Recovery Algorithm for Correlated Errors in Permutation-Invariant Quantum Codes

• URL: http://arxiv.org/abs/2607.02346v1
• Date: Thu, 02 Jul 2026 15:49:28 GMT
• Title: Recovery Algorithm for Correlated Errors in Permutation-Invariant Quantum Codes
• Abstract summary: Quantum Error Recovery (QER) uses knowledge of the error channel acting on a quantum system to find optimal recovery maps.<n>We propose a new PI code family called CAD codes with explicit examples on 4 and 9 qubits for global symmetric AD errors.<n>For the CAD4 code, which perfectly corrects 1 global symmetric AD error, the compiled recovery circuit consists of 10 system and system-ancilla gates.
• Score: 2.6097841018267616
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum Error Recovery (QER) uses knowledge of the error channel acting on a quantum system to find optimal recovery maps. The scheme restores the uncorrupted state with a fidelity exceeding that achieved by noise parameter independent quantum error correction. We use a generic coherent QER map implemented with a quantum circuit acting on the system together with ancillary qubits to recover quantum information stored in permutation invariant (PI) codes. PI codes admit tunable parameters to suit the noise model and benefit from simple recovery operation circuits with reduced addressability requirements, unlike stabilizer codes. We showcase the method by modeling QER in PI codes after collective and local symmetric correlated amplitude-damping (AD) noise, a non-Pauli noise process for which stabilizer codes often require additional overhead. We also propose a new PI code family called CAD codes with explicit examples on 4 and 9 qubits for global symmetric AD errors. We show that CAD9 (supported on 9 qubits) code beats many existing codes by more than one order of magnitude. For the CAD4 code, which perfectly corrects 1 global symmetric AD error, the compiled recovery circuit consists of 10 system and system-ancilla gates which can be realized from linear geometric phase gates. Our work provides a direct path from optimized recovery maps to experimentally implementable, low-overhead protocols.

Related papers

• Probabilistic Error Cancellation for Single-Mode Gottesman-Kitaev-Preskill Codes [45.91504150103373]
  We study a quantum error mitigation method known as probabilistic error cancellation in the context of the Gottesman-Kitaev-Preskill code.<n>We employ the stabilizer subsystem decomposition for GKP codes to obtain an effective logical channel for noisy operations.
  arXiv  Detail & Related papers  (2026-09-15T12:29:45Z)
• Error Correction of Beamsplitter-Generated Entangled GKP States [56.80803785296797]
  A promising bosonic code is the Gottesman-Kitaev-Preskill (GKP) code.<n>We generate entangled states of GKP qubits by interfering two qunaught states, which have a grid structure but carry no logical information, on a beamsplitter.<n>We generate all four Bell states with an average fidelity of 69%, and demonstrate an extension of the entangled state lifetime through the use of quantum error correction.
  arXiv  Detail & Related papers  (2026-05-08T17:01:19Z)
• Deterministic Fault-Tolerant State Preparation for Near-Term Quantum Error Correction: Automatic Synthesis Using Boolean Satisfiability [4.2955091080396075]
  We focus on the problem of automatically synthesizing fault-tolerant circuits for a broad class of quantum codes.<n>We utilize methods based on techniques from classical circuit design, such as satisfiability solving.<n>We demonstrate the correct fault-tolerant behavior of the synthesized circuits using circuit-level noise simulations.
  arXiv  Detail & Related papers  (2025-01-09T19:06:01Z)
• Universal quantum computation via scalable measurement-free error correction [45.29832252085144]
  We show that universal quantum computation can be made fault-tolerant in a scenario where the error-correction is implemented without mid-circuit measurements.<n>We introduce a measurement-free deformation protocol of the Bacon-Shor code to realize a logical $mathitCCZ$ gate.<n>In particular, our findings support that below-breakeven logical performance is achievable with a circuit-level error rate below $10-3$.
  arXiv  Detail & Related papers  (2024-12-19T18:55:44Z)
• Circuit-level fault tolerance of cat codes [0.0]
  Bosonic codes encode quantum information into a single infinite-dimensional physical system endowed with error correction capabilities.<n>Recent discussions of bosonic codes centre around correcting only boson-loss errors.<n>We show how, through waiting-time optimization and the use of squeezing, we can restore the noise requirements to a regime achievable with near-term quantum hardware.
  arXiv  Detail & Related papers  (2024-06-06T15:18:25Z)
• Noise-adapted qudit codes for amplitude-damping noise [6.320926638892934]
  We identify a $[4,1]$ qudit error correcting code tailored to protect against amplitude-damping noise.<n>We show that this four-qudit code satisfies the error correction conditions for all single-qudit and a few two-qudit damping errors.<n>We generalize this construction to a family of $[2M+2, M]$ qudit codes that can approximately correct all the single-qudit and a few two-qudit amplitude-damping errors.
  arXiv  Detail & Related papers  (2024-06-04T16:07:26Z)
• Near-optimal decoding algorithm for color codes using Population Annealing [44.99833362998488]
  We implement a decoder that finds the recovery operation with the highest success probability. We study the decoder performance on a 4.8.8 color code lattice under different noise models.
  arXiv  Detail & Related papers  (2024-05-06T18:17:42Z)
• 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)
• Noise-adapted recovery circuits for quantum error correction [1.8799303827638123]
  We present quantum circuits for a universal, noise-adapted recovery map, often referred to as the Petz map. We also present circuits that can directly estimate the fidelity between the encoded state and the recovered state. The efficacy of our noise-adapted recovery circuits is then demonstrated through ideal and noisy simulations.
  arXiv  Detail & Related papers  (2023-05-18T16:29:49Z)
• Deep Quantum Error Correction [73.54643419792453]
  Quantum error correction codes (QECC) are a key component for realizing the potential of quantum computing. In this work, we efficiently train novel emphend-to-end deep quantum error decoders. The proposed method demonstrates the power of neural decoders for QECC by achieving state-of-the-art accuracy.
  arXiv  Detail & Related papers  (2023-01-27T08:16:26Z)
• Realizing a class of stabilizer quantum error correction codes using a single ancilla and circular connectivity [0.0]
  We show that a class of "neighboring-blocks" stabilizer quantum error correction codes can be implemented in a resource-efficient manner using a single ancilla and circular near-neighbor qubit connectivity. We propose an implementation for syndrome-measurement circuits for codes from the class and illustrate its workings for cases of three-, five-, and nine-qubits stabilizer code schemes.
  arXiv  Detail & Related papers  (2022-07-27T08:25:38Z)
• Adaptive quantum codes: constructions, applications and fault tolerance [0.0]
  A perfect quantum code requires atleast five physical qubits to observe a noticeable improvement over the no-QEC scenario. We propose an adaptive QEC protocol that allows transmission of quantum information from one site to the other over a 1-d spin chain with high fidelity.
  arXiv  Detail & Related papers  (2022-03-07T10:06:16Z)
• Performance of teleportation-based error correction circuits for bosonic codes with noisy measurements [58.720142291102135]
  We analyze the error-correction capabilities of rotation-symmetric codes using a teleportation-based error-correction circuit. We find that with the currently achievable measurement efficiencies in microwave optics, bosonic rotation codes undergo a substantial decrease in their break-even potential.
  arXiv  Detail & Related papers  (2021-08-02T16:12:13Z)

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.