Related papers: QDistRnd: A GAP package for computing the distance…
This paper presents a new distance metric to compare two continuous probability density functions. The main advantage of this metric is that, unlike other statistical measurements, it can provide an analytic, closed-form expression for a…
In this work, we study the minimum/stopping distance of array low-density parity-check (LDPC) codes. An array LDPC code is a quasi-cyclic LDPC code specified by two integers q and m, where q is an odd prime and m <= q. In the literature,…
Quantum error correction suppresses noise in quantum systems to allow for high-precision computations. In this work, we introduce Multivariate Bicycle (MB) Quantum Low-Density Parity-Check (QLDPC) codes, via an extension of the framework…
Quantum Error Correction (QEC) is an essential field of research towards the realization of large-scale quantum computers. On the theoretical side, a lot of effort is put into designing error-correcting codes that protect quantum data from…
With the current interest in building quantum computers, there is a strong need for accurate and efficient characterization of the noise in quantum gate implementations. A key measure of the performance of a quantum gate is the minimum gate…
The Distance Geometry Problem (DGP) seeks to find positions for a set of points in geometric space when some distances between pairs of these points are known. The so-called discretization assumptions allow to discretize the search space of…
Quantum error correction is capable of digitizing quantum noise and increasing the robustness of qubits. Typically, error correction is designed with the target of eliminating all errors - making an error so unlikely it can be assumed that…
The intrinsic probabilistic nature of quantum systems makes error correction or mitigation indispensable for quantum computation. While current error-correcting strategies focus on correcting errors in quantum states or quantum gates, these…
In quantum information, trace distance is a basic metric of distinguishability between quantum states. However, there is no known efficient approach to estimate the value of trace distance in general. In this paper, we propose efficient…
Quantum key distribution (QKD) allows two distant parties to share encryption keys with security based on physical laws. Experimentally, it has been implemented with optical means, achieving key rates of 1.26 Megabit/s over 50 kilometres…
This paper investigates certified upper bounds on the minimum distance of an explicit family of Calderbank-Shor-Steane quantum LDPC codes constructed from affine permutation matrices. All codes considered here have active Tanner graphs of…
We perform an extended numerical search for practical fermion-to-qubit encodings with error correcting properties. Ideally, encodings should strike a balance between a number of the seemingly incompatible attributes, such as having a high…
Geometrically local quantum codes, comprised of qubits and checks embedded in $\mathbb{R}^D$ with local check operators, have been a subject of significant interest. A key challenge is identifying the optimal code construction that…
The graph edit distance (GED) measures the dissimilarity between two graphs as the minimal cost of a sequence of elementary operations transforming one graph into another. This measure is fundamental in many areas such as structural pattern…
We propose a method for constructing quantum error-correcting codes based on non-binary low-density parity-check codes with Tanner graph girth 16. While conventional constructions using circulant permutation matrices are limited to girth…
We give a construction of Quantum Low-Density Parity Check (QLDPC) codes with near-optimal rate-distance tradeoff and efficient list decoding up to the Johnson bound in polynomial time. Previous constructions of list decodable good distance…
Recent constructions of quantum low-density parity-check (QLDPC) codes provide optimal scaling of the number of logical qubits and the minimum distance in terms of the code length, thereby opening the door to fault-tolerant quantum systems…
It is widely accepted that quantum error correction is essential for realizing large-scale fault-tolerant quantum computing. Recent experiments have demonstrated error correction codes operating below threshold, primarily using local planar…
Although quantum key distribution (QKD) comes from the development of quantum theory, the implementation of a practical QKD system does involve a lot of classical process, such as key reconciliation and privacy amplification, which is…
We present discretize_distributions, a Python package that efficiently constructs discrete approximations of Gaussian mixture distributions and provides guarantees on the approximation error in Wasserstein distance. The package implements…