Related papers: A probabilistic imaginary-time evolution quantum a…
We propose an algorithm based on variational quantum imaginary time evolution for solving the Feynman-Kac partial differential equation resulting from a multidimensional system of stochastic differential equations. We utilize the…
To overcome the fast oscillatory behavior of correlation functions for extracting scattering phase shift in real-time quantum simulations encountered in Ref.\cite{Guo:2026qkx}, we propose and test two solutions in the present work. One is…
We present an efficient, nearly optimal quantum algorithm for solving linear matrix differential equations, with applications to the simulation of open quantum systems and beyond. For unitary or dissipative dynamics, the algorithm computes…
For quantum state preparation, a non-unitary operator is typically designed to decay undesirable states contained in an initial state using ancilla qubits and a probabilistic action. Probabilistic algorithms do not accelerate the…
In this work, we investigate the capability of known quantum-computing algorithms for fault-tolerant quantum computing to simulate the laser-driven electron dynamics in small molecules such as lithium hydride. These computations are…
Calculations at finite temperatures are fundamental in different scientific fields, from nuclear physics to condensed matter. Evolution in imaginary time is a prominent classical technique for preparing thermal states of quantum systems. We…
The variational quantum eigensolver (VQE) is an algorithm for finding the ground states of a given Hamiltonian. Its application to binary-formulated combinatorial optimization (CO) has been widely studied in recent years. However, typical…
This article investigates the non-stationary reaction-diffusion-advection equation, emphasizing solutions with internal layers and the associated inverse problems. We examine a nonlinear singularly perturbed partial differential equation…
Often computational models are too expensive to be solved in the entire domain of simulation, and a cheaper model would suffice away from the main zone of interest. We present for the concrete example of an evolution problem of advection…
The Quantum Lattice Boltzmann Method (QLBM) is one of the most promising approaches for realizing the potential of quantum computing in simulating computational fluid dynamics. Many recent works mostly focus on classical simulation, and…
In this article, we compare the methods implementing the real-time evolution operator generated by a unitary diagonal matrix where its entries obey a known underlying real function. When the size of the unitary diagonal matrix is small, a…
A quantum algorithm that solves the time-dependent Dirac equation on a digital quantum computer is developed and analyzed. The time evolution is performed by an operator splitting decomposition technique that allows for a mapping of the…
We present a quantum algorithm to solve systems of linear equations of the form $A\mathbf{x}=\mathbf{b}$, where $A$ is a tridiagonal Toeplitz matrix and $\mathbf{b}$ results from discretizing an analytic function, with a circuit complexity…
The mixing of scalar substances in fluid flows by stirring and diffusion is ubiquitous in natural flows, chemical engineering, and microfluidic drug delivery. Here, we present a spectral quantum algorithm for scalar mixing by solving the…
This paper is a further extension of the method proposed in Itkin, 2014 as applied to another set of jump-diffusion models: Inverse Normal Gaussian, Hyperbolic and Meixner. To solve the corresponding PIDEs we accomplish few steps. First, a…
We introduce a constructive method for mapping non-unitary dynamics to a weighted set of unitary operations. We utilize this construction to derive a new correspondence between real and imaginary time, which we term Imaginary Time Quantum…
The aim of this paper is to present a first evaluation of the potential of an asynchronous distributed computation associated to the recently proposed approach, D-iteration: the D-iteration is a fluid diffusion based iterative method, which…
The imaginary-time evolution of quantum states is integral to various fields, ranging from natural sciences to classical optimization or machine learning. Since simulating quantum imaginary-time evolution generally requires storing an…
Simulation of quantum matters is a significant application of quantum computers. In contrast to the unitary operation which can be realized naturally on a quantum computer, the implementation of nonunitary operation, widely used in…
We present efficient quantum algorithms for simulating time-dependent Hamiltonian evolution of general input states using an oracular model of a quantum computer. Our algorithms use either constant or adaptively chosen time steps and are…