Diffusive Speed Limits for U(1)-Covariant Quantum Error Correction

• URL: http://arxiv.org/abs/2608.04953v1
• Date: Wed, 05 Aug 2026 15:24:27 GMT
• Title: Diffusive Speed Limits for U(1)-Covariant Quantum Error Correction
• Abstract summary: Charge-Haar codes attain the universal adjacent-charge lower bound up to exponentially small corrections.<n>For local number-conserving circuits, diffusion of the logical charge enforces an $(n2)$ encoding-time lower bound.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Fast preparation of quantum error-correcting codes is essential for scalable quantum memories, but geometric locality and $U(1)$ charge conservation impose an unavoidable transport constraint. We combine exact complementary-channel geometry, charge-sector Haar analysis, and a gate-resolved connected-moment expansion to study one-dimensional covariant encoders under flagged erasure. Charge-Haar codes attain the universal adjacent-charge lower bound up to exponentially small corrections, yielding an exact $n^{-1/2}$ extensive-erasure law and a sharp half-erasure transition. For local number-conserving brickwork circuits, diffusion of the logical charge enforces an $Ω(n^2)$ encoding-time lower bound; we also prove an $O(n^3)$ mixing bound for the classical component and reduce the remaining full-channel upper bound to a source-restricted low-support operator-spreading problem. These results identify diffusion as an operational limit on symmetry-constrained quantum coding and establish a route to its exact formation time.

Related papers

• Quantum-classical crossover in fault-tolerant quantum dynamics simulation [56.198154828333685]
  We introduce a scalable fault-tolerant framework that combines coherent observable estimation with a space-time-efficient implementation of non-Clifford rotations.<n>A benchmark against state-of-the-art tensor-network and variational Monte Carlo algorithms reveals a concrete crossover for mixed-field Ising dynamics.
  arXiv  Detail & Related papers  (2026-07-17T16:54:25Z)
• Fault tolerant computation of the static structure factor and finite size effects [43.936586633107396]
  We develop a quantum post-processing strategy for the leading two-body finite-size correction.<n>After one-body shell effects are reduced by twist averaging, the dominant residual error is controlled by long-wavelength density fluctuations.<n>We also introduce adaptive global and local binary search procedures for identifying the infrared fitting window used to reconstruct the two-body finite size error correction.
  arXiv  Detail & Related papers  (2026-06-26T05:31:08Z)
• Asymptotic Limits of Entanglement Distribution [43.748379918040854]
  We investigate the limits of entanglement distribution across quantum networks utilizing intermediate stations and local operations.<n>We establish a strict dichotomy: the preservation of entanglement over arbitrarily long distances is possible if the underlying quantum channel admits a correctable subspace.<n>We derive a fundamental lower bound on the physical resource requirements, proving that for channels without a correctable subspace, the number of parallel channels per link must scale at least logarithmically with the number of intermediate stations to sustain a non-zero amount of entanglement.
  arXiv  Detail & Related papers  (2026-05-22T09:56:38Z)
• A Universal Circuit Set Using the $S_3$ Quantum Double [0.5231056284485742]
  We give an explicit construction of the circuits for creating, moving, and measuring all non-trivial anyons.<n>We encode each physical degree of freedom of $mathcalD(S_3)$ into a novel, quantum, error-correcting code.<n>Our proposal offers a promising path to realize robust universal topological quantum computation in the NISQ era.
  arXiv  Detail & Related papers  (2024-11-14T18:58:41Z)
• Covariant Quantum Error-Correcting Codes with Metrological Entanglement Advantage [1.6018724979340826]
  We show that a subset of the basis for the irreducible representations of a tensor-product SU(2) forms an approximate quantum error-correcting code with U(1) logical gates.<n>We demonstrate that this family of codes protects a probe state with quantum information surpassing the standard quantum limit when the sensing parameter couples to the generator of the U(1) logical gate.
  arXiv  Detail & Related papers  (2024-09-30T17:59:01Z)
• Approximate quantum error correcting codes from conformal field theory [0.0]
  We consider generic 1+1D CFT codes under extensive local dephasing channels. We show that a CFT code with continuous symmetry saturates a bound on the recovery fidelity for covariant codes.
  arXiv  Detail & Related papers  (2024-06-13T19:40:36Z)
• 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)
• Fidelity-based distance bounds for $N$-qubit approximate quantum error correction [0.0]
  Eastin-Knill theorem states that a quantum code cannot correct errors exactly, possess continuous symmetries, and implement a universal set of gates transversely. It is common to employ a complementary measure of fidelity as a way to quantify quantum state distinguishability and benchmark approximations in error correction. We address two distance measures based on the sub- and superfidelities as a way to bound error approximations, which in turn require a lower computational cost.
  arXiv  Detail & Related papers  (2022-12-08T16:10:58Z)
• Unimon qubit [42.83899285555746]
  Superconducting qubits are one of the most promising candidates to implement quantum computers. Here, we introduce and demonstrate a superconducting-qubit type, the unimon, which combines the desired properties of high non-linearity, full insensitivity to dc charge noise, insensitivity to flux noise, and a simple structure consisting only of a single Josephson junction in a resonator.
  arXiv  Detail & Related papers  (2022-03-11T12:57:43Z)
• Quantum Error Correction with Gauge Symmetries [69.02115180674885]
  Quantum simulations of Lattice Gauge Theories (LGTs) are often formulated on an enlarged Hilbert space containing both physical and unphysical sectors. We provide simple fault-tolerant procedures that exploit such redundancy by combining a phase flip error correction code with the Gauss' law constraint.
  arXiv  Detail & Related papers  (2021-12-09T19:29:34Z)
• 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)
• Charge-conserving unitaries typically generate optimal covariant quantum error-correcting codes [1.2183405753834557]
  We consider the quantum error correction capability of random covariant codes. In particular, we show that $U(1)$-covariant codes generated by Haar random $U(1)$-symmetric unitaries saturate the fundamental limits to leading order. Our results hold for symmetric variants of unitary 2-designs, and comment on the convergence problem of charge-conserving random circuits.
  arXiv  Detail & Related papers  (2021-02-23T18:11:15Z)

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.