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We propose a sequential minimal optimization method for quantum-classical hybrid algorithms, which converges faster, is robust against statistical error, and is hyperparameter-free. Specifically, the optimization problem of the…

Quantum Physics · Physics 2020-11-04 Ken M. Nakanishi , Keisuke Fujii , Synge Todo

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…

A well-recognized limitation of kernel learning is the requirement to handle a kernel matrix, whose size is quadratic in the number of training examples. Many methods have been proposed to reduce this computational cost, mostly by using a…

Machine Learning · Computer Science 2014-11-06 Nicolò Cesa-Bianchi , Yishay Mansour , Ohad Shamir

Kernel method in machine learning consists of encoding input data into a vector in a Hilbert space called the feature space and modeling the target function as a linear map on the feature space. Given a cost function, computing such an…

Quantum Physics · Physics 2022-10-18 Salman Beigi

We study fast algorithms for computing fundamental properties of a positive semidefinite kernel matrix $K \in \mathbb{R}^{n \times n}$ corresponding to $n$ points $x_1,\ldots,x_n \in \mathbb{R}^d$. In particular, we consider estimating the…

Data Structures and Algorithms · Computer Science 2021-06-21 Arturs Backurs , Piotr Indyk , Cameron Musco , Tal Wagner

As combinatorial optimization is one of the main quantum computing applications, many methods based on parameterized quantum circuits are being developed. In general, a set of parameters are being tweaked to optimize a cost function out of…

Quantum Physics · Physics 2022-05-09 Charles Moussa , Hao Wang , Thomas Bäck , Vedran Dunjko

The method is introduced for fast data processing by reducing the probability amplitudes of undesirable elements. The algorithm has a mathematical description and circuit implementation on a quantum processor. The idea is to make a quick…

Quantum Physics · Physics 2025-04-24 Karina Zakharova , Artem Chernikov , Sergey Sysoev

Kernel methods in Quantum Machine Learning (QML) have recently gained significant attention as a potential candidate for achieving a quantum advantage in data analysis. Among other attractive properties, when training a kernel-based model…

Quantum Physics · Physics 2024-04-16 Supanut Thanasilp , Samson Wang , M. Cerezo , Zoë Holmes

Suppose we have n algorithms, quantum or classical, each computing some bit-value with bounded error probability. We describe a quantum algorithm that uses O(sqrt{n}) repetitions of the base algorithms and with high probability finds the…

Quantum Physics · Physics 2017-01-03 Peter Hoyer , Michele Mosca , Ronald de Wolf

We consider the problem of estimating the expected outcomes of Monte Carlo processes whose outputs are described by multidimensional random variables. We tightly characterize the quantum query complexity of this problem for various choices…

Quantum Physics · Physics 2021-07-09 Arjan Cornelissen , Sofiene Jerbi

Machine learning methods usually depend on internal parameters -- so called hyperparameters -- that need to be optimized for best performance. Such optimization poses a burden on machine learning practitioners, requiring expert knowledge,…

Chemical Physics · Physics 2020-04-03 Annika Stuke , Patrick Rinke , Milica Todorović

We give a technique to reduce the error probability of quantum algorithms that determine whether its input has a specified property of interest. The standard process of reducing this error is statistical processing of the results of…

Computational Complexity · Computer Science 2019-07-24 Debajyoti Bera , Tharrmashastha P.

We consider a generic framework of optimization algorithms based on gradient descent. We develop a quantum algorithm that computes the gradient of a multi-variate real-valued function $f:\mathbb{R}^d\rightarrow \mathbb{R}$ by evaluating it…

Quantum Physics · Physics 2019-02-19 András Gilyén , Srinivasan Arunachalam , Nathan Wiebe

In this work we present strategies for (optimal) measurement selection in model-based sequential diagnosis. In particular, assuming a set of leading diagnoses being given, we show how queries (sets of measurements) can be computed and…

Artificial Intelligence · Computer Science 2017-05-30 Patrick Rodler , Wolfgang Schmid , Konstantin Schekotihin

We give new quantum algorithms for evaluating composed functions whose inputs may be shared between bottom-level gates. Let $f$ be an $m$-bit Boolean function and consider an $n$-bit function $F$ obtained by applying $f$ to conjunctions of…

Quantum Physics · Physics 2021-09-22 Mark Bun , Robin Kothari , Justin Thaler

Within machine learning model evaluation regimes, feature selection is a technique to reduce model complexity and improve model performance in regards to generalization, model fit, and accuracy of prediction. However, the search over the…

Machine Learning · Computer Science 2021-05-19 David Von Dollen , Florian Neukart , Daniel Weimer , Thomas Bäck

An enhanced framework of quantum approximate optimization algorithm (QAOA) is introduced and the parameter setting strategies are analyzed. The enhanced QAOA is as effective as the QAOA but exhibits greater computing power and flexibility,…

Quantum Physics · Physics 2020-12-18 Mingyou Wu , Zhihao Liu , Hanwu Chen

The quantum approximate optimisation algorithm (QAOA) is at the core of many scenarios that aim to combine the power of quantum computers and classical high-performance computing appliances for combinatorial optimisation. Several obstacles…

Quantum Physics · Physics 2026-02-26 Simon Thelen , Hila Safi , Wolfgang Mauerer

We use a Bayesian approach to optimally solve problems in noisy binary search. We deal with two variants: 1. Each comparison can be erroneous with some probability $1 - p$. 2. At each stage $k$ comparisons can be performed in parallel and a…

Quantum Physics · Physics 2011-11-09 M. Ben-Or , Avinatan Hassidim

In this paper, we introduce a quantum-enhanced algorithm for simulation-based optimization. Simulation-based optimization seeks to optimize an objective function that is computationally expensive to evaluate exactly, and thus, is…

Quantum Physics · Physics 2021-03-08 Julien Gacon , Christa Zoufal , Stefan Woerner