Entanglement-assisted Quantum Reed-Muller Tensor Product Codes
- URL: http://arxiv.org/abs/2303.08294v3
- Date: Sun, 21 Apr 2024 15:22:34 GMT
- Title: Entanglement-assisted Quantum Reed-Muller Tensor Product Codes
- Authors: Priya J. Nadkarni, Praveen Jayakumar, Arpit Behera, Shayan Srinivasa Garani,
- Abstract summary: We show that entanglement-assisted (EA) qubit Reed-Muller (RM) codes have zero coding rate and negative catalytic rate.
We also show that EA codes constructed from these same classical RM codes using the tensor product code (TPC) construction have positive coding rate.
- Score: 2.099922236065961
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We present the construction of standard entanglement-assisted (EA) qubit Reed-Muller (RM) codes and their tensor product variants from classical RM codes. We show that the EA RM codes obtained using the CSS construction have zero coding rate and negative catalytic rate. We further show that EA codes constructed from these same classical RM codes using the tensor product code (TPC) construction have positive coding rate and provide a subclass of EA RM TPCs that have positive catalytic rate, thus establishing the coding analog of superadditivity for this family of codes, useful towards quantum communications. We also generalize this analysis to obtain conditions for EA TPCs from classical codes to have positive catalytic rate when their corresponding EA CSS codes have zero rate.
Related papers
- Coherent information for CSS codes under decoherence [0.0]
A class called Calderbank-Shor-Steane (CSS) codes includes many important examples such as toric codes, color codes, and fractons.
Recent studies have revealed that the decoding transition for these QECCs could be intrinsically captured by calculating information-theoretic quantities from the mixed state.
arXiv Detail & Related papers (2024-07-02T18:00:02Z) - Uncovering LLM-Generated Code: A Zero-Shot Synthetic Code Detector via Code Rewriting [78.48355455324688]
We propose a novel zero-shot synthetic code detector based on the similarity between the code and its rewritten variants.
Our results demonstrate a notable enhancement over existing synthetic content detectors designed for general texts.
arXiv Detail & Related papers (2024-05-25T08:57:28Z) - Lifts of quantum CSS codes [0.0]
We propose a notion of lift for quantum CSS codes, inspired by the geometrical construction of Freedman and Hastings.
It is based on the existence of a canonical complex associated to any CSS code, that we introduce under the name of Tanner cone-complex.
arXiv Detail & Related papers (2024-04-25T16:44:45Z) - 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 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) - CSS code surgery as a universal construction [51.63482609748332]
We define code maps between Calderbank-Shor-Steane (CSS) codes using maps between chain complexes.
We describe code surgery between such codes using a specific colimit in the category of chain complexes.
arXiv Detail & Related papers (2023-01-31T16:17:25Z) - Neural Belief Propagation Decoding of Quantum LDPC Codes Using
Overcomplete Check Matrices [60.02503434201552]
We propose to decode QLDPC codes based on a check matrix with redundant rows, generated from linear combinations of the rows in the original check matrix.
This approach yields a significant improvement in decoding performance with the additional advantage of very low decoding latency.
arXiv Detail & Related papers (2022-12-20T13:41:27Z) - Classical product code constructions for quantum Calderbank-Shor-Steane codes [1.4699455652461726]
We introduce a new product code construction which is a natural generalisation of classical product codes to quantum codes.
We show that built-in redundancies in the parity checks result in so-called meta-checks which can be exploited to correct syndrome read-out errors.
arXiv Detail & Related papers (2022-09-27T15:48:37Z) - Grand Unification of continuous-variable codes [0.0]
Quantum error correction codes in continuous variables (also called CV codes, or single-mode bosonic codes) have been identified to be a technologically viable option for building fault-tolerant quantum computers.
Best-known examples are the GKP code and the cat-code, both of which were shown to have some advantageous properties over any discrete-variable, or qubit codes.
It was recently shown that the cat-code, as well as other kinds of CV codes, belong to a set of codes with common properties called rotation-symmetric codes.
arXiv Detail & Related papers (2022-06-03T18:00:01Z) - KO codes: Inventing Nonlinear Encoding and Decoding for Reliable
Wireless Communication via Deep-learning [76.5589486928387]
Landmark codes underpin reliable physical layer communication, e.g., Reed-Muller, BCH, Convolution, Turbo, LDPC and Polar codes.
In this paper, we construct KO codes, a computationaly efficient family of deep-learning driven (encoder, decoder) pairs.
KO codes beat state-of-the-art Reed-Muller and Polar codes, under the low-complexity successive cancellation decoding.
arXiv Detail & Related papers (2021-08-29T21:08:30Z) - Asymmetric Quantum Concatenated and Tensor Product Codes with Large
Z-Distances [27.90363292358871]
We present a new construction of asymmetric quantum codes (AQCs) by combining classical tensord codes (CCs) with tensor product codes (TPCs)
Most AQCTPCs are highly degenerate, which means they can correct many more errors than their classical counterparts.
We generalize our concatenation scheme by using the generalized CCs and TPCs.
arXiv Detail & Related papers (2020-12-01T02:43:24Z)
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.