Related papers: Distance-Finding Algorithms for Quantum Codes and …
We survey the existing techniques for calculating code distances of classical codes and apply these techniques to generic quantum codes. For classical and quantum LDPC codes, we also present a new linked-cluster technique. It reduces…
The techniques of distance verification known for general linear codes are re-applied to quantum stabilizer codes. Then distance verification is addressed for classical and quantum LDPC codes. New complexity bounds for distance verification…
The problem of finding code distance has been long studied for the generic ensembles of linear codes and led to several algorithms that substantially reduce exponential complexity of this task. However, no asymptotic complexity bounds are…
We present a linked-cluster technique for calculating the distance of a quantum LDPC code. It offers an advantage over existing deterministic techniques for codes with small relative distances (which includes all known families of quantum…
The distance of a stabilizer quantum code is a very important feature since it determines the number of errors that can be detected and corrected. We present three new fast algorithms and implementations for computing the symplectic…
Quantum error correction and the use of quantum error correction codes is likely to be essential for the realisation of practical quantum computing. Because the error models of quantum devices vary widely, quantum codes which are tailored…
This paper introduces a construction of quantum CSS codes from a tuple of component CSS codes and two collections of subsets. The resulting codes have parallelizable encoding and syndrome measurement circuits and built-in redundancy in the…
Quantum computers hold the potential to surpass classical computers in solving complex computational problems. However, the fragility of quantum information and the error-prone nature of quantum operations make building large-scale,…
As is well known, classical systems approximate quantum ones -- but how well? We introduce a definition of a "distance" on classical and quantum phase spaces that offers a measure of their separation. Such a distance scale provides a means…
We ask what is the general framework for a quantum error correcting code that is defined by a sequence of measurements. Recently, there has been much interest in Floquet codes and space-time codes. In this work, we define and study the…
Utility-scale quantum computing requires quantum error correction (QEC) to protect quantum information against noise. Currently, superconducting hardware is a promising candidate for achieving fault tolerance due to its fast gate times and…
Quantum low-density parity-check (LDPC) codes, a class of quantum error correcting codes, are considered a blueprint for scalable quantum circuits. To use these codes, one needs efficient decoding algorithms. In the classical setting, there…
Quantum computing promises to speed up some of the most challenging problems in science and engineering. Quantum algorithms have been proposed showing theoretical advantages in applications ranging from chemistry to logistics optimization.…
Lately, much attention has been given to quantum algorithms that solve pattern recognition tasks in machine learning. Many of these quantum machine learning algorithms try to implement classical models on large-scale universal quantum…
Estimating the difference between quantum data is crucial in quantum computing. However, as typical characterizations of quantum data similarity, the trace distance and quantum fidelity are believed to be exponentially-hard to evaluate in…
We suggest a technique for constructing lower (existence) bounds for the fault-tolerant threshold to scalable quantum computation applicable to degenerate quantum codes with sublinear distance scaling. We give explicit analytic expressions…
The realization of quantum error correction protocols whose logical error rates are suppressed far below physical error rates relies on an intricate combination: the error-correcting code's efficiency, the syndrome extraction circuit's…
Quantum low-density parity-check (LDPC) codes are an important class of quantum error correcting codes. In such codes, each qubit only affects a constant number of syndrome bits, and each syndrome bit only relies on some constant number of…
The minimum distance of a code is an important concept in information theory. Hence, computing the minimum distance of a code with a minimum computational cost is a crucial process to many problems in this area. In this paper, we present…
We study the hardness of the problem of finding the distance of quantum error-correcting codes. The analogous problem for classical codes is known to be NP-hard, even in approximate form. For quantum codes, various problems related to…