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Related papers: Near-Optimal Quantum Algorithms for Multivariate M…

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Quantum computing, with its potential to enhance various machine learning tasks, allows significant advancements in kernel calculation and model precision. Utilizing the one-class Support Vector Machine alongside a quantum kernel, known for…

Accurate computation of multiple eigenvalues of quantum Hamiltonians is essential in quantum chemistry, materials science, and molecular spectroscopy. Estimating excited-state energies is challenging for classical algorithms due to…

Quantum Physics · Physics 2026-05-22 Grzegorz Rajchel-Mieldzioć , Szymon Pliś , Emil Zak

We study the fundamental problems of Gaussian mean estimation and linear regression with Gaussian covariates in the presence of Huber contamination. Our main contribution is the design of the first sample near-optimal and almost linear-time…

Data Structures and Algorithms · Computer Science 2023-12-05 Ilias Diakonikolas , Daniel M. Kane , Ankit Pensia , Thanasis Pittas

We present a quantum algorithm for finding the minimum of a function based on multistep quantum computation and apply it for optimization problems with continuous variables, in which the variables of the problem are discretized to form the…

Quantum Physics · Physics 2023-07-03 Hefeng Wang , Hua Xiang

Phase estimation is a quantum algorithm for measuring the eigenvalues of a Hamiltonian. We propose and rigorously analyse a randomized phase estimation algorithm with two distinctive features. First, our algorithm has complexity independent…

Quantum Physics · Physics 2022-08-09 Kianna Wan , Mario Berta , Earl T. Campbell

Many quantum algorithms involve the evaluation of expectation values. Optimal strategies for estimating a single expectation value are known, requiring a number of state preparations that scales with the target error $\varepsilon$ as…

Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…

Quantum Physics · Physics 2025-05-14 Noah Brüstle , Nathan Wiebe

We propose an estimator for the mean of random variables in separable real Banach spaces using the empirical characteristic function. Assuming that the covariance operator of the random variable is bounded in a precise sense, we show that…

Statistics Theory · Mathematics 2020-11-04 Sohail Bahmani

We introduce two kinds of quantum algorithms to explore microcanonical and canonical properties of many-body systems. The first one is a hybrid quantum algorithm that, given an efficiently preparable state, computes expectation values in a…

Quantum Physics · Physics 2021-05-19 Sirui Lu , Mari Carmen Bañuls , J. Ignacio Cirac

Estimating correctly the quantum phase of a physical system is a central problem in quantum parameter estimation theory due to its wide range of applications from quantum metrology to cryptography. Ideally, the optimal quantum estimator is…

Quantum Physics · Physics 2021-06-09 Marco A. Rodríguez-García , Isaac Pérez Castillo , P. Barberis-Blostein

We present simple differentially private estimators for the mean and covariance of multivariate sub-Gaussian data that are accurate at small sample sizes. We demonstrate the effectiveness of our algorithms both theoretically and empirically…

Machine Learning · Statistics 2026-02-10 Sourav Biswas , Yihe Dong , Gautam Kamath , Jonathan Ullman

Quantum machine learning has the potential to provide powerful algorithms for artificial intelligence. The pursuit of quantum advantage in quantum machine learning is an active area of research. For current noisy, intermediate-scale quantum…

Quantum Physics · Physics 2023-05-11 Rui Yang , Samuel Bosch , Bobak Kiani , Seth Lloyd , Adrian Lupascu

A model of quantum noisy channel with input encoding by a classical random vector is described. An equation of optimality is derived to determine a complete set of wave functions describing quantum decodings based on quasi-measurements…

Quantum Physics · Physics 2007-05-23 V. P. Belavkin , R. L. Stratonovich

Quantum computers show potential for achieving computational advantage over classical computers, with many candidate applications in combinatorial optimisation. We present an application level benchmarking framework for near-term quantum…

The formalism of quantum estimation theory with a specific focus on classical data postprocessing is applied to a two-level system driven by an external gyrating magnetic field. We employed both Bayesian and frequentist approaches to…

Quantum Physics · Physics 2025-05-05 Chun Kit Dennis Law , József Zsolt Bernád

The quest for precision in parameter estimation is a fundamental task in different scientific areas. The relevance of this problem thus provided the motivation to develop methods for the application of quantum resources to estimation…

Quantum Physics · Physics 2024-06-18 Valeria Cimini , Emanuele Polino , Mauro Valeri , Nicolò Spagnolo , Fabio Sciarrino

Gaussian building blocks are essential for photonic quantum information processing, and universality can be practically achieved by equipping Gaussian circuits with adaptive measurement and feedforward. The number of adaptive steps then…

Quantum Physics · Physics 2026-02-17 Changhun Oh , Youngrong Lim

We give bounds on the average fidelity achievable by any quantum state estimator, which is arguably the most prominently used figure of merit in quantum state tomography. Moreover, these bounds can be computed online---that is, while the…

Quantum Physics · Physics 2015-12-16 Richard Kueng , Christopher Ferrie

Estimating the eigenvalues of non-normal matrices is a foundational problem with far-reaching implications, from modeling non-Hermitian quantum systems to analyzing complex fluid dynamics. Yet, this task remains beyond the reach of standard…

Quantum Physics · Physics 2025-10-23 Yukun Zhang , Yusen Wu , Xiao Yuan

Variational hybrid quantum-classical optimization represents one of the most promising avenue to show the advantage of nowadays noisy intermediate-scale quantum computers in solving hard problems, such as finding the minimum-energy state of…

Quantum Physics · Physics 2020-11-18 Laura Gentini , Alessandro Cuccoli , Stefano Pirandola , Paola Verrucchi , Leonardo Banchi