Related papers: Semidefinite Programming in Quantum Information Sc…
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…
The combination of machine learning and physical laws has shown immense potential for solving scientific problems driven by partial differential equations (PDEs) with the promise of fast inference, zero-shot generalisation, and the ability…
Programmability is a unifying paradigm for enacting families of quantum transformations via fixed processors and program states, with a fundamental role and broad impact in quantum computation and control. While there has been a shift from…
We investigate the use of linear programming tools for solving semidefinite programming relaxations of quadratically constrained quadratic problems. Classes of valid linear inequalities are presented, including sparse PSD cuts, and…
A rational number can be naturally presented by an arithmetic computation (AC): a sequence of elementary arithmetic operations starting from a fixed constant, say 1. The asymptotic complexity issues of such a representation are studied e.g.…
Semidefinite relaxations are widely used to compute upper bounds on the objective of optimization problems involving noncommutative polynomials. Such optimization problems are prevalent in quantum information. We present an algorithm able…
Positive maps that are not decomposable are a key resource in entanglement theory because they can detect bound entangled states, yet systematic methods for constructing them remain limited. We introduce an optimization framework based on…
Linear models are regularly used for mapping cores to tiles in a chip. System-on-Chip (SoC) design requires integration of functional units with varying sizes, but conventional models only account for identical-sized cores. Linear models…
Control of the stochastic dynamics of a quantum system is indispensable in fields such as quantum information processing and metrology. However, there is no general ready-made approach to the design of efficient control strategies. Here, we…
We introduce the notion of quantum Markov decision process (qMDP) as a semantic model of nondeterministic and concurrent quantum programs. It is shown by examples that qMDPs can be used in analysis of quantum algorithms and protocols. We…
We introduce a new method to reconstruct unknown quantum states out of incomplete and noisy information. The method is a linear convex optimization problem, therefore with a unique minimum, which can be efficiently solved with Semidefinite…
Understanding and approximating extremal energy states of local Hamiltonians is a central problem in quantum physics and complexity theory. Recent work has focused on developing approximation algorithms for local Hamiltonians, and in…
This paper studies how to solve semi-infinite polynomial programming (SIPP) problems by semidefinite relaxation method. We first introduce two SDP relaxation methods for solving polynomial optimization problems with finitely many…
Verifying entanglement between parties is essential for creating secure quantum communication. However, finite statistics can lead to false positive outcomes in any tests for entanglement. Here, we introduce a one-sided device-independent…
Computing the key rate in quantum key distribution (QKD) protocols is a long standing challenge. Analytical methods are limited to a handful of protocols with highly symmetric measurement bases. Numerical methods can handle arbitrary…
Partial differential equation (PDE) models with multiple temporal/spatial scales are prevalent in several disciplines such as physics, engineering, and many others. These models are of great practical importance but notoriously difficult to…
Semi-infinite programs are a class of mathematical optimization problems with a finite number of decision variables and infinite constraints. As shown by Blankenship and Falk (Blankenship and Falk. "Infinitely constrained optimization…
Dynamic programming (DP) is an algorithmic design paradigm for the efficient, exact solution of otherwise intractable, combinatorial problems. However, DP algorithm design is often presented in an ad-hoc manner. It is sometimes difficult to…
In this paper, we introduce a new class of nonsmooth convex functions called SOS-convex semialgebraic functions extending the recently proposed notion of SOS-convex polynomials. This class of nonsmooth convex functions covers many common…
The vast majority of the literature on stochastic semidefinite programs (stochastic SDPs) with recourse is concerned with risk-neutral models. In this paper, we introduce mean-risk models for stochastic SDPs and study structural properties…