Related papers: An Efficient Algorithm for a Sharp Approximation o…
Many fundamental properties of a quantum system are captured by its Hamiltonian and ground state. Despite the significance of ground states preparation (GSP), this task is classically intractable for large-scale Hamiltonians. Quantum neural…
A previously developed quantum search algorithm for solving 1-SAT problems in a single step is generalized to apply to a range of highly constrained k-SAT problems. We identify a bound on the number of clauses in satisfiability problems for…
This paper studies binary quadratic programs in which the objective is defined by a Euclidean distance matrix, subject to a general polyhedral constraint set. This class of nonconcave maximisation problems includes the capacitated,…
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…
This paper develops a generalization of the line-search sequential quadratic programming (SQP) algorithm with $\ell_1$-merit function that uses objective and constraint function approximations with tunable accuracy to solve smooth…
This paper addresses the challenges of storage and communication costs for large-scale datasets in resource-constrained edge devices by proposing a novel dataset quantization approach to reduce intra-sample redundancy. Unlike traditional…
Quadratically constrained quadratic programs (QCQPs) are an expressive family of optimization problems that occur naturally in many applications. It is often of interest to seek out sparse solutions, where many of the entries of the…
We present a unified quantum-classical framework for addressing NP-complete constrained combinatorial optimization problems, generalizing the recently proposed Quantum Conic Programming (QCP) approach. Accordingly, it inherits many…
Combinatorial problems stated as Constraint Satisfaction Problems (CSP) are examined. It is shown by example that any algorithm designed for the original CSP, and involving the AllDifferent constraint, has at least the same level of…
A specialized algorithm for quadratic optimization (QO, or, formerly, QP) with disjoint linear constraints is presented. In the considered class of problems, a subset of variables are subject to linear equality constraints, while variables…
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…
Outer approximation methods have long been employed to tackle a variety of optimization problems, including linear programming, in the 1960s, and continue to be effective for solving variational inequalities, general convex problems, as…
The short-path quantum algorithm introduced by Hastings (Quantum 2018, 2019) is a variant of adiabatic quantum algorithms that enables an easier worst-case analysis by avoiding the need to control the spectral gap along a long adiabatic…
Exactly solving first-order constraints (i.e., first-order formulas over a certain predefined structure) can be a very hard, or even undecidable problem. In continuous structures like the real numbers it is promising to compute approximate…
Deep neural networks have achieved exceptional results across a range of applications. As the demand for efficient and sparse deep learning models escalates, the significance of model compression, particularly pruning, is increasingly…
The exact cover problem is an NP-complete problem with broad applications. Studies show that although applying the Quantum Approximate Optimization Algorithm (QAOA) to this problem can yield improved solution quality with deeper circuit…
Quantum algorithms are demonstrated to outperform classical algorithms for certain problems and thus are promising candidates for efficient information processing. Herein we aim to provide a brief and popular introduction to quantum…
Quantum Signal Processing (QSP) and Quantum Singular Value Transformation (QSVT) currently stand as the most efficient techniques for implementing functions of block encoded matrices, a central task that lies at the heart of most prominent…
This paper explores a new class of constrained difference programming problems, where the objective and constraints are formulated as differences of functions, without requiring their convexity. To investigate such problems, novel variants…
Quantum computing is a new computational paradigm that promises applications in several fields, including machine learning. In the last decade, deep learning, and in particular Convolutional neural networks (CNN), have become essential for…