Related papers: Design of optimization tools for quantum informati…
We consider the problem of search of an unstructured list for a marked element, when one is given advice as to where this element might be located, in the form of a probability distribution. The goal is to minimise the expected number of…
Although quantum computing hardware has evolved significantly in recent years, spurred by increasing industrial and government interest, the size limitation of current generation quantum computers remains an obstacle when applying these…
Quantum state estimation plays a crucial role in ensuring reliable creation of entanglement within quantum networks, yet conventional Quantum State Tomography (QST) methods remain resource-intensive and impractical for scaling. To address…
We describe an algorithm for using a quantum computer to calculate mean values of observables and the partition function of a quantum system. Our algorithm includes two sub-algorithms. The first sub-algorithm is for calculating, with…
Large-scale eigenvalue problems pose a significant challenge to classical computers. While there are efficient quantum algorithms for unitary or Hermitian matrices, eigenvalue problems for non-normal matrices remain open in quantum…
Optimization problems in disciplines such as machine learning are commonly solved with iterative methods. Gradient descent algorithms find local minima by moving along the direction of steepest descent while Newton's method takes into…
Quantum optimization holds promise for addressing classically intractable combinatorial problems, yet a standardized framework for benchmarking its performance, particularly in terms of solution quality, computational speed, and scalability…
This paper presents a comprehensive exploration of semi-definite programming (SDP) techniques within the context of quantum information. It examines the mathematical foundations of convex optimization, duality, and SDP formulations,…
Convex optimization problems arise naturally in quantum information theory, often in terms of minimizing a convex function over a convex subset of the space of hermitian matrices. In most cases, finding exact solutions to these problems is…
Recently we find several candidates of quantum algorithms that may be implementable in near-term devices for estimating the amplitude of a given quantum state, which is a core sub- routine in various computing tasks such as the Monte Carlo…
This review is designed to introduce mathematicians and computational scientists to quantum computing (QC) through the lens of uncertainty quantification (UQ) by presenting a mathematically rigorous and accessible narrative for…
Maximum-likelihood estimation is applied to identification of an unknown quantum mechanical process represented by a ``black box''. In contrast to linear reconstruction schemes the proposed approach always yields physically sensible…
We present a variational algorithm for fault tolerant quantum computing to solve a system of linear equations which directly maximises the parameters of the target fidelity. This so-called measurement test algorithm can be applied to any…
Several combinatorial optimization problems can be solved with NISQ devices once that a corresponding quadratic unconstrained binary optimization (QUBO) form is derived. The aim of this work is to drastically reduce the variables needed for…
Studies on simulation input uncertainty often built on the availability of input data. In this paper, we investigate an inverse problem where, given only the availability of output data, we nonparametrically calibrate the input models and…
The Quantum Approximate Optimization Algorithm (QAOA) constitutes one of the often mentioned candidates expected to yield a quantum boost in the era of near-term quantum computing. In practice, quantum optimization will have to compete with…
Quantum algorithms to integrate nonlinear PDEs governing flow problems are challenging to discover but critical to enhancing the practical usefulness of quantum computing. We present here a near-optimal, robust, and end-to-end quantum…
This article consists of a short introduction to the quantum approximation optimisation algorithm (QAOA). The mathematical structure of the QAOA, as well as its basic properties, are described. The implementation of the QAOA on MaxCut…
Maximizing the precision in estimating parameters in a quantum system subject to instrumentation constraints is cast as a convex optimization problem. We account for prior knowledge about the parameter range by developing a worst-case and…
In the era of noisy-intermediate-scale quantum computers, we expect to see quantum devices with increasing numbers of qubits emerge in the foreseeable future. To practically run quantum programs, logical qubits have to be mapped to the…