Quantum Lego Expansion Pack: Enumerators from Tensor Networks
- URL: http://arxiv.org/abs/2308.05152v2
- Date: Sat, 2 Mar 2024 04:29:13 GMT
- Title: Quantum Lego Expansion Pack: Enumerators from Tensor Networks
- Authors: ChunJun Cao, Michael J. Gullans, Brad Lackey, Zitao Wang
- Abstract summary: We provide the first tensor network method for computing quantum weight enumerators in the most general form.
For non-(Pauli)-stabilizer codes, this constitutes the current best algorithm for computing the code distance.
We show that these enumerators can be used to compute logical error rates exactly and thus construct decoders for any i.i.d. single qubit or qudit error channels.
- Score: 1.489619600985197
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We provide the first tensor network method for computing quantum weight
enumerator polynomials in the most general form. If a quantum code has a known
tensor network construction of its encoding map, our method is far more
efficient, and in some cases exponentially faster than the existing approach.
As a corollary, it produces decoders and an algorithm that computes the code
distance. For non-(Pauli)-stabilizer codes, this constitutes the current best
algorithm for computing the code distance. For degenerate stabilizer codes, it
can be substantially faster compared to the current methods. We also introduce
novel weight enumerators and their applications. In particular, we show that
these enumerators can be used to compute logical error rates exactly and thus
construct (optimal) decoders for any i.i.d. single qubit or qudit error
channels. The enumerators also provide a more efficient method for computing
non-stabilizerness in quantum many-body states. As the power for these speedups
rely on a Quantum Lego decomposition of quantum codes, we further provide
systematic methods for decomposing quantum codes and graph states into a
modular construction for which our technique applies. As a proof of principle,
we perform exact analyses of the deformed surface codes, the holographic
pentagon code, and the 2d Bacon-Shor code under (biased) Pauli noise and
limited instances of coherent error at sizes that are inaccessible by brute
force.
Related papers
- List Decodable Quantum LDPC Codes [49.2205789216734]
We give a construction of Quantum Low-Density Parity Check (QLDPC) codes with near-optimal rate-distance tradeoff.
We get efficiently list decodable QLDPC codes with unique decoders.
arXiv Detail & Related papers (2024-11-06T23:08:55Z) - Engineering Quantum Error Correction Codes Using Evolutionary Algorithms [0.0]
Quantum error correction and the use of quantum error correction codes is likely to be essential for the realisation of practical quantum computing.
We present a novel evolutionary algorithm which searches for an optimal stabiliser code for a given error model.
As part of this work, we also introduce an evolutionary algorithm QDistEvol for finding the distance of quantum error correction codes.
arXiv Detail & Related papers (2024-09-19T18:00:02Z) - Fast Algorithms and Implementations for Computing the Minimum Distance of Quantum Codes [43.96687298077534]
The distance of a stabilizer quantum code determines the number of errors that can be detected and corrected.
We present three new fast algorithms and implementations for computing the symplectic distance of the associated classical code.
arXiv Detail & Related papers (2024-08-20T11:24:30Z) - Small Quantum Codes from Algebraic Extensions of Generalized Bicycle
Codes [4.299840769087443]
Quantum LDPC codes range from the surface code, which has a vanishing encoding rate, to very promising codes with constant encoding rate and linear distance.
We devise small quantum codes that are inspired by a subset of quantum LDPC codes, known as generalized bicycle (GB) codes.
arXiv Detail & Related papers (2024-01-15T10:38:13Z) - 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) - 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) - 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) - Efficient decoding up to a constant fraction of the code length for
asymptotically good quantum codes [0.38073142980732994]
Previous decoders for quantum low-density parity-check codes could only handle adversarial errors of weight $O(sqrtn log n)$.
We show that our decoder can be adapted to the Lifted Product codes of Panteleev and Kalachev.
arXiv Detail & Related papers (2022-06-15T14:46:06Z) - Entanglement and coherence in Bernstein-Vazirani algorithm [58.720142291102135]
Bernstein-Vazirani algorithm allows one to determine a bit string encoded into an oracle.
We analyze in detail the quantum resources in the Bernstein-Vazirani algorithm.
We show that in the absence of entanglement, the performance of the algorithm is directly related to the amount of quantum coherence in the initial state.
arXiv Detail & Related papers (2022-05-26T20:32:36Z) - 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) - Quantum Gram-Schmidt Processes and Their Application to Efficient State
Read-out for Quantum Algorithms [87.04438831673063]
We present an efficient read-out protocol that yields the classical vector form of the generated state.
Our protocol suits the case that the output state lies in the row space of the input matrix.
One of our technical tools is an efficient quantum algorithm for performing the Gram-Schmidt orthonormal procedure.
arXiv Detail & Related papers (2020-04-14T11:05:26Z)
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.