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The laws of quantum mechanics place fundamental limits on the accuracy of measurements and therefore on the estimation of unknown parameters of a quantum system. In this work, we prove lower bounds on the size of confidence regions reported…

Quantum Physics · Physics 2014-12-23 Michael Walter , Joseph M. Renes

We propose a novel quantum algorithm for solving nuclear resonances, which is based on the iterative Harrow-Hassidim-Lloyd algorithm and eigenvector continuation with complex scaling. To validate this approach, we compute the resonant…

Quantum Physics · Physics 2025-06-27 Hantao Zhang , Dong Bai , Zhongzhou Ren

Quantum algorithms on the noisy intermediate-scale quantum (NISQ) devices are expected to simulate quantum systems that are classically intractable to demonstrate quantum advantages. However, the non-negligible gate error on the NISQ…

Quantum Physics · Physics 2021-12-06 Joseph C. Aulicino , Trevor Keen , Bo Peng

With the advent and development of quantum computers, various quantum algorithms that can solve linear equations and eigenvalues faster than classical computers have been developed. The Harrow-Hassidim-Lloyd algorithm is an algorithm that…

Quantum Physics · Physics 2025-06-23 Hyunju Lee , Kyungtaek Jun

From the noncommutative nature of quantum mechanics, estimation of canonical observables $\hat{q}$ and $\hat{p}$ is essentially restricted in its performance by the Heisenberg uncertainty relation, $\mean{\Delta \hat{q}^2}\mean{\Delta…

Quantum Physics · Physics 2007-09-24 Naoki Yamamoto , Shinji Hara

We propose and study an algorithm for computing a nearest passive system to a given non-passive linear time-invariant system (with much freedom in the choice of the metric defining `nearest', which may be restricted to structured…

Numerical Analysis · Mathematics 2021-03-04 Antonio Fazzi , Nicola Guglielmi , Christian Lubich

In contexts where relevant problems can easily attain configuration spaces of enormous sizes, solving Linear Differential Equations (LDEs) can become a hard achievement for classical computers; on the other hand, the rise of quantum…

Quantum Physics · Physics 2023-01-31 João H. Romeiro , Frederico Brito

We derive out a complete series expression of Hamiltonian eigenvalues without any approximation and cut in the general quantum systems based on Wang's formal framework \cite{wang1}. In particular, we then propose a calculating approach of…

Quantum Physics · Physics 2009-11-12 Zhou Li , An Min Wang

A powerful method for calculating the eigenvalues of a Hamiltonian operator consists of converting the energy eigenvalue equation into a matrix equation by means of an appropriate basis set of functions. The convergence of the method can be…

Quantum Physics · Physics 2007-05-23 Paolo Amore , Alfredo Aranda , Francisco Fernandez , Hugh Jones

The implementation of optimal statistical inference protocols for high-dimensional quantum systems is often computationally expensive. To avoid the difficulties associated with optimal techniques, here I propose an alternative approach to…

Quantum Physics · Physics 2015-12-23 Mankei Tsang

We introduce a general method for transforming the equations of motion following from a Das-Jevicki-Sakita Hamiltonian, with boundary conditions, into a boundary value problem in one-dimensional quantum mechanics. For the particular case of…

High Energy Physics - Theory · Physics 2009-10-31 L. D. Paniak

Digital quantum computers provide a computational framework for solving the Schr\"{o}dinger equation for a variety of many-particle systems. Quantum computing algorithms for the quantum simulation of these systems have recently witnessed…

Quantum Physics · Physics 2022-03-21 Mario Motta , Julia Rice

We describe a new polynomial time quantum algorithm that uses the quantum fast fourier transform to find eigenvalues and eigenvectors of a Hamiltonian operator, and that can be applied in cases (commonly found in ab initio physics and…

Quantum Physics · Physics 2009-01-23 Daniel S. Abrams , Seth Lloyd

Laplacian eigenmap algorithm is a typical nonlinear model for dimensionality reduction in classical machine learning. We propose an efficient quantum Laplacian eigenmap algorithm to exponentially speed up the original counterparts. In our…

Quantum Physics · Physics 2016-11-04 Yiming Huang , Xiaoyu Li

Given an optimization problem, the Hessian matrix and its eigenspectrum can be used in many ways, ranging from designing more efficient second-order algorithms to performing model analysis and regression diagnostics. When nonlinear models…

Machine Learning · Statistics 2021-03-18 Zhenyu Liao , Michael W. Mahoney

Quantum metrology is a general term for methods to precisely estimate the value of an unknown parameter by actively using quantum resources. In particular, some classes of entangled states can be used to significantly suppress the…

Quantum Physics · Physics 2015-05-01 Takanori Sugiyama

The Harrow-Hassidim-Lloyd (HHL) quantum algorithm for sampling from the solution of a linear system provides an exponential speed-up over its classical counterpart. The problem of solving a system of linear equations has a wide scope of…

Quantum Metrology calculates the ultimate precision of all estimation strategies, measuring what is their root mean-square error (RMSE) and their Fisher information. Here, instead, we ask how many bits of the parameter we can recover,…

Quantum Physics · Physics 2017-11-22 Lorenzo Maccone , Majid Hassani , Chiara Macchiavello

Sampling noisy intermediate-scale quantum devices is a fundamental step that converts coherent quantum-circuit outputs to measurement data for running variational quantum algorithms that utilize gradient and Hessian methods in cost-function…

Quantum Physics · Physics 2023-07-04 Y. S. Teo

This paper introduces a novel method for eigenvalue computation using a distributed cooperative neural network framework. Unlike traditional techniques that face scalability challenges in large systems, our decentralized algorithm enables…

Machine Learning · Computer Science 2024-09-20 Ronald Katende