Related papers: Thermodynamic Linear Algebra
Simulating nonlinear classical dynamics on a quantum computer is an inherently challenging task due to the linear operator formulation of quantum mechanics. In this work, we provide a systematic approach to alleviate this difficulty by…
This is a survey paper on applications of mathematics of semirings to numerical analysis and computing. Concepts of universal algorithm and generic program are discussed. Relations between these concepts and mathematics of semirings are…
The construction of models from data is a significant contributor to the energetic costs of computation. Because of this, understanding how foundational thermodynamic bounds apply to modeling algorithms will be increasingly important. Here,…
Laplacian eigenmap algorithm is a typical nonlinear model for dimensionality reduction in classical machine learning. We propose an efficient quantum Laplacian eigenmap algorithm to exponentially speed up the original counterparts. In our…
Solving linear systems of equations plays a fundamental role in numerous computational problems from different fields of science. The widespread use of numerical methods to solve these systems motivates investigating the feasibility of…
With the advent of exascale computing, effective load balancing in massively parallel software applications is critically important for leveraging the full potential of high performance computing systems. Load balancing is the distribution…
This work presents a new approach for simulating the HHL linear systems of equations solver algorithm with tensor networks. First, a novel HHL in the qudits formalism, the generalization of qubits, is developed, and then its operations are…
We give a classical algorithm for linear regression analogous to the quantum matrix inversion algorithm [Harrow, Hassidim, and Lloyd, Physical Review Letters'09, arXiv:0811.3171] for low-rank matrices [Wossnig, Zhao, and Prakash, Physical…
Recent technological developments have focused the interest of the quantum computing community on investigating how near-term devices could outperform classical computers for practical applications. A central question that remains open is…
Nature is governed by precise physical laws, which can inspire the discovery of new computer-run simulation algorithms. Thermal states are the most ubiquitous for they are the equilibrium states of matter. Simulating thermal states of…
The usual representation of quantum algorithms is limited to the process of solving the problem. We extend it to the process of setting the problem. Bob, the problem setter, selects a problem-setting by the initial measurement. Alice, the…
The search for new computational machines beyond the traditional von Neumann architecture has given rise to a modern area of nonlinear science -- development of unconventional computing -- requiring the efforts of mathematicians, physicists…
Important nonlinear dynamics, such as those found in plasma and fluid systems, are typically hard to simulate on classical computers. Thus, if fault-tolerant quantum computers could efficiently solve such nonlinear problems, it would be a…
Recent works have shown that quantum computers can polynomially speed up certain SAT-solving algorithms even when the number of available qubits is significantly smaller than the number of variables. Here we generalise this approach. We…
This paper summarizes a quantum algorithm of [R.D. Somma, et.al., Phys. Rev. Lett. 101, 130504 (2008)] that simulates a classical annealing process for solving discrete optimization problems. The complexity of the quantum algorithm scales…
Analog computers can be revived as a feasible technology platform for low precision, energy efficient and fast computing. We justify this statement by measuring the performance of a modern analog computer and comparing it with that of…
In mathematical aspect, we introduce quantum algorithm and the mathematical structure of quantum computer. Quantum algorithm is expressed by linear algebra on a finite dimensional complex inner product space. The mathematical formulations…
This survey highlights the recent advances in algorithms for numerical linear algebra that have come from the technique of linear sketching, whereby given a matrix, one first compresses it to a much smaller matrix by multiplying it by a…
Faster algorithms, novel cryptographic mechanisms, and alternative methods of communication become possible when the model underlying information and computation changes from a classical mechanical model to a quantum mechanical one. Quantum…
Automated theorem proving, or more broadly automated reasoning, aims at using computer programs to automatically prove or disprove mathematical theorems and logical statements. It takes on an essential role across a vast array of…