Performance analysis of GKP error correction

• URL: http://arxiv.org/abs/2505.14775v1
• Date: Tue, 20 May 2025 18:00:01 GMT
• Title: Performance analysis of GKP error correction
• Authors: Frederik K. Marqversen, Janus H. Wesenberg, Nikolaj T. Zinner, Ulrik L. Andersen,
• Abstract summary: Gottesman-Kitaev-Preskill codes are particularly effective at correcting continuous noise, such as Gaussian noise and loss.<n>GKP error correction can be implemented using either a teleportation-based method, known as Knill error correction, or a quantum non-demolition-based approach, known as Steane error correction.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum error correction is essential for achieving fault-tolerant quantum computing. Gottesman-Kitaev-Preskill (GKP) codes are particularly effective at correcting continuous noise, such as Gaussian noise and loss, and can significantly reduce overhead when concatenated with qubit error-correcting codes like surface codes. GKP error correction can be implemented using either a teleportation-based method, known as Knill error correction, or a quantum non-demolition-based approach, known as Steane error correction. In this work, we conduct a comprehensive performance analysis of these established GKP error correction schemes, deriving an analytical expression for the post-correction GKP squeezing and displacement errors. Our results show that there is flexibility in choosing the entangling gate used with the teleportation-based Knill approach. Furthermore, when implemented using the recently introduced qunaught states, the Knill approach not only achieves superior GKP squeezing compared to other variants but is also the simplest to realize experimentally in the optical domain.

Related papers

• General Approach to Error Detection of Bosonic Codes via Phase Estimation [2.1799192736303783]
  We present a general approach to error detection of bosonic quantum error-correction codes via an adaptive quantum phase estimation algorithm.<n>The approach is applicable to a broad class of bosonic codes whose error syndromes are described by symmetry or stabilizer operators.
  arXiv  Detail & Related papers  (2025-07-05T10:55:56Z)
• Correcting biased noise using Gottesman-Kitaev-Preskill repetition code with noisy ancilla [0.6802401545890963]
  Gottesman-Kitaev-Preskill (GKP) code is proposed to correct small displacement error in phase space. If noise in phase space is biased, square-lattice GKP code can be ancillaryd with XZZX surface code or repetition code. We study the performance of GKP repetition codes with physical ancillary GKP qubits in correcting biased noise.
  arXiv  Detail & Related papers  (2023-08-03T06:14:43Z)
• Compilation of a simple chemistry application to quantum error correction primitives [44.99833362998488]
  We estimate the resources required to fault-tolerantly perform quantum phase estimation on a minimal chemical example. We find that implementing even a simple chemistry circuit requires 1,000 qubits and 2,300 quantum error correction rounds.
  arXiv  Detail & Related papers  (2023-07-06T18:00:10Z)
• Robust suppression of noise propagation in GKP error-correction [0.0]
  Recently reported generation and error-correction of GKP qubits holds great promise for the future of quantum computing. We develop efficient numerical methods to optimize our protocol parameters. Our approach circumvents the main roadblock towards fault-tolerant quantum computation with GKP qubits.
  arXiv  Detail & Related papers  (2023-02-23T15:21:50Z)
• Sharp Calibrated Gaussian Processes [58.94710279601622]
  State-of-the-art approaches for designing calibrated models rely on inflating the Gaussian process posterior variance. We present a calibration approach that generates predictive quantiles using a computation inspired by the vanilla Gaussian process posterior variance. Our approach is shown to yield a calibrated model under reasonable assumptions.
  arXiv  Detail & Related papers  (2023-02-23T12:17:36Z)
• 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)
• Analysis of loss correction with the Gottesman-Kitaev-Preskill code [0.0]
  The Gottesman-Kitaev-Preskill (GKP) code is a promising bosonic quantum error-correcting code. We show that amplification is not required to perform GKP error correction.
  arXiv  Detail & Related papers  (2021-12-02T17:15:21Z)
• 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)
• Low overhead fault-tolerant quantum error correction with the surface-GKP code [60.44022726730614]
  We propose a highly effective use of the surface-GKP code, i.e., the surface code consisting of bosonic GKP qubits instead of bare two-dimensional qubits. We show that a low logical failure rate $p_L 10-7$ can be achieved with moderate hardware requirements.
  arXiv  Detail & Related papers  (2021-03-11T23:07:52Z)
• Crosstalk Suppression for Fault-tolerant Quantum Error Correction with Trapped Ions [62.997667081978825]
  We present a study of crosstalk errors in a quantum-computing architecture based on a single string of ions confined by a radio-frequency trap, and manipulated by individually-addressed laser beams. This type of errors affects spectator qubits that, ideally, should remain unaltered during the application of single- and two-qubit quantum gates addressed at a different set of active qubits. We microscopically model crosstalk errors from first principles and present a detailed study showing the importance of using a coherent vs incoherent error modelling and, moreover, discuss strategies to actively suppress this crosstalk at the gate level.
  arXiv  Detail & Related papers  (2020-12-21T14:20:40Z)
• 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)
• Towards Scalable Bosonic Quantum Error Correction [1.6328866317851185]
  We present some new results on decoding repeated GKP error using finitely-squeezed GKP ancilla qubits. We discuss circuit-QED ways to realize CZ gates between GKP qubits and we discuss different scenario's for using GKP and regular qubits as building blocks in a scalable superconducting surface code architecture.
  arXiv  Detail & Related papers  (2020-02-25T16:29:31Z)

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.