Related papers: Noisy intermediate-scale quantum algorithm for sem…
We present a collection of optimizers tuned for usage on Noisy Intermediate-Scale Quantum (NISQ) devices. Optimizers have a range of applications in quantum computing, including the Variational Quantum Eigensolver (VQE) and Quantum…
As the title indicates, this chapter presents a brief, self-contained introduction to five fundamental problems in Quantum Information Science (QIS) that are especially well-suited to be formulated as Semi-definite Programs (SDP). We have…
Many computer vision problems can be formulated as binary quadratic programs (BQPs). Two classic relaxation methods are widely used for solving BQPs, namely, spectral methods and semidefinite programming (SDP), each with their own…
HDSDP is a numerical software solving the semidefinite programming problems. The main framework of HDSDP resembles the dual-scaling interior point solver DSDP [BY2008] and several new features, including a dual method based on the…
In this paper, we present a stabilized sequential quadratic semidefinite programming (SQSDP) method for nonlinear semidefinite programming (NSDP) problems and prove its local convergence. The stabilized SQSDP method is originally developed…
Semidefinite programs (SDPs) are standard convex problems that are frequently found in control and optimization applications. Interior-point methods can solve SDPs in polynomial time up to arbitrary accuracy, but scale poorly as the size of…
An optimization problem considering AC power flow constraints and integer decision variables can usually be posed as a mixed-integer quadratically constrained quadratic program (MIQCQP) problem. In this paper, first, a set of valid linear…
We study optimization programs given by a bilinear form over non-commutative variables subject to linear inequalities. Problems of this form include the entangled value of two-prover games, entanglement-assisted coding for classical…
This paper develops new semidefinite programming (SDP) relaxation techniques for two classes of mixed binary quadratically constrained quadratic programs (MBQCQP) and analyzes their approximation performance. The first class of problem…
This study systematically benchmarks several non-fault-tolerant quantum computing algorithms across four distinct optimization problems: max-cut, number partitioning, knapsack, and quantum spin glass. Our benchmark includes noisy…
Quantum algorithms are getting extremely popular due to their potential to significantly outperform classical algorithms. Yet, applying quantum algorithms to optimization problems meets challenges related to the efficiency of quantum…
Noisy Intermediate-Scale Quantum (NISQ) computers, despite their limitations, present opportunities for near-term quantum advantages in Nuclear and High-Energy Physics (NHEP) when paired with specially designed quantum algorithms and…
In computer vision, many problems such as image segmentation, pixel labelling, and scene parsing can be formulated as binary quadratic programs (BQPs). For submodular problems, cuts based methods can be employed to efficiently solve…
Quantum algorithms offer an exponential speedup over classical algorithms for a range of computational problems. The fundamental mechanisms underlying quantum computation required the development and construction of quantum computers. These…
Parameterized quantum circuits (PQCs) play an essential role in the application of variational quantum algorithms (VQAs) in noisy intermediate-scale quantum (NISQ) devices. The PQCs are a leading candidate to achieve a quantum advantage in…
We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are…
Integer semidefinite programming (ISDP) has recently gained attention due to its connection to binary quadratically constrained quadratic programs (BQCQPs), which can be exactly reformulated as binary semidefinite programs (BSDPs). However,…
The matching problem between two adjacency matrices can be formulated as the NP-hard quadratic assignment problem (QAP). Previous work on semidefinite programming (SDP) relaxations to the QAP have produced solutions that are often tight in…
Variational quantum algorithms (VQAs) offer the most promising path to obtaining quantum advantages via noisy intermediate-scale quantum (NISQ) processors. Such systems leverage classical optimization to tune the parameters of a…
This paper introduces a new robust interior point method analysis for semidefinite programming (SDP). This new robust analysis can be combined with either logarithmic barrier or hybrid barrier. Under this new framework, we can improve the…