Quotient Space Quantum Codes
- URL: http://arxiv.org/abs/2311.07265v4
- Date: Thu, 7 Mar 2024 15:54:28 GMT
- Title: Quotient Space Quantum Codes
- Authors: Jing-Lei Xia
- Abstract summary: This letter establishes the quotient space codes to construct quantum codes.
This new code unifies additive codes and codeword stabilized codes and can transmit classical codewords.
The quotient space approach offers a concise and clear mathematical form for the study of quantum error-correcting codes.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Additive codes and some nonadditive codes use the single and multiple
invariant subspaces of the stabilizer G to construct quantum codes,
respectively, so the selection of invariant subspaces is a key issue. In this
letter, I provide the necessary and sufficient conditions for this problem and,
for the first time, establish the quotient space codes to construct quantum
codes. This new code unifies additive codes and codeword stabilized codes and
can transmit classical codewords. New bounds for quantum codes are presented
also, and a simple proof of the quantum Singleton bound is provided. The
quotient space approach offers a concise and clear mathematical form for the
study of quantum error-correcting codes.
Related papers
- Characterization of Nearly Self-Orthogonal Quasi-Twisted Codes and Related Quantum Codes [16.55015892533456]
The construction utilizes nearly self-orthogonal codes to design quantum stabilizer codes.
A refined lower bound on the minimum distance of the resulting quantum codes is established.
We report numerous record breaking quantum codes from our randomized search for inclusion in the updated online database.
arXiv Detail & Related papers (2024-05-23T21:10:23Z) - Homological Quantum Rotor Codes: Logical Qubits from Torsion [51.9157257936691]
homological quantum rotor codes allow one to encode both logical rotors and logical qudits in the same block of code.
We show that the $0$-$pi$-qubit as well as Kitaev's current-mirror qubit are indeed small examples of such codes.
arXiv Detail & Related papers (2023-03-24T00:29:15Z) - 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) - Quantum spherical codes [55.33545082776197]
We introduce a framework for constructing quantum codes defined on spheres by recasting such codes as quantum analogues of the classical spherical codes.
We apply this framework to bosonic coding, obtaining multimode extensions of the cat codes that can outperform previous constructions.
arXiv Detail & Related papers (2023-02-22T19:00:11Z) - Gaussian conversion protocol for heralded generation of qunaught states [66.81715281131143]
bosonic codes map qubit-type quantum information onto the larger bosonic Hilbert space.
We convert between two instances of these codes GKP qunaught states and four-foldsymmetric binomial states corresponding to a zero-logical encoded qubit.
We obtain GKP qunaught states with a fidelity of over 98% and a probability of approximately 3.14%.
arXiv Detail & Related papers (2023-01-24T14:17:07Z) - 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) - Quantum Error Correction via Noise Guessing Decoding [0.0]
Quantum error correction codes (QECCs) play a central role in both quantum communications and quantum computation.
This paper shows that it is possible to both construct and decode QECCs that can attain the maximum performance of the finite blocklength regime.
arXiv Detail & Related papers (2022-08-04T16:18:20Z) - New Binary Quantum Codes Constructed from Quasi-Cyclic Codes [6.718184400443239]
It is well known that quantum codes can be constructed by means of classical symplectic dual-containing codes.
This paper considers a family of two-generator quasi-cyclic codes and derives sufficient conditions for these codes to be symplectic dual-containing.
As an application, we construct 8 binary quantum codes that exceed the best-known results.
arXiv Detail & Related papers (2021-12-14T03:22:16Z) - 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) - Constructing quantum codes from any classical code and their embedding
in ground space of local Hamiltonians [6.85316573653194]
We give an algorithm that explicitly constructs quantum codes with linear distance and constant rate.
Motivated by quantum LDPC codes and the use of physics to protect quantum information, we introduce a new 2-local frustration free quantum spin chain Hamiltonian.
arXiv Detail & Related papers (2020-12-02T19:00:19Z) - Quantum error-correcting codes and their geometries [0.6445605125467572]
This article aims to introduce the reader to the underlying mathematics and geometry of quantum error correction.
We go on to construct quantum codes: firstly qubit stabilizer codes, then qubit non-stabilizer codes, and finally codes with a higher local dimension.
This allows one to deduce the parameters of the code efficiently, deduce the inequivalence between codes that have the same parameters, and presents a useful tool in deducing the feasibility of certain parameters.
arXiv Detail & Related papers (2020-07-12T13:57:39Z)
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.