Related papers: Characterizing finite-dimensional quantum behavior
We consider a broad class of dynamic programming (DP) problems that involve a partially linear structure and some positivity properties in their system equation and cost function. We address deterministic and stochastic problems, possibly…
Semidefinite Optimization has become a standard technique in the landscape of Mathematical Programming that has many applications in finite dimensional Quantum Information Theory. This paper presents a way for finite-dimensional relaxations…
Quantum entanglement lies at the heart of quantum information science, yet its reliable detection in high-dimensional or noisy systems remains a fundamental computational challenge. Semidefinite programming (SDP) hierarchies, such as the…
Despite the numerous uses of semidefinite programming (SDP) and its universal solvability via interior point methods (IPMs), it is rarely applied to practical large-scale problems. This mainly owes to the computational cost of IPMs that…
Perfect Domination Problem (PDP), a canonical challenge in combinatorial optimization, finds critical applications in real-world systems such as error-correcting codes, wireless communication networks, and social networks. Decades of…
Quadratic unconstrained binary optimization problems (QUBOs) are intensively discussed in the realm of quantum computing and polynomial optimization. We provide a vast experimental study of semidefinite programming (SDP) relaxations of…
Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct randomized algorithm for solving large, weakly constrained SDP…
A new approach to solving a class of rankconstrained semi-definite programming (SDP) problems, which appear in many signal processing applications such as transmit beamspace design in multiple-input multiple-output (MIMO) radar, downlink…
Certifying the safety or robustness of neural networks against input uncertainties and adversarial attacks is an emerging challenge in the area of safe machine learning and control. To provide such a guarantee, one must be able to bound the…
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…
This paper studies a fundamental problem in convex optimization, which is to solve semidefinite programming (SDP) with high accuracy. This paper follows from the existing robust SDP-based interior point method analysis due to [Huang, Jiang,…
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…
In quantum thermodynamics, a system is described by a Hamiltonian and a list of non-commuting charges representing conserved quantities like particle number or electric charge, and an important goal is to determine the system's minimum…
We consider optimization problems with polynomial inequality constraints in non-commuting variables. These non-commuting variables are viewed as bounded operators on a Hilbert space whose dimension is not fixed and the associated polynomial…
While current network intrusion detection systems achieve satisfactory accuracy, they often lack explainability. Subgroup Discovery (SD) addresses this by building interpretable rules that characterize feature interactions associated with…
Moment-based distributionally robust optimization (DRO) provides an optimization framework to integrate statistical information with traditional optimization approaches. Under this framework, one assumes that the underlying joint…
We present a technique for reducing the computational requirements by several orders of magnitude in the evaluation of semidefinite relaxations for bounding the set of quantum correlations arising from finite-dimensional Hilbert spaces. The…
Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…
This thesis explores algorithmic applications and limitations of convex relaxation hierarchies for approximating some discrete and continuous optimization problems. - We show a dichotomy of approximability of constraint satisfaction…
We study the limits and capability of public-data assisted differentially private (PA-DP) algorithms. Specifically, we focus on the problem of stochastic convex optimization (SCO) with either labeled or unlabeled public data. For…