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Hybrid classical quantum optimization methods have become an important tool for efficiently solving problems in the current generation of NISQ computers. These methods use an optimization algorithm executed in a classical computer, fed with…
We establish the potential of continuous-variable Gaussian states of linear dynamical systems for machine learning tasks. Specifically, we consider reservoir computing, an efficient framework for online time series processing. As a…
We present a numerical method for solving the separability problem of Gaussian quantum states in continuous-variable quantum systems. We show that the separability problem can be cast as an equivalent problem of determining the feasibility…
A symbolic approach to decentralized set-valued state estimation and prediction for systems that admit a hybrid state machine representations is proposed. The decentralized computational scheme represents a conj unction of a finite number…
Probabilistic ideas and tools have recently begun to permeate into several fields where they had traditionally not played a major role, including fields such as numerical linear algebra and optimization. One of the key ways in which these…
We investigate quantum inspired algorithms to compute physical observables of quantum many-body systems at finite energies. They are based on the quantum algorithms proposed in [Lu et al. PRX Quantum 2, 020321 (2021)], which use the quantum…
Variational quantum algorithms (VQAs) are promising hybrid quantum-classical methods designed to leverage the computational advantages of quantum computing while mitigating the limitations of current noisy intermediate-scale quantum (NISQ)…
Quantum master equations are an important tool in quantum optics and quantum information theory. For systems comprising a small to medium number of atoms (or qubits), the non-truncated equations are usually solved numerically. In this…
Variational quantum algorithms (VQAs) are prominent candidates for near-term quantum advantage but lack rigorous guarantees of convergence and generalization. By contrast, quantum phase estimation (QPE) provides provable performance under…
Universal quantum algorithms (UQA) implemented on fault-tolerant quantum computers are expected to achieve an exponential speedup over classical counterparts. However, the deep quantum circuits makes the UQA implausible in the current era.…
In this paper we describe a quantum algorithm to solve sparse systems of nonlinear differential equations whose nonlinear terms are polynomials. The algorithm is nondeterministic and its expected resource requirements are polylogarithmic in…
Stochastic dynamical systems are fundamental in state estimation, system identification and control. System models are often provided in continuous time, while a major part of the applied theory is developed for discrete-time systems.…
We present methods for the numerical evaluation of the master integrals that appear in the calculation of scattering amplitudes at higher order in perturbative quantum field theory. We follow the general strategy of solving first-order…
An efficient approximate version of implicit Taylor methods for initial-value problems of systems of ordinary differential equations (ODEs) is introduced. The approach, based on an approximate formulation of Taylor methods, produces a…
For many systems of differential equations modeling problems in science and engineering, there are natural splittings of the right hand side into two parts, one non-stiff or mildly stiff, and the other one stiff. For such systems…
As a method of universal approximation deep neural networks (DNNs) are capable of finding approximate solutions to problems posed with little more constraints than a suitably-posed mathematical system and an objective function.…
In the realm of quantum information processing, the efficient characterization of entangled states poses an overwhelming challenge, rendering the traditional methods including quantum tomography unfeasible and impractical. To tackle this…
An idea of hybrid maps is proposed to establish standard entanglement purification protocols which guarantee to purify any distillable state to a desired maximally entangled pure state all by the standard purification local operations and…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
We present two quantum interior point methods for semidefinite optimization problems, building on recent advances in quantum linear system algorithms. The first scheme, more similar to a classical solution algorithm, computes an inexact…