相关论文: Group Sparse Matrix Optimization for Efficient Qua…
This paper introduces an efficient first-order method based on the alternating direction method of multipliers (ADMM) to solve semidefinite programs (SDPs) arising from sum-of-squares (SOS) programming. We exploit the sparsity of the…
In this paper, we propose an algorithmic framework, dubbed inertial alternating direction methods of multipliers (iADMM), for solving a class of nonconvex nonsmooth multiblock composite optimization problems with linear constraints. Our…
We study quantum sparse recovery in non-orthogonal, overcomplete dictionaries: given coherent quantum access to a state and a dictionary of vectors, the goal is to reconstruct the state up to $\ell_2$ error using as few vectors as possible.…
The matching problem between two adjacency matrices can be formulated as the NP-hard quadratic assignment problem (QAP). Previous work on semidefinite programming (SDP) relaxations to the QAP have produced solutions that are often tight in…
Quantum state tomography (QST) is an indispensable tool for characterizing many-body quantum systems. However, due to the exponential scaling of the cost of the protocol with system size, many approaches have been developed for quantum…
Determining ground state energies of quantum systems by hybrid classical/quantum methods has emerged as a promising candidate application for near-term quantum computational resources. Short of large-scale fault-tolerant quantum computers,…
It is proposed to give up the description of physical states in terms of ensembles of state vectors with various probabilities, relying instead solely on the density matrix as the description of reality. With this definition of a physical…
We present an efficient algorithm for twirling a multi-qudit quantum state. The algorithm can be used for approximating the twirling operation in an ensemble of physical systems in which the systems cannot be individually accessed. It can…
In the case of quantum systems interacting with multiple environments, the time-evolution of the reduced density matrix is described by the Liouvillian. For a variety of physical observables, the long-time limit or steady state solution is…
Quantum technologies exploit entanglement to enhance various tasks beyond their classical limits including computation, communication and measurements. Quantum metrology aims to increase the precision of a measured quantity that is…
We consider the quantum complexity of estimating matrix elements of unitary irreducible representations of groups. For several finite groups including the symmetric group, quantum Fourier transforms yield efficient solutions to this…
We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…
We consider a class of Riemannian optimization problems where the objective is the sum of a smooth function and a nonsmooth function, considered in the ambient space. This class of problems finds important applications in machine learning…
Semidefinite programs (SDPs) are a particular class of convex optimization problems with applications in combinatorial optimization, operational research, and quantum information science. Seminal work by Brand\~{a}o and Svore shows that a…
State preparation is a necessary component of many quantum algorithms. In this work, we combine a method for efficiently representing smooth differentiable probability distributions using matrix product states with recently discovered…
Quantum state tomography is an integral part of quantum computation and offers the starting point for the validation of various quantum devices. One of the central tasks in the field of state tomography is to reconstruct with high fidelity,…
Polynomial optimization problems are infinite-dimensional, nonconvex, NP-hard, and are often handled in practice with the moment-sums of squares hierarchy of semidefinite programming bounds. We consider problems where the objective function…
Estimation of physical observables for unknown quantum states is an important problem that underlies a wide range of fields, including quantum information processing, quantum physics, and quantum chemistry. In the context of quantum…
This paper addresses the challenge of preparing mixed quantum states -- both arbitrary states in general and highly sparse ones in particular -- an area that has received far less attention than the preparation of pure states. We present…
Effective state transfer is one of the most important problems in quantum information processing. Typically, a quantum information device is composed of many subsystems with multi-input ports. In this paper, we develop a general theory…