Related papers: A Catalyst Framework for the Quantum Linear System…
Quantum principal component analysis (QPCA) ignited a new development toward quantum machine learning algorithms. Initially showcasing as an active way for analyzing a quantum system using the quantum state itself, QPCA also found potential…
The accelerated proximal point algorithm (APPA), also known as "Catalyst", is a well-established reduction from convex optimization to approximate proximal point computation (i.e., regularized minimization). This reduction is conceptually…
Finding shape correspondences can be formulated as an NP-hard quadratic assignment problem (QAP) that becomes infeasible for shapes with high sampling density. A promising research direction is to tackle such quadratic optimization problems…
Quantum computers hold promise for solving problems intractable for classical computers, especially those with high time or space complexity. Practical quantum advantage can be said to exist for such problems when the end-to-end time for…
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 a quantum algorithm to solve systems of nonlinear algebraic equations. In the ideal case the complexity of the algorithm is linear in the number of variables $n$, which means our algorithm's complexity is less than $O(n^{3})$ of…
We outline refined versions of two major quantum algorithms for performing principal component analysis and solving linear equations. Our methods are exponentially faster than their classical counterparts and even previous quantum…
In this paper, we develop a parameterized proximal point algorithm (P-PPA) for solving a class of separable convex programming problems subject to linear and convex constraints. The proposed algorithm is provable to be globally convergent…
We propose a novel quantum algorithm for solving linear optimization problems by quantum-mechanical simulation of the central path. While interior point methods follow the central path with an iterative algorithm that works with successive…
Solving linear systems of equations is a fundamental problem with a wide variety of applications across many fields of science, and there is increasing effort to develop quantum linear solver algorithms. [Suba\c{s}i et al., Phys. Rev. Lett.…
The emergence of huge-scale, data-intensive linear optimization (LO) problems in applications such as machine learning has driven the need for more computationally efficient interior point methods (IPMs). While conventional IPMs are…
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…
The growing demand for solving large-scale, data-intensive linear and conic optimization problems, particularly in applications such as artificial intelligence and machine learning, has highlighted the limitations of classical interior…
Quantum signal processing (QSP) is a powerful quantum algorithm to exactly implement matrix polynomials on quantum computers. Asymptotic analysis of quantum algorithms based on QSP has shown that asymptotically optimal results can in…
The finite element method is used to approximately solve boundary value problems for differential equations. The method discretises the parameter space and finds an approximate solution by solving a large system of linear equations. Here we…
We present an efficient quantum algorithm to simulate nonlinear differential equations with polynomial vector fields of arbitrary degree on quantum platforms. Models of physical systems that are governed by ordinary differential equations…
Nonlinear convex problems arise in various areas of applied mathematics and engineering. Classical techniques such as the relaxed proximal point algorithm (PPA) and the prediction correction (PC) method were proposed for linearly…
Approximation algorithms for classical constraint satisfaction problems are one of the main research areas in theoretical computer science. Here we define a natural approximation version of the QMA-complete local Hamiltonian problem and…
Simulating the unitary dynamics of a quantum system is a fundamental problem of quantum mechanics, in which quantum computers are believed to have significant advantage over their classical counterparts. One prominent such instance is the…
Demonstrating quantum advantage has been a pressing challenge in the field. Most claimed quantum speedups rely on a subroutine in which classical information can be accessed in a coherent quantum manner, which imposes a crucial constraint…