Related papers: Quantum Goemans-Williamson Algorithm with the Hada…
We present an exact quantum algorithm for solving the Exact Satisfiability (XSAT) problem, which belongs to the important NP-complete complexity class. The algorithm is based on an intuitive approach that can be divided into two parts:…
Quantum computing may speed up numerical problems involving large matrices that are demanding for classical computers, and active research on this possibility is ongoing. In this work, we propose quantum algorithms for the exact simulation…
Quantum algorithms for diverse problems, including search and optimization problems, require the implementation of a reflection operator over a target state. Commonly, such reflections are approximately implemented using phase estimation.…
There is a strong interest in finding challenging instances of NP-hard problems, from the perspective of showing quantum advantage. Due to the limits of near-term NISQ devices, it is moreover useful if these instances are small. In this…
Adiabatic quantum computing is a universal model for quantum computing whose implementation using a gate-based quantum computer requires depths that are unreachable in the early fault-tolerant era. To mitigate the limitations of near-term…
MaxCut is a key NP-Hard combinatorial optimization graph problem with extensive theoretical and industrial applications, including the Ising model and chip design. While quantum computing offers new solutions for such combinatorial…
We extend results known for the randomized Gauss-Seidel and the Gauss-Southwell methods for the case of a Hermitian and positive definite matrix to certain classes of non-Hermitian matrices. We obtain convergence results for a whole range…
In this article we provide an experimental algorithm that in many cases gives us an upper bound of the global infimum of a real polynomial on $\R^{n}$. It is very well known that to find the global infimum of a real polynomial on $\R^{n}$,…
Gaussian processes are widely known for their ability to provide probabilistic predictions in supervised machine learning models. Their non-parametric nature and flexibility make them particularly effective for regression tasks. However,…
We provide a numerical scheme to approximate as closely as desired the Gaussian or exponential measure $\mu(\om)$ of (not necessarily compact) basic semi-algebraic sets$\om\subset\R^n$. We obtain two monotone (non increasing and non…
We present explicit expressions for the central piece of a variational method developed by Shi et al. which extends variational wave functions that are efficiently computable on classical computers beyond mean-field to generalized Gaussian…
We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations (ODEs), which may be generated from partial differential equations in plasma physics. We map a…
We discuss classical algorithms for approximating the largest eigenvalue of quantum spin and fermionic Hamiltonians based on semidefinite programming relaxation methods. First, we consider traceless $2$-local Hamiltonians $H$ describing a…
We present a new quantum algorithm for estimating the mean of a real-valued random variable obtained as the output of a quantum computation. Our estimator achieves a nearly-optimal quadratic speedup over the number of classical i.i.d.…
Sequential algorithms are popular for experimental design, enabling emulation, optimisation and inference to be efficiently performed. For most of these applications bespoke software has been developed, but the approach is general and many…
Due to the increasing demand for high performance and cost reduction within the framework of complex system design, numerical optimization of computationally costly problems is an increasingly popular topic in most engineering fields. In…
In this paper, we present a generic framework to extend existing uniformly optimal convex programming algorithms to solve more general nonlinear, possibly nonconvex, optimization problems. The basic idea is to incorporate a local search…
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…
In this paper, we study quantitative properties of quantum programs. Properties of interest include (positive) almost-sure termination, expected runtime or expected cost, that is, for example, the expected number of applications of a given…
Quantum algorithms have been widely studied in the context of combinatorial optimization problems. While this endeavor can often analytically and practically achieve quadratic speedups, theoretical and numeric studies remain limited,…