Related papers: EIQP: Execution-time-certified and Infeasibility-d…
Quadratic Programming (QP) is the well-studied problem of maximizing over {-1,1} values the quadratic form \sum_{i \ne j} a_{ij} x_i x_j. QP captures many known combinatorial optimization problems, and assuming the unique games conjecture,…
Quantum relative entropy optimization refers to a class of convex problems in which a linear functional is minimized over an affine section of the epigraph of the quantum relative entropy function. Recently, the self-concordance of a…
We propose an interior point method (IPM) for solving semidefinite programming problems (SDPs). The standard interior point algorithms used to solve SDPs work in the space of positive semidefinite matrices. Contrary to that the proposed…
In this paper, we propose a catalog of iterative methods for solving the Split Feasibility Problem in the non-convex setting. We study four different optimization formulations of the problem, where each model has advantageous in different…
The NP-hard problem of optimizing a quadratic form over the unimodular vector set arises in radar code design scenarios as well as other active sensing and communication applications. To tackle this problem (which we call unimodular…
We present a general-purpose solver for convex quadratic programs based on the alternating direction method of multipliers, employing a novel operator splitting technique that requires the solution of a quasi-definite linear system with the…
We introduce a class of specially structured linear programming (LP) problems, which has favorable modeling capability for important application problems in different areas such as optimal transport, discrete tomography and economics. To…
Since the beginning of the development of interior-point methods, there exists a puzzling gap between the results in theory and the observations in numerical experience, i.e., algorithms with good polynomial bound are not computationally…
Constraint satisfiability problems, crucial to several applications, are solved on a quantum computer using Grover's search algorithm, leading to a quadratic improvement over the classical case. The solutions are obtained with high…
Quadratic programming (QP) is a fundamental optimization model with wide-ranging applications in decision-making and machine learning, yet efficiently solving large-scale instances remains a major computational challenge. Building upon the…
The class of commuting quantum circuits known as IQP (instantaneous quantum polynomial-time) has been shown to be hard to simulate classically, assuming certain complexity-theoretic conjectures. Here we study the power of IQP circuits in…
We develop polynomial-time heuristic methods to solve unimodular quadratic programs (UQPs) approximately, which are known to be NP-hard. In the UQP framework, we maximize a quadratic function of a vector of complex variables with unit…
Quantum phase estimation (QPE) is one of the core algorithms for quantum computing. It has been extensively studied and applied in a variety of quantum applications such as the Shor's factoring algorithm, quantum sampling algorithms and the…
For typical quantum subroutines in the gate-based model of quantum computing, explicit decompositions of circuits in terms of single-qubit and two-qubit entangling gates may exist. However, they often lead to large-depth circuits that are…
As research on building scalable quantum computers advances, it is important to be able to certify their correctness. Due to the exponential hardness of classically simulating quantum computation, straight-forward verification through…
We propose an inexact infeasible arc-search interior-point method for solving linear optimization problems. The method combines an arc-search strategy with inexact solutions to Newton systems and admits a polynomial iteration complexity…
Ever since entanglement was identified as a computational and cryptographic resource, researchers have sought efficient ways to tell whether a given density matrix represents an unentangled, or separable, state. This paper gives the first…
This study considers the control problem with signal temporal logic (STL) specifications. Prior works have adopted smoothing techniques to address this problem within a feasible time frame and solve the problem by applying sequential…
In this paper, we propose an infeasible arc-search interior-point algorithm for solving nonlinear programming problems. Most algorithms based on interior-point methods are categorized as line search, since they compute a next iterate on a…
Instantaneous Quantum Polynomial-time (IQP) circuits are a candidate for demonstrating near-term quantum advantage, as their sampling task is believed to be classically hard in the ideal theoretical setting under standard…