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In this paper, we explore an efficient online algorithm for quantum state estimation based on a matrix-exponentiated gradient method previously used in the context of machine learning. The state update is governed by a learning rate that…

Quantum Physics · Physics 2019-03-28 Akram Youssry , Christopher Ferrie , Marco Tomamichel

We consider random bipartite quantum states obtained by tracing out one subsystem from a random, uniformly distributed, tripartite pure quantum state. We compute thresholds for the dimension of the system being traced out, so that the…

Mathematical Physics · Physics 2015-09-23 Maria Anastasia Jivulescu , Nicolae Lupa , Ion Nechita

We study the problem of measuring errors in non-trace-preserving quantum operations, with a focus on their impact on quantum computing. We propose an error metric that efficiently provides an upper bound on the trace distance between the…

Quantum Physics · Physics 2023-10-10 Yu Shi , Edo Waks

In the present paper, the trace distance is exposed within the quantum operations formalism. The definition of the trace distance in terms of a maximum over all quantum operations is given. It is shown that for any pair of different states,…

Quantum Physics · Physics 2009-11-13 A. E. Rastegin

A milestone in the field of quantum computing will be solving problems in quantum chemistry and materials faster than state-of-the-art classical methods. The current understanding is that achieving quantum advantage in this area will…

Quantum Physics · Physics 2023-11-08 Guoming Wang , Daniel Stilck França , Ruizhe Zhang , Shuchen Zhu , Peter D. Johnson

We provide more sample-efficient versions of some basic routines in quantum data analysis, along with simpler proofs. Particularly, we give a quantum "Threshold Search" algorithm that requires only $O((\log^2 m)/\epsilon^2)$ samples of a…

Quantum Physics · Physics 2024-08-07 Costin Bădescu , Ryan O'Donnell

We study two-state discrimination in chaotic quantum systems. Assuming that one of two $N$-qubit pure states has been randomly selected, the probability to correctly identify the selected state from an optimally chosen experiment involving…

Quantum Physics · Physics 2023-05-30 Joaquim Telles de Miranda , Tobias Micklitz

Distinguishing quantum states with minimal sampling overhead is of fundamental importance to teach quantum data to an algorithm. Recently, the quantum Wasserstein distance emerged from the theory of quantum optimal transport as a promising…

Quantum Physics · Physics 2025-12-02 Gonzalo Camacho , Benedikt Fauseweh

Geometry and topology have generated impacts far beyond their pure mathematical primitive, providing a solid foundation for many applicable tools. Typically, real-world data are represented as vectors, forming a linear subspace for a given…

Quantum Physics · Physics 2024-05-01 Nhat A. Nghiem

Quantum-phase-estimation algorithms are critical subroutines in many applications for quantum computers and in quantum-metrology protocols. These algorithms estimate the unknown strength of a unitary evolution. By using coherence or…

Quantum Physics · Physics 2023-03-06 Joseph G. Smith , Crispin H. W. Barnes , David R. M. Arvidsson-Shukur

In this work we study the properties of an purification-based entropic metric for measuring the distance between both quantum states and quantum processes. This metric is defined as the square root of the entropy of the average of two…

Quantum Physics · Physics 2015-06-15 Tristan M. Osan , Pedro W. Lamberti

In this paper numerical methods of computing distances between two Radon measures on R are discussed. Efficient algorithms for Wasserstein-type metrics are provided. In particular, we propose a novel algorithm to compute the flat metric…

Numerical Analysis · Mathematics 2013-04-15 Jedrzej Jablonski , Anna Marciniak-Czochra

We analyse the problem of finding sets of quantum states that can be deterministically discriminated. From a geometric point of view this problem is equivalent to that of embedding a simplex of points whose distances are maximal with…

Quantum Physics · Physics 2008-06-09 D. Markham , J. A. Miszczak , Z. Puchala , K. Zyczkowski

In this paper we present a search algorithm that finds useful optical quantum states which can be created with current technology. We apply the algorithm to the field of quantum metrology with the goal of finding states that can measure a…

Quantum Physics · Physics 2016-08-03 P. A. Knott

We define the quantum Wasserstein distance such that the optimization of the coupling is carried out over bipartite separable states rather than bipartite quantum states in general, and examine its properties. Surprisingly, we find that the…

Quantum Physics · Physics 2023-10-17 Géza Tóth , József Pitrik

Quantum state tomography is a powerful, but resource-intensive, general solution for numerous quantum information processing tasks. This motivates the design of robust tomography procedures that use relevant resources as sparingly as…

Quantum Physics · Physics 2022-01-17 Fernando G. S. L. Brandão , Richard Kueng , Daniel Stilck França

We consider the problem of deciding whether a given state preparation, i.e., a source of quantum states, is accurate, namely produces states close to a target one within a prescribed threshold. We show that, when multiple measurements need…

Quantum Physics · Physics 2024-01-22 Weichao Liang , Francesco Ticozzi , Giuseppe Vallone

The minimum distance of a code is an important concept in information theory. Hence, computing the minimum distance of a code with a minimum computational cost is a crucial process to many problems in this area. In this paper, we present…

Information Theory · Computer Science 2024-05-01 Fernando Hernando , Francisco D. Igual , Gregorio Quintana-Ortí

In this work we examine recently proposed distance-based classification method designed for near-term quantum processing units with limited resources. We further study possibilities to reduce the quantum resources without any efficiency…

Quantum Physics · Physics 2018-03-05 Przemysław Sadowski

We prove a tight and close-to-optimal lower bound on the effectiveness of local quantum measurements (without classical communication) at discriminating any two bipartite quantum states. Our result implies, for example, that any two…

Quantum Physics · Physics 2022-10-26 Willian H. G. Corrêa , Ludovico Lami , Carlos Palazuelos