Related papers: A Quantum Algorithm for Simulating Nonunitary Dyna…
We present a quantum algorithm based on the Generalized Quantum Master Equation (GQME) approach to simulate open quantum system dynamics on noisy intermediate-scale quantum (NISQ) computers. This approach overcomes the limitations of the…
Simulating open quantum systems on quantum computers presents a fundamental challenge: open quantum dynamics are intrinsically nonunitary, whereas quantum computers operate through unitary evolution. Conventional approaches overcome this…
With the rapid progress in quantum hardware, there has been an increased interest in new quantum algorithms to describe complex many-body systems searching for the still-elusive goal of 'useful quantum advantage'. Surprisingly, quantum…
We present a quantum algorithm for simulating the wave equation under Dirichlet and Neumann boundary conditions. The algorithm uses Hamiltonian simulation and quantum linear system algorithms as subroutines. It relies on factorizations of…
Variational Quantum Algorithms are among the most promising systems to implement quantum computing under the Noisy-Intermediate Scale Quantum (NISQ) technology. In variational quantum algorithm, wavefunction represented by a parametrized…
Simulating the dynamics and the non-equilibrium steady state of an open quantum system are hard computational tasks on conventional computers. For the simulation of the time evolution, several efficient quantum algorithms have recently been…
The paper presents a variational quantum algorithm to solve initial-boundary value problems described by second-order partial differential equations. The approach uses hybrid classical/quantum hardware that is well suited for quantum…
Dissipation and irreversibility are central to most physical processes, yet they lead to non-unitary dynamics that are challenging to realise on quantum processors. High-order operator splitting is an attractive approach for simulating…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
The Fokker-Planck equation models rare events across sciences, but its high-dimensional nature challenges classical computers. Quantum algorithms for such non-unitary dynamics often suffer from exponential {decay in} success probability. We…
We explore the possibility of adding complex absorbing potential at the boundaries when solving the one-dimensional real-time Schr\"odinger evolution on a grid using a quantum computer with a fully quantum algorithm described on a $n$ qubit…
We present a quantum algorithm for computational fluid dynamics based on the Lattice-Boltzmann method. Our approach involves a novel encoding strategy and a modified collision operator, assuming full relaxation to the local equilibrium…
This paper develops a distributed variational quantum algorithm for solving large-scale linear equations. For a linear system of the form $Ax=b$, the large square matrix $A$ is partitioned into smaller square block submatrices, each of…
This paper introduces a novel approach to implementing non-unitary linear transformations of basis on quantum computational platforms, a significant leap beyond the conventional unitary methods. By integrating Singular Value Decomposition…
Unitary and non-unitary diagonal operators are fundamental building blocks in quantum algorithms with applications in the resolution of partial differential equations, Hamiltonian simulations, the loading of classical data on quantum…
For quantum computers to become useful tools to physicists, engineers and computational scientists, quantum algorithms for solving nonlinear differential equations need to be developed. Despite recent advances, the quest for a solver that…
Inspired by random walk on graphs, diffusion map (DM) is a class of unsupervised machine learning that offers automatic identification of low-dimensional data structure hidden in a high-dimensional dataset. In recent years, among its many…
The accurate (or even approximate) solution of the equations that govern the dynamics of dissipative quantum systems remains a challenging task for quantum science. While several algorithms have been designed to solve those equations with…
A computational tool for coarse-graining nonlinear systems of ordinary differential equations in time is discussed. Three illustrative model examples are worked out that demonstrate the range of capability of the method. This includes the…
We present a quantum algorithm for the dynamical simulation of time-dependent Hamiltonians. Our method involves expanding the interaction-picture Hamiltonian as a sum of generalized permutations, which leads to an integral-free Dyson series…