Related papers: Quantum algorithms for the fractional Poisson equa…
Graph sparsification underlies a large number of algorithms, ranging from approximation algorithms for cut problems to solvers for linear systems in the graph Laplacian. In its strongest form, "spectral sparsification" reduces the number of…
Quantum simulation is a foundational application for quantum computers, projected to offer insights into complex quantum systems beyond the reach of classical computation. However, with the exception of Trotter-based methods, which suffer…
We present a simple new way - called Schrodingerisation - to simulate general linear partial differential equations via quantum simulation. Using a simple new transform, referred to as the warped phase transformation, any linear partial…
Variational algorithms are a promising paradigm for utilizing near-term quantum devices for modeling electronic states of molecular systems. However, previous bounds on the measurement time required have suggested that the application of…
We give a quantum algorithm for solving the Bounded Distance Decoding (BDD) problem with a subexponential approximation factor on a class of integer lattices. The quantum algorithm uses a well-known but challenging-to-use quantum state on…
Feedback-based quantum optimization is a quantum approach to combinatorial optimization. In this paper, we introduce the classical counterpart of feedback-based quantum optimization by using the quantum-classical correspondence of spin…
This paper extends the energy-based version of the stochastic linearization method, known for classical nonlinear systems, to open quantum systems with canonically commuting dynamic variables governed by quantum stochastic differential…
We present an algorithm of the reduction of the differential equations for master integrals the Fuchsian form with the right-hand side matrix linearly depending on dimensional regularization parameter $\epsilon$. We consider linear…
In this paper, the Quantum Approximate Optimization Algorithm (QAOA) is analyzed by leveraging symmetries inherent in problem Hamiltonians. We focus on the generalized formulation of optimization problems defined on the sets of $n$-element…
We present substantially generalized and improved quantum algorithms over prior work for inhomogeneous linear and nonlinear ordinary differential equations (ODE). Specifically, we show how the norm of the matrix exponential characterizes…
Different hybrid quantum-classical algorithms have recently been developed as a near-term way to solve linear systems of equations on quantum devices. However, the focus has so far been mostly on the methods, rather than the problems that…
Fractional calculus has been used to describe physical systems with complexity. Here, we show that a fractional calculus approach can restore or include complexity in any physical systems that can be described by partial differential…
In this paper, we present a new numerical method to solve fractional differential equations. Given a fractional derivative of arbitrary real order, we present an approximation formula for the fractional operator that involves integer-order…
We introduce a quantum approximate optimization algorithm (QAOA) for continuous optimization. The algorithm is based on the dynamics of a quantum system moving in an energy potential which encodes the objective function. By approximating…
One of the most promising applications of quantum computers is solving partial differential equations (PDEs). By using the Schrodingerisation technique - which converts non-conservative PDEs into Schrodinger equations - the problem can be…
Combinatorial problems are formulated to find optimal designs within a fixed set of constraints. They are commonly found across diverse engineering and scientific domains. Understanding how to best use quantum computers for combinatorial…
In the present paper, we precisely conduct a q-calculus method for the numerical solutions of PDEs. A nonlinear Schrodinger equation is considered. Instead of the classical discretization methods we consider subdomains according to…
The Schr\"odingerisation method combined with the autonomozation technique in \cite{cjL23} converts general non-autonomous linear differential equations with non-unitary dynamics into systems of autonomous Schr\"odinger-type equations, via…
Optimization problems in disciplines such as machine learning are commonly solved with iterative methods. Gradient descent algorithms find local minima by moving along the direction of steepest descent while Newton's method takes into…
The Schrieffer-Wolff transformation aims to solve degenerate perturbation problems and give an effective Hamiltonian that describes the low-energy dynamics of the exact Hamiltonian in the low-energy subspace of unperturbed Hamiltonian. This…