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It is difficult to calculate the energy levels and eigenstates of a large physical system on a classical computer because of the exponentially growing size of the Hilbert space. In this work, we experimentally demonstrate a quantum…

Quantum Physics · Physics 2019-03-12 Zhaokai Li , Xiaomei Liu , Hefeng Wang , Sahel Ashhab , Jiangyu Cui , Hongwei Chen , Xinhua Peng , Jiangfeng Du

Quantum computers are expected to be able to solve mathematical problems that cannot be solved using conventional computers. Many of these problems are of practical importance, especially in the areas of cryptography and secure…

Quantum Physics · Physics 2007-05-23 T. B. Pittman , B. C. Jacobs , J. D. Franson

Geometry and dimensionality have played crucial roles in our understanding of the fundamental laws of nature, with examples ranging from curved space-time in general relativity to modern theories of quantum gravity. In quantum many-body…

Quantum Physics · Physics 2025-04-10 Qiming Wu , Yue Shi , Jiehang Zhang

Quantum machine learning is an approach that aims to improve the performance of machine learning methods by leveraging the properties of quantum computers. In quantum circuit learning (QCL), a supervised learning method that can be…

The finite element method is used to approximately solve boundary value problems for differential equations. The method discretises the parameter space and finds an approximate solution by solving a large system of linear equations. Here we…

Quantum Physics · Physics 2016-03-23 Ashley Montanaro , Sam Pallister

In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then…

Quantum Physics · Physics 2021-11-08 Jonas Landman

Suppressing errors is the central challenge for useful quantum computing, requiring quantum error correction for large-scale processing. However, the overhead in the realization of error-corrected ``logical'' qubits, where information is…

We introduce Unitaria, a Python library that brings the simplicity of classical linear algebra toolkits such as NumPy and SciPy to the implementation of quantum algorithms based on block encodings, a general-purpose abstraction in which a…

Quantum Physics · Physics 2026-05-12 Matthias Deiml , Oliver Hüttenhofer , Ram Mosco , Jakob S. Kottmann , Daniel Peterseim

We construct quantum circuits for solving one-dimensional Schr\"odinger equations. Simulations of three typical examples, i.e., harmonic oscillator, square-well and Coulomb potential, show that reasonable results can be obtained with eight…

Quantum Physics · Physics 2009-07-21 K. Nakao , A. Matsuyama

We present a constructive method to translate small quantum circuits into their optical analogues, using linear components of present-day quantum optics technology only. These optical circuits perform precisely the computation that the…

Quantum Physics · Physics 2007-05-23 C. Adami , N. J. Cerf

Modeling composite systems of spins or electrons coupled to bosonic modes is of significant interest for many fields of applied quantum physics and chemistry. A quantum simulation can allow for the solution of quantum problems beyond…

Quantum machines are among the most promising technologies expected to provide significant improvements in the following years. However, bridging the gap between real-world applications and their implementation on quantum hardware is still…

In this paper, we present and analyze methods for solving a system of linear equations over idempotent semifields. The first method is based on the pseudo-inverse of the system matrix. We then present a specific version of Cramer's rule…

Commutative Algebra · Mathematics 2019-06-25 Fateme Olia , Shaban Ghalandarzadeh , Amirhossein Amiraslani , Sedighe Jamshidvand

Advances in development of quantum computing processors brought ample opportunities to test the performance of various quantum algorithms with practical implementations. In this paper we report on implementations of quantum compression…

Quantum Physics · Physics 2022-09-22 Matej Pivoluska , Martin Plesch

Quantum process tomography is an experimental technique to fully characterize an unknown quantum process. Standard quantum process tomography suffers from exponentially scaling of the number of measurements with the increasing system size.…

Quantum Physics · Physics 2022-08-02 Shichuan Xue , Yong Liu , Yang Wang , Pingyu Zhu , Chu Guo , Junjie Wu

The classification of big data usually requires a mapping onto new data clusters which can then be processed by machine learning algorithms by means of more efficient and feasible linear separators. Recently, Lloyd et al. have advanced the…

Violation of Mermin inequalities is tested on the 5-qubit IBM quantum computer. For 3, 4 and 5 parties, quantum states that violate the corresponding Mermin inequalities are constructed using quantum circuits on superconducting qubits.…

Quantum Physics · Physics 2016-07-13 Daniel Alsina , José Ignacio Latorre

Given a linear unknown system with $m$ inputs, $p$ outputs, $n$ dimensional state vector, and $q$ dimensional ecosystem, the problem of the adaptive optimal output regulation of this system boils down to iteratively solving a set of linear…

Optimization and Control · Mathematics 2023-09-28 Liquan Lin , Jie Huang

Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct…

Quantum Physics · Physics 2013-03-22 Xiao-Qi Zhou , Pruet Kalasuwan , Timothy C. Ralph , Jeremy L. O'Brien

The emergence of huge-scale, data-intensive linear optimization (LO) problems in applications such as machine learning has driven the need for more computationally efficient interior point methods (IPMs). While conventional IPMs are…