Existence of Pauli-like stabilizers for every quantum error-correcting code

• URL: http://arxiv.org/abs/2308.15437v1
• Date: Tue, 29 Aug 2023 17:01:17 GMT
• Title: Existence of Pauli-like stabilizers for every quantum error-correcting code
• Authors: Jhih-Yuan Kao and Hsi-Sheng Goan
• Abstract summary: We will show that every quantum error-correcting code has a similar structure, in that the code can be stabilized by commutative Paulian'' operators. Examples concerning codeword stabilized codes and bosonic codes will be presented.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: The Pauli stabilizer formalism is perhaps the most thoroughly studied means of procuring quantum error-correcting codes, whereby the code is obtained through commutative Pauli operators and ``stabilized'' by them. In this work we will show that every quantum error-correcting code, including Pauli stabilizer codes and subsystem codes, has a similar structure, in that the code can be stabilized by commutative ``Paulian'' operators which share many features with Pauli operators and which form a \textbf{Paulian stabilizer group}. By facilitating a controlled gate we can measure these Paulian operators to acquire the error syndrome. Examples concerning codeword stabilized codes and bosonic codes will be presented; specifically, one of the examples has been demonstrated experimentally and the observable for detecting the error turns out to be Paulian, thereby showing the potential utility of this approach. This work provides a possible approach to implement error-correcting codes and to find new codes.

Related papers

• Belief Propagation Decoding of Quantum LDPC Codes with Guided Decimation [55.8930142490617]
  We propose a decoder for QLDPC codes based on BP guided decimation (BPGD) BPGD significantly reduces the BP failure rate due to non-convergence.
  arXiv  Detail & Related papers  (2023-12-18T05:58:07Z)
• A family of permutationally invariant quantum codes [54.835469342984354]
  We show that codes in the new family correct quantum deletion errors as well as spontaneous decay errors. Our construction contains some of the previously known permutationally invariant quantum codes. For small $t$, these conditions can be used to construct new examples of codes by computer.
  arXiv  Detail & Related papers  (2023-10-09T02:37:23Z)
• 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)
• Exponential suppression of Pauli errors in Majorana qubits via quasiparticle detection [0.0]
  Error-detecting Majorana stabilizer codes are constructed whose stabilizers can be measured by means of Wannier position operators. For a logical qubit encoded in one of these codes, the Pauli error rates are exponentially suppressed in the code distance. The work also demonstrates that the theory of Wannier functions could lead to error correcting codes beyond the standard stabilizer codes.
  arXiv  Detail & Related papers  (2023-07-17T23:50:09Z)
• Pauli Manipulation Detection codes and Applications to Quantum Communication over Adversarial Channels [0.08702432681310403]
  We introduce and explicitly construct a quantum code we coin a "Pauli Manipulation Detection" code (or PMD), which detects every Pauli error with high probability. We apply them to construct the first near-optimal codes for two tasks in quantum communication over adversarial channels.
  arXiv  Detail & Related papers  (2023-04-13T05:05:35Z)
• Experimental realization of deterministic and selective photon addition in a bosonic mode assisted by an ancillary qubit [50.591267188664666]
  Bosonic quantum error correcting codes are primarily designed to protect against single-photon loss. Error correction requires a recovery operation that maps the error states -- which have opposite parity -- back onto the code states. Here, we realize a collection of photon-number-selective, simultaneous photon addition operations on a bosonic mode.
  arXiv  Detail & Related papers  (2022-12-22T23:32:21Z)
• Transforming Collections of Pauli Operators into Equivalent Collections of Pauli Operators over Minimal Registers [0.0]
  We prove the obtainable lower-bound for the number of qubits needed to represent such Pauli operations. We provide a procedure for determining such a set of minimal register Pauli operations.
  arXiv  Detail & Related papers  (2022-06-27T04:22:30Z)
• 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)
• Pauli channels can be estimated from syndrome measurements in quantum error correction [0.7264378254137809]
  We show that a stabilizer code can be used to estimate Pauli channels with correlations across a number of qubits given by the pure distance. It also allows for measurement errors within the framework of quantum data-syndrome codes. It is our hope that this work opens up interesting applications, such as the online adaptation of a decoder to time-varying noise.
  arXiv  Detail & Related papers  (2021-07-29T18:01:10Z)
• Short Codes for Quantum Channels with One Prevalent Pauli Error Type [6.548580592686076]
  We investigate the design of stabilizer QECC able to correct a given number eg of generic Pauli errors, plus eZ Pauli errors of a specified type. These codes can be of interest when the quantum channel is asymmetric in that some types of error occur more frequently than others.
  arXiv  Detail & Related papers  (2021-04-09T13:51:51Z)
• Coherent randomized benchmarking [68.8204255655161]
  We show that superpositions of different random sequences rather than independent samples are used. We show that this leads to a uniform and simple protocol with significant advantages with respect to gates that can be benchmarked.
  arXiv  Detail & Related papers  (2020-10-26T18:00:34Z)

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.