Related papers: Solutions for the MaxEnt problem with symmetry con…
This thesis is focused on some solvable quantum mechanical models and their associated symmetries.
The maximum-entropy sampling problem is a fundamental and challenging combinatorial-optimization problem, with application in spatial statistics. It asks to find a maximum-determinant order-$s$ principal submatrix of an order-$n$ covariance…
We present an algorithm to compute the number of solutions of the (constrained) number partitioning problem. A concrete implementation of the algorithm on an Ising-type quantum computer is given.
We introduce a novel algorithm for the task of coherently controlling a quantum mechanical system to implement any chosen unitary dynamics. It performs faster than existing state of the art methods by one to three orders of magnitude…
This paper deals with optimal control problems for systems affine in the control variable. We consider nonnegativity constraints on the control, and finitely many equality and inequality constraints on the final state. First, we obtain…
Engineering quantum systems offers great opportunities both technologically and scientifically for communication, computation, and simulation. The construction and operation of large scale quantum information devices presents a grand…
Constraints make hard optimization problems even harder to solve on quantum devices because they are implemented with large energy penalties and additional qubit overhead. The parity mapping, which has been introduced as an alternative to…
A general prescription for the treatment of constrained quantum motion is outlined. We consider in particular constraints defined by algebraic submanifolds of the quantum state space. The resulting formalism is applied to obtain solutions…
We provide a new quantum algorithm that efficiently determines the quality of a least-squares fit over an exponentially large data set by building upon an algorithm for solving systems of linear equations efficiently (Harrow et al., Phys.…
Important properties of a quantum system are not directly measurable, but they can be disclosed by how fast the system changes under controlled perturbations. In particular, asymmetry and entanglement can be verified by reconstructing the…
New measures for the quantization of systems with constraints are discussed and applied to several examples, in particular, examples of alternative but equivalent formulations of given first-class constraints, as well as a comparison of…
We provide quantitative bounds on the characterisation of multiparticle separable states by states that have locally symmetric extensions. The bounds are derived from two-particle bounds and relate to recent studies on quantum versions of…
We show that if an efficient classical representation of the dynamics exists, optimal control problems on many-body quantum systems can be solved efficiently with finite precision. We show that the size of the space of parameters necessary…
Necessary optimality conditions and numerical methods for solving an optimal control problem for a linear continuous-time dynanical system with controlled coefficients and quadratic goal functional are discussed.
We develop an approach for the treatment of one--dimensional bounded quantum--mechanical models by straightforward modification of a successful method for unbounded ones. We apply the new approach to a simple example and show that it…
In this paper, we propose two new methods for solving Set Constraint Problems, as well as a potential polynomial solution for NP-Complete problems using quantum computation. While current methods of solving Set Constraint Problems focus on…
We consider the problem of designing an optimal quantum detector to minimize the probability of a detection error when distinguishing between a collection of quantum states, represented by a set of density operators. We show that the design…
In this paper, motivated by the study of optimal control problems for infinite dimensional systems with endpoint state constraints, we introduce the notion of finite codimensional (exact/approximate) controllability. Some equivalent…
Convex optimization problems arise naturally in quantum information theory, often in terms of minimizing a convex function over a convex subset of the space of hermitian matrices. In most cases, finding exact solutions to these problems is…
We present a systematic introduction to first-order optimality conditions for mathematical programs with equilibrium constraints (MPECs), emphasizing the limitations of classical nonlinear programming techniques. The goal is twofold. First,…