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We present a sublinear time algorithm that allows one to sample multiple edges from a distribution that is pointwise $\epsilon$-close to the uniform distribution, in an \emph{amortized-efficient} fashion. We consider the adjacency list…

Data Structures and Algorithms · Computer Science 2021-07-21 Talya Eden , Saleet Mossel , Ronitt Rubinfeld

Convex composition optimization is an emerging topic that covers a wide range of applications arising from stochastic optimal control, reinforcement learning and multi-stage stochastic programming. Existing algorithms suffer from…

Optimization and Control · Mathematics 2020-09-01 Tianyi Lin , Chenyou Fan , Mengdi Wang , Michael I. Jordan

We describe an algorithm for quantum state tomography that converges in polynomial time to an estimate, together with a rigorous error bound on the fidelity between the estimate and the true state. The result suggests that state tomography…

Quantum Physics · Physics 2010-02-23 Steven T. Flammia , David Gross , Stephen D. Bartlett , Rolando Somma

We consider the distribution of high-dimensional entangled states to multiple parties via noisy channels and the subsequent probabilistic conversion of these states to desired target states using stochastic local operations and classical…

Quantum Physics · Physics 2022-06-01 Simon Morelli , David Sauerwein , Michalis Skotiniotis , Nicolai Friis

The problem of optimally estimating an unknown unitary quantum operation with the aid of entanglement is addressed. The idea is to prepare an entangled pair, apply the unknown unitary to one of the two parts and then measure the joint…

Quantum Physics · Physics 2007-05-23 Manuel A. Ballester

We study exact, non-deterministic conversion of multipartite pure quantum states into one-another via local operations and classical communication (LOCC) and asymptotic entanglement transformation under such channels. In particular, we…

Quantum Physics · Physics 2018-08-17 Asger Kjærulff Jensen , Péter Vrana

We present one-shot compression protocols that optimally encode ensembles of $N$ identically prepared mixed states into $O(\log N)$ qubits. In contrast to the case of pure-state ensembles, we find that the number of encoding qubits drops…

Quantum Physics · Physics 2016-03-02 Yuxiang Yang , Giulio Chiribella , Daniel Ebler

We propose an ordered set of experimentally accessible conditions for detecting entanglement in mixed states. The $k$-th condition involves comparing moments of the partially transposed density operator up to order $k$. Remarkably, the…

Entanglement, one of the central mysteries of quantum mechanics, plays an essential role in numerous applications of quantum information theory. A natural question of both theoretical and experimental importance is whether universal…

We describe an algorithm for studying the entanglement entropy and spectrum of 2D systems, as a coupled array of $N$ one dimensional chains in their continuum limit. Using the algorithm to study the quantum Ising model in 2D, (both in its…

Statistical Mechanics · Physics 2015-03-31 A. J. A. James , R. M. Konik

Approximating the $k$-th spectral gap $\Delta_k=|\lambda_k-\lambda_{k+1}|$ and the corresponding midpoint $\mu_k=\frac{\lambda_k+\lambda_{k+1}}{2}$ of an $N\times N$ Hermitian matrix with eigenvalues…

Quantum Physics · Physics 2026-05-12 Almudena Carrera Vazquez , Aleksandros Sobczyk

This paper makes three contributions to estimating the number of perfect matching in bipartite graphs. First, we prove that the popular sequential importance sampling algorithm works in polynomial time for dense bipartite graphs. More…

Probability · Mathematics 2022-07-07 Yeganeh Alimohammadi , Persi Diaconis , Mohammad Roghani , Amin Saberi

Quantum-enhanced sensing promises to improve the performance of sensing tasks using non-classical probes and measurements that require far fewer scene-modulated photons than the best classical schemes, thereby granting…

Quantum Physics · Physics 2021-08-11 Michael R. Grace , Christos N. Gagatsos , Saikat Guha

We consider the problem of estimating the frequency components of a mixture of s complex sinusoids from a random subset of n regularly spaced samples. Unlike previous work in compressed sensing, the frequencies are not assumed to lie on a…

Information Theory · Computer Science 2013-07-12 Gongguo Tang , Badri Narayan Bhaskar , Parikshit Shah , Benjamin Recht

The state overlap, quantified via $\tr[\rho \sigma]$, is a metric widely used to assess the closeness between two quantum states $\rho$ and $\sigma$. Although global state overlap alone does not directly capture entanglement properties, we…

Quantum tomography is a fundamental technique for characterizing, benchmarking, and verifying quantum states and devices. It plays a crucial role in advancing quantum technologies and deepening our understanding of quantum mechanics.…

Graph spectra have been successfully used to classify network types, compute the similarity between graphs, and determine the number of communities in a network. For large graphs, where an eigen-decomposition is infeasible, iterative moment…

Machine Learning · Statistics 2019-03-27 Diego Granziol , Binxin Ru , Stefan Zohren , Xiaowen Dong , Michael Osborne , Stephen Roberts

We propose new quantum algorithms for estimating spectral sums of positive semi-definite (PSD) matrices. The spectral sum of an PSD matrix $A$, for a function $f$, is defined as $ \text{Tr}[f(A)] = \sum_j f(\lambda_j)$, where $\lambda_j$…

Quantum Physics · Physics 2024-06-11 Alessandro Luongo , Changpeng Shao

Quantum state tomography is a fundamental problem in quantum computing. Given $n$ copies of an unknown $N$-qubit state $\rho \in \mathbb{C}^{d \times d},d=2^N$, the goal is to learn the state up to an accuracy $\epsilon$ in trace distance,…

Quantum Physics · Physics 2025-02-26 Jayadev Acharya , Abhilash Dharmavarapu , Yuhan Liu , Nengkun Yu

The area of sublinear algorithms have recently received a lot of attention. In this setting, one has to choose specific access model for the input, as the algorithm does not have time to pre-process or even to see the whole input. A…

Data Structures and Algorithms · Computer Science 2020-09-24 Jakub Tětek