Low-overhead pieceable fault-tolerant construction of logical controlled-phase circuit for degenerate quantum code

• URL: http://arxiv.org/abs/2105.07133v8
• Date: Wed, 29 Nov 2023 13:26:34 GMT
• Title: Low-overhead pieceable fault-tolerant construction of logical controlled-phase circuit for degenerate quantum code
• Authors: Chen Lin, Guowu Yang
• Abstract summary: We search for a non-transversal but fault-tolerant construction of a logical controlled-phase gate for quantum code. We find a 3-piece fault-tolerant logical CZ circuit on this code.
• Score: 11.106110829349221
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: We designed an search algorithm in order to find a non-transversal but fault-tolerant construction of a logical controlled-phase gate for general [[n,1,d]] degenerate quantum code. Then we give an example to illustrate our algorithm for a quantum code called bare [[7, 1, 3]] code. This code is obtained under certain search criteria, and it possesses a simpler flag-assisted fault-tolerant syndrome measurement circuit under a standard depolarizing error model. Since a syndrome extraction circuit requiring fewer ancillary qubit resources would facilitate the realization of large-scale quantum computations, such as concatenated high level elementary logical gate circuits when aim to achieve lower logical error rates, we follow our search scheme and find a 3-pieceable fault-tolerant logical CZ circuit on this code. Numerical simulations are also performed to further analyze the logical error rate of our circuit.

Related papers

• Algorithmic Fault Tolerance for Fast Quantum Computing [37.448838730002905]
  We show that fault-tolerant logical operations can be performed with constant time overhead for a broad class of quantum codes. We prove that the deviation from the ideal measurement result distribution can be made exponentially small in the code distance. Our work sheds new light on the theory of fault tolerance, potentially reducing the space-time cost of practical fault-tolerant quantum computation by orders of magnitude.
  arXiv  Detail & Related papers  (2024-06-25T15:43:25Z)
• Benchmarking logical three-qubit quantum Fourier transform encoded in the Steane code on a trapped-ion quantum computer [3.2821436094760026]
  We logically encoded three-qubit circuits for the quantum transform (QFT) We benchmark the circuits on the Quantinuum H2-11 trapped-ion quantum computer. We compare the logical QFT benchmark results to predictions based on the logical component benchmarks.
  arXiv  Detail & Related papers  (2024-04-12T17:27:27Z)
• Experimental fault-tolerant code switching [1.9088985324817254]
  We present the first experimental implementation of fault-tolerant code switching between two codes. We construct logical circuits and prepare 12 different logical states which are not accessible in a fault-tolerant way within a single code. Our results experimentally open up a new route towards deterministic control over logical qubits with low auxiliary qubit overhead.
  arXiv  Detail & Related papers  (2024-03-20T16:40:57Z)
• Low-density parity-check representation of fault-tolerant quantum circuits [5.064729356056529]
  This paper presents a toolkit for designing and analysing fault-tolerant quantum circuits. We introduce a framework for representing stabiliser circuits using classical low-density parity-check codes. We outline the procedure for generating LDPC codes from circuits using the Tanner graph notation.
  arXiv  Detail & Related papers  (2024-03-15T12:56:38Z)
• 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)
• A Quantum Algorithm for Computing All Diagnoses of a Switching Circuit [73.70667578066775]
  Faults are by nature while most man-made systems, and especially computers, work deterministically. This paper provides such a connecting via quantum information theory which is an intuitive approach as quantum physics obeys probability laws.
  arXiv  Detail & Related papers  (2022-09-08T17:55:30Z)
• Fault-tolerant circuit synthesis for universal fault-tolerant quantum computing [0.0]
  We present a quantum circuit synthesis algorithm for implementing universal fault-tolerant quantum computing based on geometricd codes. We show how to synthesize the set of universal fault-tolerant protocols for $[[7,1,3]]$ Steane code and the syndrome measurement protocol of $[[23, 1, 7]]$ Golay code.
  arXiv  Detail & Related papers  (2022-06-06T15:43:36Z)
• Quantum circuit debugging and sensitivity analysis via local inversions [62.997667081978825]
  We present a technique that pinpoints the sections of a quantum circuit that affect the circuit output the most. We demonstrate the practicality and efficacy of the proposed technique by applying it to example algorithmic circuits implemented on IBM quantum machines.
  arXiv  Detail & Related papers  (2022-04-12T19:39:31Z)
• Logical blocks for fault-tolerant topological quantum computation [55.41644538483948]
  We present a framework for universal fault-tolerant logic motivated by the need for platform-independent logical gate definitions. We explore novel schemes for universal logic that improve resource overheads. Motivated by the favorable logical error rates for boundaryless computation, we introduce a novel computational scheme.
  arXiv  Detail & Related papers  (2021-12-22T19:00:03Z)
• Finding the disjointness of stabilizer codes is NP-complete [77.34726150561087]
  We show that the problem of calculating the $c-disjointness, or even approximating it to within a constant multiplicative factor, is NP-complete. We provide bounds on the disjointness for various code families, including the CSS codes,$d codes and hypergraph codes. Our results indicate that finding fault-tolerant logical gates for generic quantum error-correcting codes is a computationally challenging task.
  arXiv  Detail & Related papers  (2021-08-10T15:00:20Z)
• Hardware-Encoding Grid States in a Non-Reciprocal Superconducting Circuit [62.997667081978825]
  We present a circuit design composed of a non-reciprocal device and Josephson junctions whose ground space is doubly degenerate and the ground states are approximate codewords of the Gottesman-Kitaev-Preskill (GKP) code. We find that the circuit is naturally protected against the common noise channels in superconducting circuits, such as charge and flux noise, implying that it can be used for passive quantum error correction.
  arXiv  Detail & Related papers  (2020-02-18T16:45:09Z)

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.