Related papers: Inapproximability of Positive Semidefinite Permane…
Finding a good way to model probability densities is key to probabilistic inference. An ideal model should be able to concisely approximate any probability while being also compatible with two main operations: multiplications of two models…
Binary quadratic programming problems have attracted much attention in the last few decades due to their potential applications. This type of problems are NP-hard in general, and still considered a challenge in the design of efficient…
We propose a high efficiency tomographic scheme to reconstruct an unknown quantum state of the qubits by using a series of quantum nondemolition (QND) measurements. The proposed QND measurements of the qubits are implemented by probing the…
Common tools for obtaining physical density matrices in experimental quantum state tomography are shown here to cause systematic errors. For example, using maximum likelihood or least squares optimization for state reconstruction, we…
In this article, we present a geometric theoretical analysis of semidefinite feasibility problems (SDFPs). This is done by decomposing a SDFP into smaller problems, in a way that preserves most feasibility properties of the original…
The density matrix is a positive semidefinite operator of trace 1 characterizing the state of a quantum system. We consider the inverse problem to reconstruct such density matrices from indirect measurements, also known as quantum state…
Several important applications, such as streaming PCA and semidefinite programming, involve a large-scale positive-semidefinite (psd) matrix that is presented as a sequence of linear updates. Because of storage limitations, it may only be…
Regions of quantum states generalize the classical notion of error bars. High posterior density (HPD) credible regions are the most powerful of region estimators. However, they are intractably hard to construct in general. This paper…
In quantum information transformation and quantum computation, the most critical issues are security and accuracy. These features, therefore, stimulate research on quantum state characterization. A characterization tool, Quantum state…
It is imperative that useful quantum computers be very difficult to simulate classically; otherwise classical computers could be used for the applications envisioned for the quantum ones. Perfect quantum computers are unarguably…
The cone of positive-semidefinite (PSD) matrices is fundamental in convex optimization, and we extend this notion to tensors, defining PSD tensors, which correspond to separable quantum states. We study the convex optimization problem over…
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…
In order to find the outcome probabilities of quantum mechanical systems like the optical networks underlying Boson sampling, it is necessary to be able to compute the permanents of unitary matrices, a computationally hard task. Here we…
Quantum tomography is the main method used to assess the quality of quantum information processing devices, but its complexity presents a major obstacle for the characterization of even moderately large systems. The number of experimental…
Quantum State Tomography is the task of determining an unknown quantum state by making measurements on identical copies of the state. Current algorithms are costly both on the experimental front -- requiring vast numbers of measurements --…
In this paper, we present a characterization of compact quantum metric spaces in terms of finite dimensional approximations. This characterization naturally leads to the introduction of a matrix analogue of a compact quantum metric space.…
Using the the convex semidefinite programming method and superoperator formalism we obtain the finite quantum tomography of some mixed quantum states such as: qudit tomography, N-qubit tomography, phase tomography and coherent spin state…
Postive semidefinite (PSD) cone is the cone of positive semidefinite matrices, and is the object of interest in semidefinite programming (SDP). A computational efficient approximation of the PSD cone is the $k$-PSD closure, $1 \leq k < n$,…
The Geometric Bin Packing (GBP) problem is a generalization of Bin Packing where the input is a set of $d$-dimensional rectangles, and the goal is to pack them into unit $d$-dimensional cubes efficiently. It is NP-Hard to obtain a PTAS for…
A Fixed-Parameter Tractable (\FPT) $\rho$-approximation algorithm for a minimization (resp. maximization) parameterized problem $P$ is an FPT algorithm that, given an instance $(x, k)\in P$ computes a solution of cost at most $k \cdot…