Related papers: Hybrid quantum-classical algorithms for complex no…
Fluid simulations, especially at high Reynolds numbers, are computationally expensive on classical computers, making them promising application targets for quantum computing. Recent studies have combined the lattice Boltzmann method (LBM)…
We propose a complete quantum-classical hybrid branch-and-bound algorithm (QCBB) to solve binary linear programs with equality constraints. That includes bound calculation, convergence metrics and optimality guarantee to the quantum…
Noise is ubiquitous in real quantum systems, leading to non-Hermitian quantum dynamics, and may affect the fundamental states of matter. Here we report in experiment a quantum simulation of the two-dimensional non-Hermitian quantum…
We address the problem of integrating operator equations concomitant with the dynamics of non autonomous quantum systems by taking advantage of the use of time-dependent canonical transformations. In particular, we proceed to a discussion…
We present a novel variational quantum framework for linear partial differential equation (PDE) constrained optimization problems. Such problems arise in many scientific and engineering domains. For instance, in aerodynamics, the PDE…
The non-commutativity of the position and momentum operators is formulated as an effective potential in classical phase space and expanded as a series of successive many-body terms, with the pair term being dominant. A non-linear partial…
Variational quantum algorithms are one of the most promising methods that can be implemented on noisy intermediate-scale quantum (NISQ) machines to achieve a quantum advantage over classical computers. This article describes the use of a…
We establish sharp energy decay rates for a large class of nonlinearly first-order damped systems, and we design discretization schemes that inherit of the same energy decay rates, uniformly with respect to the space and/or time…
Vortices produce locally concentrated field configurations and are solutions to the nonlinear partial differential equations systems of complicated structures. In this paper, we establish the existence and uniqueness for solutions of the…
Vortex flows are ubiquitous in both natural processes and engineering applications, including phenomena such as typhoons, water currents, and aerospace fluid dynamics. The vortex particle method, a computational approach grounded in vortex…
In type-II superconductors, the dynamics of superconducting vortices determine their transport properties. In the Ginzburg-Landau theory, vortices correspond to topological defects in the complex order parameter. Extracting their precise…
Collective orders and photo-induced phase transitions in quantum matter can evolve on timescales which are orders of magnitude slower than the femtosecond processes related to electronic motion in the solid. Quantum Boltzmann equations can…
We propose mixed quantum-classical equations of motion that unify electronic coherence and phase evolution simultaneously within the exact factorization framework. Our derivation shows that incorporating the second-order electron-nuclear…
We propose a quantum algorithm to solve systems of nonlinear differential equations. Using a quantum feature map encoding, we define functions as expectation values of parametrized quantum circuits. We use automatic differentiation to…
We assess the use of variational quantum imaginary time evolution for solving partial differential equations. Our results demonstrate that real-amplitude ansaetze with full circular entangling layers lead to higher-fidelity solutions…
We give efficient quantum algorithms to estimate the partition function of (i) the six vertex model on a two-dimensional (2D) square lattice, (ii) the Ising model with magnetic fields on a planar graph, (iii) the Potts model on a quasi 2D…
Classical-quantum hybrid algorithms have recently garnered significant attention, which are characterized by combining quantum and classical computing protocols to obtain readout from quantum circuits of interest. Recent progress due to…
We present a dequantization algorithm for the Vlasov--Poisson (VP) system, termed the dequantized particle algorithm, by systematically dequantizing the underlying many-body quantum theory. Starting from the second-quantized Hamiltonian…
Numerical methods in spin-foam models have significantly advanced in the last few years, yet challenges remain in efficiently extracting results for amplitudes with many quantum degrees of freedom. In this paper we sketch a proposal for a…
Quantum algorithms for partial differential equations (PDEs) face severe practical constraints on near-term hardware: limited qubit counts restrict spatial resolution to coarse grids, while circuit depth limitations prevent accurate…