Related papers: A Catalyst Framework for the Quantum Linear System…
We describe a quantum algorithm based on an interior point method for solving a linear program with $n$ inequality constraints on $d$ variables. The algorithm explicitly returns a feasible solution that is $\varepsilon$-close to optimal,…
Algorithms based on non-unitary evolution have attracted much interest for ground state preparation on quantum computers. One recently proposed method makes use of ancilla qubits and controlled unitary operators to implement weak…
Gaussian processes (GPs) are important models in supervised machine learning. Training in Gaussian processes refers to selecting the covariance functions and the associated parameters in order to improve the outcome of predictions, the core…
This paper introduces an advanced framework leveraging Large Language Model-based Multi-Agent Systems (LLMMA) for the automated search and optimization of Quantum Machine Learning (QML) algorithms. Inspired by Google DeepMind's FunSearch,…
Quantum linear system algorithms (QLSAs) can provide exponential speedups for the solution of linear systems, but the growth of the condition number for finite element problems can eliminate the exponential speedup. QLSAs are also incapable…
Quantum computers have the potential of solving certain problems exponentially faster than classical computers. Recently, Harrow, Hassidim and Lloyd proposed a quantum algorithm for solving linear systems of equations: given an $N\times{N}$…
The Fokker-Planck equation models rare events across sciences, but its high-dimensional nature challenges classical computers. Quantum algorithms for such non-unitary dynamics often suffer from exponential {decay in} success probability. We…
In this dissertation, we study the intersection of quantum computing and supervised machine learning algorithms, which means that we investigate quantum algorithms for supervised machine learning that operate on classical data. This area of…
Quantum signal processing (QSP) has emerged as a unifying subroutine in quantum algorithms. In QSP, we are given a function $f$ and a unitary black-box $U$, and the goal is to construct a quantum circuit for implementing $f(U)$ to a given…
We consider saddle point problems which objective functions are the average of $n$ strongly convex-concave individual components. Recently, researchers exploit variance reduction methods to solve such problems and achieve linear-convergence…
Achieving a provable exponential quantum speedup for an important machine learning task has been a central research goal since the seminal HHL quantum algorithm for solving linear systems and the subsequent quantum recommender systems…
In adiabatic quantum computing the aim is to track an eigenstate as the Hamiltonian changes. In the usual setup this is achieved using the natural time-dependent Hamiltonian evolution of the system and the main technical tool is the…
Nonlinear programming (NLP) plays a critical role in domains such as power energy systems, chemical engineering, communication networks, and financial engineering. However, solving large-scale, nonconvex NLP problems remains a significant…
The Lasserre Hierarchy is a set of semidefinite programs which yield increasingly tight bounds on optimal solutions to many NP-hard optimization problems. The hierarchy is parameterized by levels, with a higher level corresponding to a more…
Group convolutions and cross-correlations, which are equivariant to the actions of group elements, are commonly used in mathematics to analyze or take advantage of symmetries inherent in a given problem setting. Here, we provide efficient…
This paper presents a quantum algorithm for solving the fractional Poisson equation \((-\Delta)^s u = f\) with \(s \in (0,1)\) on bounded domains. The proposed approach combines rational approximation techniques with quantum linear system…
Quantum machine learning (QML) seeks to exploit the intrinsic properties of quantum mechanical systems, including superposition, coherence, and quantum entanglement for classical data processing. However, due to the exponential growth of…
Quantum interior point methods (QIPMs) promise polynomial speed-ups over classical solvers for linear programming by outsourcing the solution of Newton linear systems to quantum linear solvers (QLSAs). However, asymptotic speed-ups do not…
While quantum computing proposes promising solutions to computational problems not accessible with classical approaches, due to current hardware constraints, most quantum algorithms are not yet capable of computing systems of practical…
This thesis studies three topics in quantum computation and information: The approximability of quantum problems, quantum proof systems, and non-classical correlations in quantum systems. In the first area, we demonstrate a polynomial-time…