Single-shot error correction of three-dimensional homological product codes

• URL: http://arxiv.org/abs/2009.11790v2
• Date: Wed, 16 Dec 2020 12:14:08 GMT
• Title: Single-shot error correction of three-dimensional homological product codes
• Authors: Armanda O. Quintavalle, Michael Vasmer, Joschka Roffe, Earl T. Campbell
• Abstract summary: Single-shot error correction corrects data noise using only a single round of noisy measurements on the data qubits. We introduce a general concept of confinement for quantum codes, which roughly stipulates qubit errors cannot grow without triggering more measurement syndromes.
• Score: 3.6748639131154315
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Single-shot error correction corrects data noise using only a single round of noisy measurements on the data qubits, removing the need for intensive measurement repetition. We introduce a general concept of confinement for quantum codes, which roughly stipulates qubit errors cannot grow without triggering more measurement syndromes. We prove confinement is sufficient for single-shot decoding of adversarial errors and linear confinement is sufficient for single-shot decoding of local stochastic errors. Further to this, we prove that all three-dimensional homological product codes exhibit confinement in their $X$-components and are therefore single-shot for adversarial phase-flip noise. For local stochastic phase-flip noise, we numerically explore these codes and again find evidence of single-shot protection. Our Monte Carlo simulations indicate sustainable thresholds of $3.08(4)\%$ and $2.90(2)\%$ for 3D surface and toric codes respectively, the highest observed single-shot thresholds to date. To demonstrate single-shot error correction beyond the class of topological codes, we also run simulations on a randomly constructed 3D homological product code.

Related papers

• Single-shot preparation of hypergraph product codes via dimension jump [0.0]
  We present a protocol that prepares the codespace of constant-rate hypergraph product codes in constant depth with $O(sqrtn)$ spatial overhead. We show that the protocol is robust even in the presence of measurement errors.
  arXiv  Detail & Related papers  (2024-10-07T16:29:13Z)
• Single-shot error correction on toric codes with high-weight stabilizers [0.49109372384514843]
  Single-shot error correction allows for an error threshold with only one round of noisy syndrome measurements regardless of the code size. The single-shot check operators result in a sustainable threshold at 5.62% for an error model with noisy measurements. For this error model, the conventional check operators with multiple measurements yields a lower logical error rate.
  arXiv  Detail & Related papers  (2023-10-24T20:06:19Z)
• Correcting phenomenological quantum noise via belief propagation [7.469588051458094]
  Quantum stabilizer codes often face the challenge of syndrome errors due to error-prone measurements. In this paper, we consider phenomenological decoding problems, where data qubit errors may occur between two syndrome extractions. We propose a method to construct effective redundant stabilizer checks for single-shot error correction.
  arXiv  Detail & Related papers  (2023-10-19T12:23:05Z)
• Fault-Tolerant Computing with Single Qudit Encoding [49.89725935672549]
  We discuss stabilizer quantum-error correction codes implemented in a single multi-level qudit. These codes can be customized to the specific physical errors on the qudit, effectively suppressing them. We demonstrate a Fault-Tolerant implementation on molecular spin qudits, showcasing nearly exponential error suppression with only linear qudit size growth.
  arXiv  Detail & Related papers  (2023-07-20T10:51:23Z)
• Correcting non-independent and non-identically distributed errors with surface codes [0.8039067099377079]
  We develop and investigate the properties of topological surface codes adapted to a known noise structure by Clifford conjugations. We show that the surface code locally tailored to non-uniform single-qubit noise in conjunction with a scalable matching decoder yields an increase in error thresholds and exponential suppression of sub-threshold failure rates.
  arXiv  Detail & Related papers  (2022-08-03T16:21:44Z)
• Improved single-shot decoding of higher dimensional hypergraph product codes [5.33024001730262]
  We study the single-shot performance of higher dimensional hypergraph product codes decoded using belief-propagation and ordered-statistics. We find that decoding data qubit and syndrome measurement errors together in a single stage leads to single-shot thresholds that greatly exceed all previously observed single-shot thresholds for these codes.
  arXiv  Detail & Related papers  (2022-06-07T08:55:34Z)
• 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)
• 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)
• Entanglement purification by counting and locating errors with entangling measurements [62.997667081978825]
  We consider entanglement purification protocols for multiple copies of qubit states. We use high-dimensional auxiliary entangled systems to learn about number and positions of errors in the noisy ensemble.
  arXiv  Detail & Related papers  (2020-11-13T19:02:33Z)
• Efficient and robust certification of genuine multipartite entanglement in noisy quantum error correction circuits [58.720142291102135]
  We introduce a conditional witnessing technique to certify genuine multipartite entanglement (GME) We prove that the detection of entanglement in a linear number of bipartitions by a number of measurements scales linearly, suffices to certify GME. We apply our method to the noisy readout of stabilizer operators of the distance-three topological color code and its flag-based fault-tolerant version.
  arXiv  Detail & Related papers  (2020-10-06T18:00:07Z)
• Cellular automaton decoders for topological quantum codes with noisy measurements and beyond [68.8204255655161]
  We propose an error correction procedure based on a cellular automaton, the sweep rule, which is applicable to a broad range of codes beyond topological quantum codes. For simplicity, we focus on the three-dimensional (3D) toric code on the rhombic dodecahedral lattice with boundaries and prove that the resulting local decoder has a non-zero error threshold. We find that this error correction procedure is remarkably robust against measurement errors and is also essentially insensitive to the details of the lattice and noise model.
  arXiv  Detail & Related papers  (2020-04-15T18:00:01Z)

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.