Low overhead fault-tolerant quantum error correction with the surface-GKP code

• URL: http://arxiv.org/abs/2103.06994v2
• Date: Sat, 29 Jan 2022 05:35:49 GMT
• Title: Low overhead fault-tolerant quantum error correction with the surface-GKP code
• Authors: Kyungjoo Noh, Christopher Chamberland, Fernando G.S.L. Brand\~ao
• Abstract summary: 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.
• Score: 60.44022726730614
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Fault-tolerant quantum error correction is essential for implementing quantum algorithms of significant practical importance. In this work, 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. In our proposal, we use error-corrected two-qubit gates between GKP qubits and introduce a maximum likelihood decoding strategy for correcting shift errors in the two-GKP-qubit gates. Our proposed decoding reduces the total CNOT failure rate of the GKP qubits, e.g., from $0.87\%$ to $0.36\%$ at a GKP squeezing of $12$dB, compared to the case where the simple closest-integer decoding is used. Then, by concatenating the GKP code with the surface code, we find that the threshold GKP squeezing is given by $9.9$dB under the the assumption that finite-squeezing of the GKP states is the dominant noise source. More importantly, we show that a low logical failure rate $p_{L} < 10^{-7}$ can be achieved with moderate hardware requirements, e.g., $291$ modes and $97$ qubits at a GKP squeezing of $12$dB as opposed to $1457$ bare qubits for the standard rotated surface code at an equivalent noise level (i.e., $p=0.36\%$). Such a low failure rate of our surface-GKP code is possible through the use of space-time correlated edges in the matching graphs of the surface code decoder. Further, all edge weights in the matching graphs are computed dynamically based on analog information from the GKP error correction using the full history of all syndrome measurement rounds. We also show that a highly-squeezed GKP state of GKP squeezing $\gtrsim 12$dB can be experimentally realized by using a dissipative stabilization method, namely, the Big-small-Big method, with fairly conservative experimental parameters. Lastly, we introduce a three-level ancilla scheme to mitigate ancilla decay errors during a GKP state preparation.

Related papers

• Bit-flipping Decoder Failure Rate Estimation for (v,w)-regular Codes [84.0257274213152]
  We propose a new technique to provide accurate estimates of the DFR of a two-iterations (parallel) bit flipping decoder. We validate our results, providing comparisons of the modeled and simulated weight of the syndrome, incorrectly-guessed error bit distribution at the end of the first iteration, and two-itcrypteration Decoding Failure Rates (DFR)
  arXiv  Detail & Related papers  (2024-01-30T11:40:24Z)
• 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)
• Biased Gottesman-Kitaev-Preskill repetition code [0.0]
  Continuous-variable quantum computing architectures based upon the Gottesmann-Kitaev-Preskill (GKP) encoding have emerged as a promising candidate. We study the code-capacity behaviour of a rectangular-lattice GKP encoding with a repetition code under an isotropic Gaussian displacement channel.
  arXiv  Detail & Related papers  (2022-12-21T22:56:05Z)
• Quantum computation on a 19-qubit wide 2d nearest neighbour qubit array [59.24209911146749]
  This paper explores the relationship between the width of a qubit lattice constrained in one dimension and physical thresholds. We engineer an error bias at the lowest level of encoding using the surface code. We then address this bias at a higher level of encoding using a lattice-surgery surface code bus.
  arXiv  Detail & Related papers  (2022-12-03T06:16:07Z)
• Concatenation of the Gottesman-Kitaev-Preskill code with the XZZX surface code [1.2999413717930821]
  An important category of bosonic codes called the Gottesman-Kitaev-Preskill (GKP) code has aroused much interest recently. The error correction ability of GKP code is limited since it can only correct small shift errors in position and momentum quadratures. A natural approach to promote the GKP error correction for large-scale, fault-tolerant quantum computation is concatenating encoded GKP states with a stabilizer code.
  arXiv  Detail & Related papers  (2022-07-10T04:50:33Z)
• Normalized/Clipped SGD with Perturbation for Differentially Private Non-Convex Optimization [94.06564567766475]
  DP-SGD and DP-NSGD mitigate the risk of large models memorizing sensitive training data. We show that these two algorithms achieve similar best accuracy while DP-NSGD is comparatively easier to tune than DP-SGD.
  arXiv  Detail & Related papers  (2022-06-27T03:45:02Z)
• Improved decoding of circuit noise and fragile boundaries of tailored surface codes [61.411482146110984]
  We introduce decoders that are both fast and accurate, and can be used with a wide class of quantum error correction codes. Our decoders, named belief-matching and belief-find, exploit all noise information and thereby unlock higher accuracy demonstrations of QEC. We find that the decoders led to a much higher threshold and lower qubit overhead in the tailored surface code with respect to the standard, square surface code.
  arXiv  Detail & Related papers  (2022-03-09T18:48:54Z)
• Quantum error correction with the color-Gottesman-Kitaev-Preskill code [5.780815306252637]
  The Gottesman-Kitaev-Preskill (GKP) code is an important type of bosonic quantum error-correcting code. In this paper, we consider the concatenation of the single-mode GKP code with the two-dimension (2D) color code.
  arXiv  Detail & Related papers  (2021-12-29T08:19:36Z)
• 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)
• Enhanced noise resilience of the surface-GKP code via designed bias [0.0]
  We study the code obtained by concatenating the standard single-mode Gottesman-Kitaev-Preskill (GKP) code with the surface code. We show that the noise tolerance of this surface-GKP code with respect to (Gaussian) displacement errors improves when a single-mode squeezing unitary is applied to each mode.
  arXiv  Detail & Related papers  (2020-04-01T16:08:52Z)

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.