Related papers: A general algorithm for computing bound states in …
Calculating bounds of properties of many-body quantum systems is of paramount importance, since they guide our understanding of emergent quantum phenomena and complement the insights obtained from estimation methods. Recent semidefinite…
We develop an algorithm for computing bounded reachability probability for hybrid systems, i.e., the probability that the system reaches an unsafe region within a finite number of discrete transitions. In particular, we focus on hybrid…
The one-to-one relation between the winding number and the number of robust zero-energy edge states, known as bulk-boundary correspondence, is a celebrated feature of 1d systems with chiral symmetry. Although this property can be explained…
We investigate robust linear consensus over networks under capacity-constrained communication. The capacity of each edge is encoded as an upper bound on the number of state variables that can be communicated instantaneously. When the edge…
The ability to efficiently simulate random quantum circuits using a classical computer is increasingly important for developing Noisy Intermediate-Scale Quantum devices. Here we present a tensor network states based algorithm specifically…
The exploration of quantum phenomena in complex materials such as moir\'e superlattices is limited by the O(N^3) scaling of conventional electronic structure methods. Here we introduce a high-performance tight-binding framework that reduces…
Infinite-dimensional linear systems with unbounded input and output operators are considered. For the purpose of finite-dimensional observer-based state feedback, an observer approximation scheme will be developed which can be directly…
In this paper we study quasilinear elliptic systems with nonlinear boundary condition with fully coupled perturbations even on the boundary. Under very general assumptions our main result says that each weak solution of such systems belongs…
We develop a universally applicable embedded boundary finite difference method, which results in a symmetric positive definite linear system and does not suffer from small cell stiffness. Our discretization is efficient for the wave, heat…
We study compression strategies for multipartite entanglement distribution under uncertainty in the partitioning of the quantum state. When the partition is not known at the time of state preparation, we show that a joint design of the…
In this paper, we consider finite difference approximations of the second order wave equation. We use finite difference operators satisfying the summation-by-parts property to discretize the equation in space. Boundary conditions and grid…
Majorana bound states are zero-energy excitations of topological superconductors which obey non-Abelian exchange statistics and are basic building blocks for topological quantum computation. In order to observe and exploit their…
In this paper, the problem of finding state bounds is considered, for the first time, for a class of positive time-delay coupled differential-difference equations (CDDEs) with bounded disturbances. First, we present a novel method, which is…
Competition between magnetism and superconductivity can lead to unconventional and topological superconductivity. However, the experimental confirmation of the presence of Majorana edge states and unconventional pairing currently poses a…
Moir\'e superlattices have emerged as a versatile platform for exploring a wide range of ex- otic quantum phenomena. Unlike angstrom-scale materials, the moir\'e length-scale system contains a large number of atoms, and its electronic…
A quantum spin chain with non-conventional boundary conditions is studied. The distinct nature of these boundary conditions arises from the conversion of a soliton to an anti-soliton after being reflected to the boundary, hence the…
Zero--energy Majorana quasiparticles can be induced at the edge of a low dimensional systems. Non--Abelian statistics of this state makes it a good candidate for the realization of quantum computing. From the practical point of view, it is…
In this paper, we present a method to solve the quantum marginal problem for symmetric $d$-level systems. The method is built upon an efficient semi-definite program that determines the compatibility conditions of an $m$-body reduced…
In this paper, we present a learning algorithm aimed at learning states obtained from computational basis states by Clifford circuits doped with a finite number $t$ of $T$-gates. The algorithm learns an exact tomographic description of…
We analyze propagation of quantum information along chiral Majorana edge states in two-dimensional topological materials. The use of edge states may facilitate the braiding operation, an important ingredient in topological quantum…