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We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…

Quantum Physics · Physics 2019-09-11 Juan Miguel Arrazola , Timjan Kalajdzievski , Christian Weedbrook , Seth Lloyd

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…

Quantum Physics · Physics 2026-04-03 Tong Shen , Zeru Zhu , Ji Liu

We investigate the problem of recovering coefficients in scalar nonlinear ordinary differential equations that can be exactly linearized. This contribution builds upon prior work by Lyakhov, Gerdt, and Michels, which focused on obtaining a…

Symbolic Computation · Computer Science 2024-04-03 Dmitry A. Lyakhov , Dominik L. Michels

Solving linear ordinary differential equations (ODE) is one of the most promising applications for quantum computers to demonstrate exponential advantages. The challenge of designing a quantum ODE algorithm is how to embed non-unitary…

Quantum Physics · Physics 2025-10-30 Zhong-Xia Shang , Naixu Guo , Dong An , Qi Zhao

In this article using Cuckoo Optimization Algorithm and simple additive weighting method the hybrid COAW algorithm is presented to solve multi-objective problems. Cuckoo algorithm is an efficient and structured method for solving nonlinear…

Neural and Evolutionary Computing · Computer Science 2016-11-03 Zeinab Borhanifar , Elham Shadkam

Time-dependent linear differential equations are a common type of problem that needs to be solved in classical physics. Here we provide a quantum algorithm for solving time-dependent linear differential equations with logarithmic dependence…

Quantum Physics · Physics 2024-06-19 Dominic W. Berry , Pedro C. S. Costa

Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…

Quantum Physics · Physics 2014-02-21 Dominic W. Berry

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…

Quantum Physics · Physics 2021-05-20 Oleksandr Kyriienko , Annie E. Paine , Vincent E. Elfving

Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…

We propose and implement a family of quantum-informed recursive optimization (QIRO) algorithms for combinatorial optimization problems. Our approach leverages quantum resources to obtain information that is used in problem-specific…

Markov chains have been widely employed as a fundamental model in the studies of probabilistic and stochastic communicating and concurrent systems. It is well-understood that decomposition techniques play a key role in reachability analysis…

Quantum Physics · Physics 2018-02-15 Ji Guan , Yuan Feng , Mingsheng Ying

With the advent of quantum computers, many quantum computing algorithms are being developed. Solving linear systems is one of the most fundamental problems in almost all science and engineering. The Harrow-Hassidim-Lloyd algorithm, a…

Quantum Physics · Physics 2022-01-25 Kyungtaek Jun

Solving linear systems of equations is essential for many problems in science and technology, including problems in machine learning. Existing quantum algorithms have demonstrated the potential for large speedups, but the required quantum…

Quantum Physics · Physics 2019-12-17 Hsin-Yuan Huang , Kishor Bharti , Patrick Rebentrost

Although quantum computing holds promise for solving Combinatorial Optimization Problems (COPs), the limited qubit capacity of NISQ hardware makes large-scale instances intractable. Conventional methods attempt to bridge this gap through…

Quantum Physics · Physics 2026-01-21 Yuhan Huang , Siyuan Jin , Yichi Zhang , Qi Zhao , Jun Qi , Qiming Shao

Differentiable models of physical systems provide a powerful platform for gradient-based algorithms, with particular impact on parameter estimation and optimal control. Quantum systems present a particular challenge for such…

Quantum Physics · Physics 2025-09-09 David L. Craig , Natalia Ares , Erik M. Gauger

Solving optimisation problems is a promising near-term application of quantum computers. Quantum variational algorithms leverage quantum superposition and entanglement to optimise over exponentially large solution spaces using an…

Quantum Physics · Physics 2022-10-13 Edric Matwiejew , Jason Pye , Jingbo B. Wang

The Quantum Approximate Optimisation Algorithm (QAOA) is a widely studied quantum-classical iterative heuristic for combinatorial optimisation. While QAOA targets problems in complexity class NP, the classical optimisation procedure…

Quantum Physics · Physics 2025-11-12 Tom Krüger , Wolfgang Mauerer

Solving linear systems and computing eigenvalues are two fundamental problems in linear algebra. For solving linear systems, many efficient quantum algorithms have been discovered. For computing eigenvalues, currently, we have efficient…

Quantum Physics · Physics 2020-09-22 Changpeng Shao

Linear equations play a pivotal role in many areas of science and engineering, making efficient solutions to linear systems highly desirable. The development of quantum algorithms for solving linear systems has been a significant…

Quantum Physics · Physics 2025-02-20 Nhat A. Nghiem

Optimization problems are critical across various domains, yet existing quantum algorithms, despite their great potential, struggle with scalability and accuracy due to excessive reliance on entanglement. To address these limitations, we…

Quantum Physics · Physics 2025-03-04 Seongmin Kim , In-Saeng Suh