相关论文: QDistRnd: A GAP package for computing the distance…

To well understand the behavior of quantum error correction codes (QECC) in noise processes, we need to obtain explicit coding maps for QECC. Due to extraordinary amount of computational labor that they entails, explicit coding maps are a…

We propose a fault-tolerant quantum computation scheme that is broadly applicable to quantum low-density parity-check (qLDPC) codes. The scheme achieves constant qubit overhead and a time overhead of $O(d^{a+o(1)})$ for any $[[n,k,d]]$…

The quantum Wasserstein distance (W-distance) is a fundamental metric for quantifying the distinguishability of quantum operations, with critical applications in quantum error correction. However, computing the W-distance remains…

It is an important task to construct quantum maximum-distance-separable (MDS) codes with good parameters. In the present paper, we provide six new classes of q-ary quantum MDS codes by using generalized Reed-Solomon (GRS) codes and…

Reconciliation is an important step to correct errors in Quantum Key Distribution (QKD). In QKD, after comparing basis, two legitimate parties possess two correlative keys which have some differences and they could obtain identical keys…

The dimension reduction method enables security proofs of quantum key distribution (QKD) protocols that are originally formulated in infinite dimensions via reduction to a tractable finite-dimensional optimization. The reduction of…

We introduce the problem of determining if the mode of the output distribution of a quantum circuit (given as a black-box) is larger than a given threshold, named HighDist, and a similar problem based on the absolute values of the…

High-quality quantum state generation is essential for advanced quantum information processing, including quantum communication, quantum sensing, and quantum computing. In practice, various error sources degrade the quality of quantum…

Quantum error correction has recently been shown to benefit greatly from specific physical encodings of the code qubits. In particular, several researchers have considered the individual code qubits being encoded with the continuous…

Approximating a probability distribution using a set of particles is a fundamental problem in machine learning and statistics, with applications including clustering and quantization. Formally, we seek a weighted mixture of Dirac measures…

We consider the Quantum Natural Gradient Descent (QNGD) scheme which was recently proposed to train variational quantum algorithms. QNGD is Steepest Gradient Descent (SGD) operating on the complex projective space equipped with the…

Code distance is an important parameter for quantum stabilizer codes (QSCs). Directly precisely computing it is an NP-complete problem. However, the upper bound of code distance can be computed by some efficient methods. In this paper,…

In this paper, we study the problem of approximating the minimum cut in a distributed message-passing model, the CONGEST model. The minimum cut problem has been well-studied in the context of centralized algorithms. However, there were no…

Let $p$ be a prime and let $q$ be a power of $p$. In this paper, by using generalized Reed-Solomon (GRS for short) codes and extended GRS codes, we construct two new classes of quantum maximum-distance- separable (MDS) codes with parameters…

This paper gives simple distributed algorithms for the fundamental problem of computing graph distances in the Congested Clique model. One of the main components of our algorithms is fast matrix multiplication, for which we show an…

Guessing Codeword Decoding (GCD) is a recently proposed soft-input forward error correction decoder for arbitrary binary linear codes. Inspired by recent proposals that leverage binary linear codebook structure to reduce the number of…

We consider a special case of the generalized minimum spanning tree problem (GMST) and the generalized travelling salesman problem (GTSP) where we are given a set of points inside the integer grid (in Euclidean plane) where each grid cell…

We devise an analytically simple as well as invertible approximate expression, which describes the relation between the minimum distance of a binary code and the corresponding maximum attainable code-rate. For example, for a rate-(1/4),…

We present new deterministic algorithms for computing distributed weighted minimum weight cycle (MWC) in undirected and directed graphs and distributed weighted all nodes shortest cycle (ANSC) in directed graphs. Our algorithms for these…

Quantum Key Distribution (QKD) is rapidly transitioning from cutting-edge laboratory research to real-world deployment in established communication networks. Although QKD promises future-proof security, practical challenges stil exist due…