Related papers: Quantum Algorithms for Stochastic Differential Equ…
Linear response theory and Green's functions provide a universal framework for understanding dynamical correlations in strongly correlated open quantum systems. While the theoretical foundation for non-Hermitian linear response has been…
We explore the utilization of higher-order discretization techniques in optimizing the gate count needed for quantum computer based solutions of partial differential equations. To accomplish this, we present an efficient approach for…
This paper argues that the requirement of applicableness of quantum linearity to any physical level from molecules and atoms to the level of macroscopic extensional world, which leads to a main foundational problem in quantum theory…
The time-dependent one-dimensional nonlinear Schr\"odinger equation (NLSE) is solved numerically by a hybrid pseudospectral-variational quantum algorithm that connects a pseudospectral step for the Hamiltonian term with a variational step…
Quantum computers can produce a quantum encoding of the solution of a system of differential equations exponentially faster than a classical algorithm can produce an explicit description. However, while high-precision quantum algorithms for…
Noisy quantum simulation is challenging since one has to take into account the stochastic nature of the process. The dominating method for it is the density matrix approach. In this paper, we evaluate conditions for which this method is…
A natural non-Markovian extension of the theory of white noise quantum trajectories is presented. In order to introduce memory effects in the formalism an Ornstein-Uhlenbeck coloured noise is considered as the output driving process. Under…
Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same…
We propose a hybrid protocol to classify quantum noises using supervised classical machine learning models and simple quantum key distribution protocols. We consider the quantum bit error rates (QBERs) generated in QKD schemes under…
Quantum algorithms and complexity have recently been studied not only for discrete, but also for some numerical problems. Most attention has been paid so far to the integration problem, for which a speed-up is shown by quantum computers…
The main purpose of the paper is an essentially probabilistic analysis of relativistic quantum mechanics. It is based on the assumption that whenever probability distributions arise, there exists a stochastic process that is either…
The standard setting of quantum computation for continuous problems uses deterministic queries and the only source of randomness for quantum algorithms is through measurement. This setting is related to the worst case setting on a classical…
We use the stochastic quantization method to study systems with complex valued path integral weights. We assume a Langevin equation with a memory kernel and Einstein's relations with colored noise. The equilibrium solution of this…
Quantum machine learning promises great speedups over classical algorithms, but it often requires repeated computations to achieve a desired level of accuracy for its point estimates. Bayesian learning focuses more on sampling from…
The main purpose of the paper is an essentially probabilistic analysis of relativistic quantum mechanics. It is based on the assumption that whenever probability distributions arise, there exists a stochastic process that is either…
This paper concerns quantum heuristics able to extend the domain of quantum computing, defining a promising way in the large number of well-known classical algorithms. Quantum approximate heuristics take advantage of alternation between a…
Recent advances in quantum computers are demonstrating the ability to solve problems at a scale beyond brute force classical simulation. As such, a widespread interest in quantum algorithms has developed in many areas, with optimization…
A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not…
The presence of noise is currently one of the main obstacles to achieving large-scale quantum computation. Strategies to characterise and understand noise processes in quantum hardware are a critical part of mitigating it, especially as the…
We present a practical algorithm based on symplectic splitting methods to integrate numerically in time the Schr\"odinger equation. When discretized in space, the Schr\"odinger equation can be recast as a classical Hamiltonian system…