Theory of quasi-exact fault-tolerant quantum computing and valence-bond-solid codes

• URL: http://arxiv.org/abs/2105.14777v1
• Date: Mon, 31 May 2021 08:17:30 GMT
• Title: Theory of quasi-exact fault-tolerant quantum computing and valence-bond-solid codes
• Authors: Dong-Sheng Wang, Yun-Jiang Wang, Ningping Cao, Bei Zeng, Raymond Laflamme
• Abstract summary: We develop the theory of quasi-exact fault-tolerant quantum computation, which uses qubits encoded into quasi-exact quantum error-correction codes ("quasi codes") The model of QEQ lies in between the two well-known ones: the usual noisy quantum universality without error correction and the usual fault-tolerant quantum computation, but closer to the later.
• Score: 3.6192409729339223
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: In this work, we develop the theory of quasi-exact fault-tolerant quantum (QEQ) computation, which uses qubits encoded into quasi-exact quantum error-correction codes ("quasi codes"). By definition, a quasi code is a parametric approximate code that can become exact by tuning its parameters. The model of QEQ computation lies in between the two well-known ones: the usual noisy quantum computation without error correction and the usual fault-tolerant quantum computation, but closer to the later. Many notions of exact quantum codes need to be adjusted for the quasi setting. Here we develop quasi error-correction theory using quantum instrument, the notions of quasi universality, quasi code distances, and quasi thresholds, etc. We find a wide class of quasi codes which are called valence-bond-solid codes, and we use them as concrete examples to demonstrate QEQ computation.

Related papers

• Weakly Fault-Tolerant Computation in a Quantum Error-Detecting Code [0.0]
  Many current quantum error correcting codes that achieve full fault-tolerance suffer from having low ratios of logical to physical qubits and significant overhead. We propose a middle ground: constructions in the [[n,n-2,2]] quantum error detecting code that can detect any error from a single faulty gate.
  arXiv  Detail & Related papers  (2024-08-27T07:25:36Z)
• Many-hypercube codes: High-rate quantum error-correcting codes for high-performance fault-tolerant quantum computing [0.0]
  We propose high-rate small-size quantum error-detecting codes as a new family of high-rate quantum codes. Their simple structure allows for a geometrical interpretation using hypercubes corresponding to logical qubits. We achieve high error thresholds even in a circuit-level noise model.
  arXiv  Detail & Related papers  (2024-03-24T07:46:26Z)
• Single-shot decoding of good quantum LDPC codes [38.12919328528587]
  We prove that quantum Tanner codes facilitate single-shot quantum error correction (QEC) of adversarial noise. We show that in order to suppress errors over multiple repeated rounds of QEC, it suffices to run the parallel decoding algorithm for constant time in each round.
  arXiv  Detail & Related papers  (2023-06-21T18:00:01Z)
• Quantum process tomography of continuous-variable gates using coherent states [49.299443295581064]
  We demonstrate the use of coherent-state quantum process tomography (csQPT) for a bosonic-mode superconducting circuit. We show results for this method by characterizing a logical quantum gate constructed using displacement and SNAP operations on an encoded qubit.
  arXiv  Detail & Related papers  (2023-03-02T18:08:08Z)
• Simple Tests of Quantumness Also Certify Qubits [69.96668065491183]
  A test of quantumness is a protocol that allows a classical verifier to certify (only) that a prover is not classical. We show that tests of quantumness that follow a certain template, which captures recent proposals such as (Kalai et al., 2022) can in fact do much more. Namely, the same protocols can be used for certifying a qubit, a building-block that stands at the heart of applications such as certifiable randomness and classical delegation of quantum computation.
  arXiv  Detail & Related papers  (2023-03-02T14:18:17Z)
• Quantum Worst-Case to Average-Case Reductions for All Linear Problems [66.65497337069792]
  We study the problem of designing worst-case to average-case reductions for quantum algorithms. We provide an explicit and efficient transformation of quantum algorithms that are only correct on a small fraction of their inputs into ones that are correct on all inputs.
  arXiv  Detail & Related papers  (2022-12-06T22:01:49Z)
• Theory of Quantum Generative Learning Models with Maximum Mean Discrepancy [67.02951777522547]
  We study learnability of quantum circuit Born machines (QCBMs) and quantum generative adversarial networks (QGANs) We first analyze the generalization ability of QCBMs and identify their superiorities when the quantum devices can directly access the target distribution. Next, we prove how the generalization error bound of QGANs depends on the employed Ansatz, the number of qudits, and input states.
  arXiv  Detail & Related papers  (2022-05-10T08:05:59Z)
• Quantum variational learning for quantum error-correcting codes [5.627733119443356]
  VarQEC is a noise-resilient variational quantum algorithm to search for quantum codes with a hardware-efficient encoding circuit. In principle, VarQEC can find quantum codes for any error model, whether additive or non-additive, or non-degenerate, pure or impure.
  arXiv  Detail & Related papers  (2022-04-07T16:38:27Z)
• Depth-efficient proofs of quantumness [77.34726150561087]
  A proof of quantumness is a type of challenge-response protocol in which a classical verifier can efficiently certify quantum advantage of an untrusted prover. In this paper, we give two proof of quantumness constructions in which the prover need only perform constant-depth quantum circuits.
  arXiv  Detail & Related papers  (2021-07-05T17:45:41Z)
• Quantum Low-Density Parity-Check Codes [9.13755431537592]
  We discuss a particular class of quantum codes called low-density parity-check (LDPC) quantum codes. We introduce the zoo of LDPC quantum codes and discuss their potential for making quantum computers robust against noise.
  arXiv  Detail & Related papers  (2021-03-10T19:19:37Z)
• Fault-tolerant Coding for Quantum Communication [71.206200318454]
  encode and decode circuits to reliably send messages over many uses of a noisy channel. For every quantum channel $T$ and every $eps>0$ there exists a threshold $p(epsilon,T)$ for the gate error probability below which rates larger than $C-epsilon$ are fault-tolerantly achievable. Our results are relevant in communication over large distances, and also on-chip, where distant parts of a quantum computer might need to communicate under higher levels of noise.
  arXiv  Detail & Related papers  (2020-09-15T15:10:50Z)

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.