Fast and fault-tolerant logical measurements: Auxiliary hypergraphs and transversal surgery

• URL: http://arxiv.org/abs/2510.14895v1
• Date: Thu, 16 Oct 2025 17:12:36 GMT
• Title: Fast and fault-tolerant logical measurements: Auxiliary hypergraphs and transversal surgery
• Authors: Alexander Cowtan, Zhiyang He, Dominic J. Williamson, Theodore J. Yoder,
• Abstract summary: Quantum code surgery is a promising technique to perform fault-tolerant computation on quantum low-density parity-check codes.<n>We present a general set of conditions that ensure fault-tolerant surgery operations can be performed with constant time overhead.<n>We further investigate surgery operations with intermediate time overhead, between $O(1)$ and $O(d)$, which apply to quantum locally testable codes.
• Score: 39.98920557126034
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum code surgery is a promising technique to perform fault-tolerant computation on quantum low-density parity-check codes. Recent developments have significantly reduced the space overhead of surgery. However, generic surgery operations still require $O(d)$ rounds of repeated syndrome extraction to be made fault-tolerant. In this work, we focus on reducing the time overhead of surgery. We first present a general set of conditions that ensure fault-tolerant surgery operations can be performed with constant time overhead. This fast surgery necessarily makes use of an auxiliary complex described by a hypergraph rather than a graph. We then introduce a concrete scheme called block reading, which performs transversal surgery across multiple code blocks. We further investigate surgery operations with intermediate time overhead, between $O(1)$ and $O(d)$, which apply to quantum locally testable codes. Finally, we establish a circuit equivalence between homomorphic measurement and hypergraph surgery and derive bounds on the time overhead of generic logical measurement schemes. Overall, our results demonstrate that reducing the time cost of code surgery is not reliant on the quantum memory being single-shot. Instead it is chiefly the connectivity between a code and its measurement ancilla system that determines the achievable measurement time overhead.

Related papers

• Constant-Time Surgery on 2D Hypergraph Product Codes with Near-Constant Space Overhead [1.7884907807711146]
  Generalized code surgery is a versatile and low-overhead technique for performing fault-tolerant computation.<n>In this work, we construct surgery gadgets that perform parallel logical measurements on 2D hypergraph product codes in constant time overhead.
  arXiv  Detail & Related papers  (2026-03-02T18:21:52Z)
• Fast correlated decoding of transversal logical algorithms [67.01652927671279]
  Quantum error correction (QEC) is required for large-scale computation, but incurs a significant resource overhead.<n>Recent advances have shown that by jointly decoding logical qubits in algorithms composed of logical gates, the number of syndrome extraction rounds can be reduced.<n>Here, we reform the problem of decoding circuits by directly decoding relevant logical operator products as they propagate through the circuit.
  arXiv  Detail & Related papers  (2025-05-19T18:00:00Z)
• Demonstrating real-time and low-latency quantum error correction with superconducting qubits [52.08698178354922]
  We demonstrate low-latency feedback with a scalable FPGA decoder integrated into a superconducting quantum processor. We observe logical error suppression as the number of decoding rounds is increased. The decoder throughput and latency developed in this work, combined with continued device improvements, unlock the next generation of experiments.
  arXiv  Detail & Related papers  (2024-10-07T17:07:18Z)
• SSIP: automated surgery with quantum LDPC codes [55.2480439325792]
  We present Safe Surgery by Identifying Pushouts (SSIP), an open-source lightweight Python package for automating surgery between qubit CSS codes. Under the hood, it performs linear algebra over $mathbbF$ governed by universal constructions in the category of chain complexes. We show that various logical measurements can be performed cheaply by surgery without sacrificing the high code distance.
  arXiv  Detail & Related papers  (2024-07-12T16:50:01Z)
• GLSFormer : Gated - Long, Short Sequence Transformer for Step Recognition in Surgical Videos [57.93194315839009]
  We propose a vision transformer-based approach to learn temporal features directly from sequence-level patches. We extensively evaluate our approach on two cataract surgery video datasets, Cataract-101 and D99, and demonstrate superior performance compared to various state-of-the-art methods.
  arXiv  Detail & Related papers  (2023-07-20T17:57:04Z)
• A High Performance Compiler for Very Large Scale Surface Code Computations [38.26470870650882]
  We present the first high performance compiler for very large scale quantum error correction. It translates an arbitrary quantum circuit to surface code operations based on lattice surgery. The compiler can process millions of gates using a streaming pipeline at a speed geared towards real-time operation of a physical device.
  arXiv  Detail & Related papers  (2023-02-05T19:06:49Z)
• Transversal Injection: A method for direct encoding of ancilla states for non-Clifford gates using stabiliser codes [55.90903601048249]
  We introduce a protocol to potentially reduce this overhead for non-Clifford gates. Preliminary results hint at high quality fidelities at larger distances.
  arXiv  Detail & Related papers  (2022-11-18T06:03:10Z)
• New magic state distillation factories optimized by temporally encoded lattice surgery [0.0]
  Timelike failures during lattice surgery protocols can result in logical failures during the execution of an algorithm. We introduce an improved TELS protocol and subsequently augment it with the ability to correct low-weight classical errors. We also explore large families of classical error correcting codes for a wide range of parallelizable Pauli set sizes.
  arXiv  Detail & Related papers  (2022-10-28T00:34:37Z)
• A circuit-level protocol and analysis for twist-based lattice surgery [3.222802562733787]
  Lattice surgery is a technique for performing fault-tolerant quantum computation in two dimensions. We provide an explicit twist-based lattice surgery protocol and its requisite connectivity layout. We also provide new stabilizer measurement circuits for measuring twist defects.
  arXiv  Detail & Related papers  (2022-01-14T21:16:27Z)
• Universal quantum computing with twist-free and temporally encoded lattice surgery [3.222802562733787]
  We introduce a decoder capable of correcting spacelike and timelike errors during lattice surgery protocols. We compute logical failure rates of a lattice surgery protocol for a biased circuit-level noise model. We propose a layout for a quantum processor that is more efficient for rectangular surface codes exploiting noise bias.
  arXiv  Detail & Related papers  (2021-09-06T21:18:01Z)

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.