Transversal dimension jump for product qLDPC codes

• URL: http://arxiv.org/abs/2510.07269v1
• Date: Wed, 08 Oct 2025 17:35:07 GMT
• Title: Transversal dimension jump for product qLDPC codes
• Authors: Christine Li, John Preskill, Qian Xu,
• Abstract summary: We introduce a code-switching protocol for dimension lifted product (LP) quantum low-density parity-check (qLDPC) codes across different chain-complex dimensions.<n>We implement one-way CNOTs between a 3D code and its 2D component codes, enabling teleportation-based switching.<n>This yields high-rate quantum logical computation with high thresholds and low space-time costs.
• Score: 2.8610973865376486
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce transversal dimension jump, a code-switching protocol for lifted product (LP) quantum low-density parity-check (qLDPC) codes across different chain-complex dimensions, enabling universal fault-tolerant quantum computation with low overhead. The construction leverages the product structure of LP codes to implement one-way transversal CNOTs between a 3D code and its 2D component codes, enabling teleportation-based switching. Combined with constant-depth CCZ gates in 3D LP codes and low-overhead transversal Clifford gates in 2D LP codes, this yields universal, high-rate quantum logical computation with high thresholds and low space-time costs. Beyond asymptotic schemes, we identify explicit 3D-2D LP code pairs supporting cup-product CCZ gates, including bivariate tricycle-bicycle families such as the $[[81,3,5]]$-$[[54,2,6]]$ pair, where the 3D tricycle codes admit depth-2 CCZ, weight-6 stabilizers, and pseudo-thresholds $\gtrsim 0.4\%$. As a byproduct, we show that the 3D codes enable highly efficient magic-state preparation: a single round of stabilizer measurements followed by depth-2 CCZ and postselection produces states with error $<10^{-9}$ and success probability $\sim 35\%$. Our results establish a native integration of qLDPC codes with complementary transversal gates-covering nearly all practically relevant families known so far-and open a broad design space for scalable, low-overhead universal quantum computation.

Related papers

• Addressable fault-tolerant universal quantum gate operations for high-rate lift-connected surface codes [0.8919684307774216]
  Quantum low-density parity check (qLDPC) codes are among the leading candidates to realize error-corrected quantum memories with low qubit overhead.<n>In this work, we introduce a construction to implement all Clifford quantum gate operations on the recently introduced lift-connected surface (LCS) codes.
  arXiv  Detail & Related papers  (2025-11-13T11:01:44Z)
• Magic tricycles: efficient magic state generation with finite block-length quantum LDPC codes [0.02394004496538737]
  We introduce a class of finite block-length quantum LDPC codes which we name tricycle codes.<n>These codes can support constant-depth physical circuits that implement logical CCZ gates between three code blocks.<n>We show that these tricycle codes enable magic state generation with single-shot state-preparation and error correction.
  arXiv  Detail & Related papers  (2025-08-14T14:56:50Z)
• Single-Shot Decoding and Fault-tolerant Gates with Trivariate Tricycle Codes [3.1952340441132474]
  We introduce tri tricycle (TT) codes, qLDPC codes that combine several desirable features.<n>TT codes have high thresholds under a circuit-level noise model, partial single-shot decodability for low-time-overhead decoding.<n> codes possess several $CZ gates that can partially address logical qubits between two code blocks.
  arXiv  Detail & Related papers  (2025-08-11T17:11:23Z)
• Non-local resources for error correction in quantum LDPC codes [0.0]
  High performing qLDPC codes have non-local stabilizers that are challenging to measure.<n>Recent advancements have shown how to deterministically perform high-fidelity, cavity mediated many-body gates.<n>We propose a compatible tri-layer architectural layout for scheduling stabilizer measurements.
  arXiv  Detail & Related papers  (2024-09-09T17:28:41Z)
• Transversal Clifford and T-gate codes of short length and high distance [0.6138671548064355]
  We construct three kinds of codes encoding a single logical qubit for distances up to $31$.<n>To our knowledge, these are the smallest known triorthogonal codes for their respective distances.
  arXiv  Detail & Related papers  (2024-08-22T22:45:47Z)
• Transform Arbitrary Good Quantum LDPC Codes into Good Geometrically Local Codes in Any Dimension [11.695180823001566]
  A key challenge is identifying the optimal code construction that maximizes both dimension and distance. Recent advancements have produced several constructions, but these either depend on specific good quantum low-density parity-check (qLDPC) codes or are limited to three dimensions. We introduce a construction that can transform any good qLDPC code into an optimal geometrically local quantum code.
  arXiv  Detail & Related papers  (2024-08-03T12:46:05Z)
• 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)
• Homological Quantum Rotor Codes: Logical Qubits from Torsion [47.52324012811181]
  homological quantum rotor codes allow one to encode both logical rotors and logical qudits in the same block of code.<n>We show that the $0$-$pi$-qubit as well as Kitaev's current-mirror qubit are indeed small examples of such codes.
  arXiv  Detail & Related papers  (2023-03-24T00:29:15Z)
• Gaussian conversion protocol for heralded generation of qunaught states [66.81715281131143]
  bosonic codes map qubit-type quantum information onto the larger bosonic Hilbert space. We convert between two instances of these codes GKP qunaught states and four-foldsymmetric binomial states corresponding to a zero-logical encoded qubit. We obtain GKP qunaught states with a fidelity of over 98% and a probability of approximately 3.14%.
  arXiv  Detail & Related papers  (2023-01-24T14:17:07Z)
• Finding the disjointness of stabilizer codes is NP-complete [77.34726150561087]
  We show that the problem of calculating the $c-disjointness, or even approximating it to within a constant multiplicative factor, is NP-complete. We provide bounds on the disjointness for various code families, including the CSS codes,$d codes and hypergraph codes. Our results indicate that finding fault-tolerant logical gates for generic quantum error-correcting codes is a computationally challenging task.
  arXiv  Detail & Related papers  (2021-08-10T15:00:20Z)
• Realization of arbitrary doubly-controlled quantum phase gates [62.997667081978825]
  We introduce a high-fidelity gate set inspired by a proposal for near-term quantum advantage in optimization problems. By orchestrating coherent, multi-level control over three transmon qutrits, we synthesize a family of deterministic, continuous-angle quantum phase gates acting in the natural three-qubit computational basis.
  arXiv  Detail & Related papers  (2021-08-03T17:49:09Z)
• Single-shot quantum error correction with the three-dimensional subsystem toric code [77.34726150561087]
  We introduce a new topological quantum code, the three-dimensional subsystem toric code (3D STC) The 3D STC can be realized by measuring geometrically-local parity checks of weight at most three on the cubic lattice with open boundary conditions.
  arXiv  Detail & Related papers  (2021-06-04T17:35:00Z)
• The cost of universality: A comparative study of the overhead of state distillation and code switching with color codes [63.62764375279861]
  We compare two leading FT implementations of the T gate in 2D color codes under circuit noise. We find a circuit noise threshold of 0.07(1)% for the T gate via code switching, almost an order of magnitude below that achievable by state distillation in the same setting.
  arXiv  Detail & Related papers  (2021-01-06T19:00:01Z)

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.