相关论文: Limitations of the Macaulay matrix approach for us…
The Poisson equation has many applications across the broad areas of science and engineering. Most quantum algorithms for the Poisson solver presented so far, either suffer from lack of accuracy and/or are limited to very small sizes of the…
Solving systems of linear equations is a fundamental problem, but it can be computationally intensive for classical algorithms in high dimensions. Existing quantum algorithms can achieve exponential speedups for the quantum linear system…
In this paper we introduce a multistep generalization of the guess-and-determine or hybrid strategy for solving a system of multivariate polynomial equations over a finite field. In particular, we propose performing the exhaustive…
Quantum algorithm, as compared to classical algorithm, plays a notable role in solving linear systems of equations with an exponential speedup. Here, we demonstrate a method for solving a particular system of equations by using the concept…
Many engineering problems involve the optimization of computationally expensive models for which derivative information is not readily available. The Bayesian optimization (BO) framework is a particularly promising approach for solving…
Constrained combinatorial optimization with strict linear constraints underpins applications in drug discovery, power grids, logistics, and finance, yet remains computationally demanding for classical algorithms, especially at large scales.…
The Bures metric and the associated Bures-Hall measure is arguably the best choice for studying the spectrum of the quantum mechanical density matrix with no apriori knowledge of the system. We investigate the probability of a gap in the…
Quantum computing has the potential to speed up some optimization methods. One can use quantum computers to solve linear systems via Quantum Linear System Algorithms (QLSAs). QLSAs can be used as a subroutine for algorithms that require…
Large-scale optimization problems arising from the discretization of problems involving PDEs sometimes admit solutions that can be well approximated by low-rank matrices. In this paper, we will exploit this low-rank approximation property…
We present an exact and complete algorithm to isolate the real solutions of a zero-dimensional bivariate polynomial system. The proposed algorithm constitutes an elimination method which improves upon existing approaches in a number of…
Quadratic Unconstrained Binary Optimization (QUBO) is a broad class of optimization problems with many practical applications. To solve its hard instances in an exact way, known classical algorithms require exponential time and several…
Inspired by the quantum computing algorithms for Linear Algebra problems [HHL,TaShma] we study how the simulation on a classical computer of this type of "Phase Estimation algorithms" performs when we apply it to solve the Eigen-Problem of…
This paper presents a new method to reduce the optimization of a pseudo-Boolean function to QUBO problem which can be solved by quantum annealer. The new method has two aspects, one is coefficient optimization and the other is variable…
We propose a method of optimizing monotone Boolean circuits by re-writing them in a simpler, equivalent form. We use in total six heuristics: Hill Climbing, Simulated Annealing, and variations of them, which operate on the representation of…
Current quantum devices support interactions only between physically adjacent qubits, preventing quantum circuits from being directly executed on these devices. Therefore, SWAP gates are required to remap logical qubits to physical qubits,…
Traditional logic programming relies on symbolic computation on the CPU, which can limit performance for large-scale inference tasks. Recent advances in GPU hardware enable high-throughput matrix operations, motivating a shift toward…
Numerous scientific and engineering applications require numerically solving systems of equations. Classically solving a general set of polynomial equations requires iterative solvers, while linear equations may be solved either by direct…
The following paper presents a heuristic method by which sum-of-product Boolean expressions can be simplified with a specific focus on the removal of redundant and selective prime implicants. Existing methods, such as the Karnaugh map and…
Quantum algorithms offer significant speed-ups over their classical counterparts in various applications. In this paper, we develop quantum algorithms for the Kalman filter widely used in classical control engineering using the block…
This study proposes a new constraint handling technique for assisting metaheuristic optimization algorithms to solve constrained optimization problems more effectively and efficiently. Given any two solutions of any constrained optimization…