Related papers: Optimal self-concordant barriers for quantum relat…

We introduce a quantum algorithm that produces approximate solutions for combinatorial optimization problems. The algorithm depends on a positive integer p and the quality of the approximation improves as p is increased. The quantum circuit…

This thesis focuses on the intersection of mathematical and computational optimization and quantum information. Main contributions are open-source software code: A hybrid approach mixing "traditional" nonconvex and convex methods can make…

This paper presents a family of algorithms for decentralized convex composite problems. We consider the setting of a network of agents that cooperatively minimize a global objective function composed of a sum of local functions plus a…

We study a broad class of quantum process discrimination problems that can handle many optimization strategies such as the Bayes, Neyman-Pearson, and unambiguous strategies, where each process can consist of multiple time steps and can have…

Mathematical models use information from past observations to generate predictions about the future. If two models make identical predictions the one that needs less information from the past to do this is preferred. It is already known…

We revisit the classical dual ascent algorithm for minimization of convex functionals in the presence of linear constraints, and give convergence results which apply even for non-convex functionals. We describe limit points in terms of the…

Quantum machine learning (QML) represents a promising frontier in the quantum technologies. In this pursuit of quantum advantage, the quantum kernel method for support vector machine has emerged as a powerful approach. Entanglement, a…

An elimination problem in semidefinite programming is solved by means of tensor algebra. It concerns families of matrix cube problems whose constraints are the minimum and maximum eigenvalue function on an affine space of symmetric…

We study quantum corrections to hypersurfaces of dimension $d+1>2$ embedded in generic higher-dimensional spacetimes. Manifest covariance is maintained throughout the analysis and our methods are valid for arbitrary co-dimension and…

Using convex optimization, we propose entanglement-assisted quantum error correction procedures that are optimized for given noise channels. We demonstrate through numerical examples that such an optimized error correction method achieves…

After quantum quenches in many-body systems, finite subsystems evolve non-trivially in time, eventually approaching a stationary state. In typical situations, the reduced density matrix of a given subsystem begins and ends this endeavour as…

Entropic uncertainty relations play a fundamental role in quantum information theory. However, determining optimal (tight) entropic uncertainty relations for general observables remains a formidable challenge and has so far been achieved…

We present a simple proof of the approximate Eastin-Knill theorem, which connects the quality of a quantum error-correcting code (QECC) with its ability to achieve a universal set of transversal logical gates. Our derivation employs…

We give new upper and lower bounds on the concavity of quantum entropy. Comparisons are given with other results in the literature.

We propose a novel quantum algorithm for solving linear optimization problems by quantum-mechanical simulation of the central path. While interior point methods follow the central path with an iterative algorithm that works with successive…

We investigate the possibility of solving continuous non-convex optimization problems using a network of interacting quantum optical oscillators. We propose a native encoding of continuous variables in analog signals associated with the…

Let psi: R^n --> R^k be a map defined by k positive definite quadratic forms on R^n. We prove that the relative entropy (Kullback-Leibler) distance from the convex hull of the image of psi to the image of psi is bounded above by an absolute…

Methods of optimal control are applied to a model system of interacting two-level particles (e.g., spin-half atomic nuclei or electrons or two-level atoms) to produce high-fidelity quantum gates while simultaneously negating the detrimental…

This article introduces a new physics-guided Machine Learning framework, with which we solve the generally non-invertible, ill-conditioned problems through an analytical approach and constrain the solution to the approximate inverse with…

We address the characterization of two-qubit gates, focusing on bounds to precision in the joint estimation of the three parameters that define their Cartan decomposition. We derive the optimal probe states that jointly maximize precision,…