Related papers: A Quantum Interior-Point Predictor-Corrector Algor…
Solving optimization problems is the key to decision making in many real-life analytics applications. However, the coefficients of the optimization problems are often uncertain and dependent on external factors, such as future demand or…
We provide several quantum algorithms for continuous optimization that do not require gradient estimation. Instead, we encode the optimization problem into the dynamics of a physical system and coherently simulate the time evolution. We…
Quantum computing, a prominent non-Von Neumann paradigm beyond Moore's law, can offer superpolynomial speedups for certain problems. Yet its advantages in efficiency for tasks like machine learning remain under investigation, and quantum…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
We present quantum algorithms to efficiently perform discriminant analysis for dimensionality reduction and classification over an exponentially large input data set. Compared with the best-known classical algorithms, the quantum algorithms…
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…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
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…
Impossibility of finding local realistic models for quantum correlations due to entanglement is an important fact in foundations of quantum physics, gaining now new applications in quantum information theory. We present an in-depth…
This paper studies a fundamental problem in convex optimization, which is to solve semidefinite programming (SDP) with high accuracy. This paper follows from the existing robust SDP-based interior point method analysis due to [Huang, Jiang,…
We develop a new `subspace layered least squares' interior point method (IPM) for solving linear programs. Applied to an $n$-variable linear program in standard form, the iteration complexity of our IPM is up to an $O(n^{1.5} \log n)$…
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…
Through recent progress in hardware development, quantum computers have advanced to the point where benchmarking of (heuristic) quantum algorithms at scale is within reach. Particularly in combinatorial optimization - where most algorithms…
The Harrow-Hassidim-Lloyd (HHL) quantum algorithm for sampling from the solution of a linear system provides an exponential speed-up over its classical counterpart. The problem of solving a system of linear equations has a wide scope of…
Interior-point algorithms constitute a very interesting class of algorithms for solving linear-programming problems. In this paper we study efficient implementations of such algorithms for solving the linear program that appears in the…
Linear programming (LP) is an extremely useful tool which has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
The logarithm-determinant is an widely-present operation in many areas of physics and computer science. Derivatives of the logarithm-determinant compute physically relevant quantities in statistical physics models, quantum field theories,…
We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially…
Linear regression is a basic and widely-used methodology in data analysis. It is known that some quantum algorithms efficiently perform least squares linear regression of an exponentially large data set. However, if we obtain values of the…
Quantum algorithms for solving the Quantum Linear System (QLS) problem are among the most investigated quantum algorithms of recent times, with potential applications including the solution of computationally intractable differential…