Related papers: Certification of the QR factor R, and of lattice b…
A new architecture called integer-forcing (IF) linear receiver has been recently proposed for multiple-input multiple-output (MIMO) fading channels, wherein an appropriate integer linear combination of the received symbols has to be…
The next-to-leading order (NLO) ($\mathcal{O}(\alpha_s^3)$) corrections for gluon fragmentation functions to a heavy quark-antiquark pair in ${^{3}\hspace{-0.6mm}P_{J}^{[1,8]}}$ states are calculated within the NRQCD factorization. We use…
Establishing stability certificates for closed-loop systems under reinforcement learning (RL) policies is essential to move beyond empirical performance and offer guarantees of system behavior. Classical Lyapunov methods require a strict…
Quantum computing devices are believed to be powerful in solving the prime factorization problem, which is at the heart of widely deployed public-key cryptographic tools. However, the implementation of Shor's quantum factorization algorithm…
The stabilization of a quantum computer by repeated error correction can be reduced almost entirely to repeated preparation of blocks of qubits in quantum codeword states. These are multi-particle entangled states with a high degree of…
The error floor phenomenon observed with LDPC codes and their graph-based, iterative, message-passing (MP) decoders is commonly attributed to the existence of error-prone substructures -- variously referred to as near codewords, trapping…
Computing a basis for the exponent lattice of algebraic numbers is a basic problem in the field of computational number theory with applications to many other areas. The main cost of a well-known algorithm…
Shor's factorisation algorithm is a combination of classical pre- and post-processing and a quantum period finding (QPF) subroutine which allows an exponential speed up over classical factoring algorithms. We consider the stability of this…
Quantum error correction protects fragile quantum information by encoding it into a larger quantum system. These extra degrees of freedom enable the detection and correction of errors, but also increase the operational complexity of the…
Quantum computing promises advantages over classical computing in many problems. Nevertheless, noise in quantum devices prevents most quantum algorithms from achieving the quantum advantage. Quantum error mitigation provides a variety of…
In the certification problem, the algorithm is given a function $f$ with certificate complexity $k$ and an input $x^\star$, and the goal is to find a certificate of size $\le \text{poly}(k)$ for $f$'s value at $x^\star$. This problem is in…
Many problems in interprocedural program analysis can be modeled as the context-free language (CFL) reachability problem on graphs and can be solved in cubic time. Despite years of efforts, there are no known truly sub-cubic algorithms for…
Matrix factorization is an important representation learning algorithm, e.g., recommender systems, where a large matrix can be factorized into the product of two low dimensional matrices termed as latent representations. This paper…
Non-negative matrix factorisation (NMF) has been extensively applied to the problem of corrupted image data. Standard NMF approach minimises Euclidean distance between data matrix and factorised approximation. The traditional NMF technique…
This paper considers the problem of quantum compilation from an optimization perspective by fixing a circuit structure of CNOTs and rotation gates then optimizing over the rotation angles. We solve the optimization problem classically and…
Quantum error correction is widely thought to be the key to fault-tolerant quantum computation. However, determining the most suited encoding for unknown error channels or specific laboratory setups is highly challenging. Here, we present a…
Integer factorization has been one of the cornerstone applications of the field of quantum computing since the discovery of an efficient algorithm for factoring by Peter Shor. Unfortunately, factoring via Shor's algorithm is well beyond the…
Coherent errors are a dominant noise process in many quantum computing architectures. Unlike stochastic errors, these errors can combine constructively and grow into highly detrimental overrotations. To combat this, we introduce a simple…
The NP-hardness of the closest vector problem (CVP) is an important basis for quantum-secure cryptography, in much the same way that integer factorisation's conjectured hardness is at the foundation of cryptosystems like RSA. Recent work…
Quantum error correction (QEC) requires the execution of deep quantum circuits with large numbers of physical qubits to protect information against errors. Designing protocols that can reduce gate and space-time overheads of QEC is…