weight at most $5$.
  arXiv  Detail & Related papers  (2021-02-19T17:01:29Z)
• Describing quantum metrology with erasure errors using weight distributions of classical codes [9.391375268580806]
  We consider using quantum probe states with a structure that corresponds to classical $[n,k,d]$ binary block codes of minimum distance. We obtain bounds on the ultimate precision that these probe states can give for estimating the unknown magnitude of a classical field.
  arXiv  Detail & Related papers  (2020-07-06T16:22:40Z)
• Quantum Gram-Schmidt Processes and Their Application to Efficient State Read-out for Quantum Algorithms [87.04438831673063]
  We present an efficient read-out protocol that yields the classical vector form of the generated state. Our protocol suits the case that the output state lies in the row space of the input matrix. One of our technical tools is an efficient quantum algorithm for performing the Gram-Schmidt orthonormal procedure.
  arXiv  Detail & Related papers  (2020-04-14T11:05:26Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.