Related papers: Best separable approximation with semi-definite pr…
In a second seminal paper on the application of semidefinite programming to graph partitioning problems, Goemans and Williamson showed how to formulate and round a complex semidefinite program to give what is to date still the best-known…
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…
It is not possible to disentangle a qubit in an unknown state $|\psi>$ from a set of (N-1) ancilla qubits prepared in a specific reference state $|0>$. That is, it is not possible to {\em perfectly} perform the transformation…
Building on the blueprint from Goemans and Williamson (1995) for the Max-Cut problem, we construct a polynomial-time approximation algorithm for orthogonally constrained quadratic optimization problems. First, we derive a semidefinite…
Lie-Trotter-Suzuki decompositions are an efficient way to approximate operator exponentials $\exp(t H)$ when $H$ is a sum of $n$ (non-commuting) terms which, individually, can be exponentiated easily. They are employed in time-evolution…
Quantum state discrimination is a fundamental primitive in quantum information processing, underpinning tasks in quantum communication, sensing, and learning. We consider the general Bayes framework, as introduced by Helstrom, for state…
This paper presents a computationally efficient decoder for multiple antenna systems. The proposed algorithm can be used for any constellation (QAM or PSK) and any labeling method. The decoder is based on matrix-lifting Semi-Definite…
Approximate linear programming (ALP) is an efficient approach to solving large factored Markov decision processes (MDPs). The main idea of the method is to approximate the optimal value function by a set of basis functions and optimize…
The technique of semidefinite programming (SDP) relaxation can be used to obtain a nontrivial bound on the optimal value of a nonconvex quadratically constrained quadratic program (QCQP). We explore concave quadratic inequalities that hold…
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…
In this paper, we develop a new decomposition technique for solving bi-objective linear programming problems. The proposed methodology combines the bi-objective simplex algorithm with Benders decomposition and can be used to obtain a…
The probability that a generic real, complex or quaternionic two-qubit state is separable can be considered to be the sum of three contributions. One is from those states that are absolutely separable, that is those (which can not be…
Two novel schemes are proposed for the dissipative preparation of large W states, of the order of ten qubits, within the context of Cavity QED. By utilizing properties of the irreducible representations of su(3), we are able to construct…
We propose and analyze a posteriori error estimators for an optimal control problem that involves an elliptic partial differential equation as state equation and a control variable that enters the state equation as a coefficient; pointwise…
We present a new generic approach to the condensed-matter ground-state problem which is complementary to variational techniques and works directly in the thermodynamic limit. Relaxing the ground-state problem, we obtain semidefinite…
Linear systems with a tensor product structure arise naturally when considering the discretization of Laplace type differential equations or, more generally, multidimensional operators with separable coefficients. In this work, we focus on…
The infinite projected entangled pair states (iPEPS) technique [J. Jordan {\it et al.}, Phys. Rev. Lett. {\bf 101}, 250602 (2008)] has been widely used in the recent years to assess the properties of two-dimensional quantum systems, working…
We consider the feedback design for stabilizing a rigid body system by making and breaking multiple contacts with the environment without prespecifying the timing or the number of occurrence of the contacts. We model such a system as a…
This paper presents a method to approximately solve stochastic optimal control problems in which the cost function and the system dynamics are polynomial. For stochastic systems with polynomial dynamics, the moments of the state can be…
A $q$-deformed Weyl-Heisenberg algebra is used to define a deformed displacement operator giving rise to a naturally normalized nonlinear coherent states type. Robust maximally entangled deformed coherent states are studied and the effect…