Universal Optimization and Tighter Fidelity Bounds for Approximate Quantum Error Correction

• URL: http://arxiv.org/abs/2607.24968v1
• Date: Mon, 27 Jul 2026 18:18:58 GMT
• Title: Universal Optimization and Tighter Fidelity Bounds for Approximate Quantum Error Correction
• Abstract summary: Approximate quantum error correction (AQEC) dictates the performance of discrete- and continuous-variable quantum error correction codes.<n>Finding the optimal recovery channel to maximize entanglement fidelity via standard semidefinite programming is computationally bottlenecked by the exponentially growing number of Kraus operators.<n>We establish an efficient framework by leveraging the duality between recovery and environment decoupling.
• Score: 5.2107604548805915
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Approximate quantum error correction (AQEC) not only dictates the performance of discrete- and continuous-variable quantum error correction codes but also serves as a unifying framework across various physical disciplines. Identifying the optimal recovery channel to maximize the entanglement fidelity via standard semidefinite programming is computationally bottlenecked by the exponentially growing number of Kraus operators with system size, rendering large-scale optimization prohibitive. While analytical near-optimal maps exist, they typically work only when the Knill-Laflamme conditions are nearly satisfied. In this Letter, we establish an efficient framework by leveraging the duality between recovery and environment decoupling. This framework yields a tighter analytical lower bound on entanglement fidelity than the conventional limit set by the transpose channel. Furthermore, by exploiting the decayed weights of noise Kraus operators, we introduce a framework based on principal component analysis to reduce the dimension. In thermal loss channels where the weights decay exponentially, our approach achieves a 33-fold computational speedup while maintaining rigorous accuracy. Our approach enables high-precision optimization for AQEC codes that were previously intractable due to the curse of dimensionality.

Related papers

• Hardware-Aware QUBO Reformulation of Constrained Binary Optimization via the Walsh-Fourier Transform [1.3423094548772225]
  We present a novel framework for reformulating constrained binary optimization as Quadratic Unconstrained Binary Optimization (QUBO)<n>We show that this hardware-native surrogate can outperform denser full-pairwise projections, despite being drawn from a strictly smaller approximation space.<n>This advantage widens once the QUBO is embedded and sampled on quantum annealers, yielding samples with the lowest worst-case and mean objective gaps compared to unbalanced penalization and a hardware-blind projection onto all quadratic terms.
  arXiv  Detail & Related papers  (2026-07-28T23:45:18Z)
• Optimality-Preserving Decomposition for Scalable QAOA in Natural-Language-Guided Multi-Drone Assignment [1.189955933770711]
  We present an end-to-end framework integrating a fine-tuned Large Language Model front-end with a highly scalable, domain-specific quantum-classical backend.<n>Our framework features a novel constraint-preserving graph partitioner and a compressed separator-based dynamic programming (DP) merge.<n> Empirical results demonstrate that this architecture circumvents classical scaling walls, recovering the global optimum on 100% of idealized cases and 96.3% under real QAOA sampling.
  arXiv  Detail & Related papers  (2026-06-12T08:31:14Z)
• Closed-form Bayesian quantum estimation of Gaussian states [0.0]
  We introduce a variational framework reducing the optimisation over measurements and estimators to a finite-dimensional linear problem.<n>We show that the framework yields experimentally feasible strategies based on Gaussian operations and quadrature measurements.
  arXiv  Detail & Related papers  (2026-05-16T12:56:59Z)
• EQE-QAOA: An Equivalence-Preserving Qubit Efficient Framework for Combinatorial Optimization [54.05451096499336]
  Existing techniques rely on qubit reduction at the cost of information loss, leading to degraded computational performance.<n>We propose the Equivalence-preserving Qubit Efficient QAOA, which significantly reduces the required number of qubits without degrading performance.<n>We show that it is broadly applicable to large-scale optimization problems, excluding only unconstrained problems with completely independent variables.
  arXiv  Detail & Related papers  (2026-04-20T13:57:49Z)
• Stability and Generalization of Push-Sum Based Decentralized Optimization over Directed Graphs [55.77845440440496]
  Push-based decentralized communication enables optimization over communication networks, where information exchange may be asymmetric.<n>We develop a unified uniform-stability framework for the Gradient Push (SGP) algorithm.<n>A key technical ingredient is an imbalance-aware generalization bound through two quantities.
  arXiv  Detail & Related papers  (2026-02-24T05:32:03Z)
• Continual Quantum Architecture Search with Tensor-Train Encoding: Theory and Applications to Signal Processing [68.35481158940401]
  CL-QAS is a continual quantum architecture search framework.<n>It mitigates challenges of costly encoding amplitude and forgetting in variational quantum circuits.<n>It achieves controllable robustness expressivity, sample-efficient generalization, and smooth convergence without barren plateaus.
  arXiv  Detail & Related papers  (2026-01-10T02:36:03Z)
• Kernelized Decoded Quantum Interferometry [0.0]
  We introduce textbf Kernelized Decoded Quantum Interferometry (k-DQI), a unified framework that integrates spectral engineering directly into the quantum circuit architecture.<n>We prove a textbfMonotonic Improvement Theorem, which establishes that maximizing $_K$ guarantees higher decoding success rates under local depolarizing noise.
  arXiv  Detail & Related papers  (2025-11-25T07:35:03Z)
• Reliable Optimization Under Noise in Quantum Variational Algorithms [0.05219568203653522]
  We show that Variational Quantum Eigensolver is severely challenged by finite-shot sampling noise.<n>We identify adaptive metaheuristics as the most effective and resilient strategies.
  arXiv  Detail & Related papers  (2025-11-11T14:21:43Z)
• CAGE: Curvature-Aware Gradient Estimation For Accurate Quantization-Aware Training [73.46600457802693]
  We introduce a new method that counteracts the loss induced by quantization.<n>CAGE significantly improves upon the state-of-theart methods in terms of accuracy, for similar computational cost.<n>For QAT pre-training of Llama models, CAGE matches the accuracy achieved at 4-bits (W4A4) with the prior best method.
  arXiv  Detail & Related papers  (2025-10-21T16:33:57Z)
• MPQ-DMv2: Flexible Residual Mixed Precision Quantization for Low-Bit Diffusion Models with Temporal Distillation [74.34220141721231]
  We present MPQ-DMv2, an improved textbfMixed textbfPrecision textbfQuantization framework for extremely low-bit textbfDiffusion textbfModels.
  arXiv  Detail & Related papers  (2025-07-06T08:16:50Z)
• The Near-optimal Performance of Quantum Error Correction Codes [2.670972517608388]
  We derive the near-optimal channel fidelity, a concise and optimization-free metric for arbitrary codes and noise. Compared to conventional optimization-based approaches, the reduced computational cost enables us to simulate systems with previously inaccessible sizes. We analytically derive the near-optimal performance for the thermodynamic code and the Gottesman-Kitaev-Preskill (GKP) code.
  arXiv  Detail & Related papers  (2024-01-04T01:44:53Z)
• Fault-tolerant quantum architectures based on erasure qubits [49.227671756557946]
  We exploit the idea of erasure qubits, relying on an efficient conversion of the dominant noise into erasures at known locations. We propose and optimize QEC schemes based on erasure qubits and the recently-introduced Floquet codes. Our results demonstrate that, despite being slightly more complex, QEC schemes based on erasure qubits can significantly outperform standard approaches.
  arXiv  Detail & Related papers  (2023-12-21T17:40:18Z)

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.