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Quantum computing can empower machine learning models by enabling kernel machines to leverage quantum kernels for representing similarity measures between data. Quantum kernels are able to capture relationships in the data that are not…

We examine the number T of queries that a quantum network requires to compute several Boolean functions on {0,1}^N in the black-box model. We show that, in the black-box model, the exponential quantum speed-up obtained for partial functions…

Quantum Physics · Physics 2007-05-23 Robert Beals , Harry Buhrman , Richard Cleve , Michele Mosca , Ronald de Wolf

The $k$'th frequency moment of a sequence of integers is defined as $F_k = \sum_j n_j^k$, where $n_j$ is the number of times that $j$ occurs in the sequence. Here we study the quantum complexity of approximately computing the frequency…

Quantum Physics · Physics 2016-08-05 Ashley Montanaro

Quantum kernel methods are among the leading candidates for achieving quantum advantage in supervised learning. A key bottleneck is the cost of inference: evaluating a trained model on new data requires estimating a weighted sum…

Quantum Physics · Physics 2026-04-20 Elies Gil-Fuster , Seongwook Shin , Sofiene Jerbi , Jens Eisert , Maximilian J. Kramer

A quantum algorithm is a set of instructions for a quantum computer, however, unlike algorithms in classical computer science their results cannot be guaranteed. Quantum search algorithm can be described as the rotation of state vectors in…

Quantum Physics · Physics 2021-12-30 Bikramaditya Das , Kamal Gurnani , Bikash K. Behera , Prasanta K. Panigrahi

We describe a quantum black-box network computing the majority of N bits with zero-sided error eps using only 2N/3 + O(sqrt{N (log log N + log 1/eps)}) queries: the algorithm returns the correct answer with probability at least 1 - eps, and…

Quantum Physics · Physics 2007-05-23 Thomas Hayes , Samuel Kutin , Dieter van Melkebeek

The quantum hybrid algorithm has become a very promising and speedily method today for solving the larger-scale optimization in the noisy intermediate-scale quantum (NISQ) era. The unit commitment (UC) problem is a fundamental problem in…

Quantum Physics · Physics 2025-10-10 Jian Liu , Xu Zhou , Zhuojun Zhou , Le Luo

We obtain a query lower bound for quantum algorithms solving the phase estimation problem. Our analysis generalizes existing lower bound approaches to the case where the oracle Q is given by controlled powers Q^p of Q, as it is for example…

Quantum Physics · Physics 2007-05-23 Arvid J. Bessen

A new quantum algorithm for a search problem and its computational complexity are discussed. It is shown in the search problem containing 2^n objects that our algorithm runs in polynomial time.

Quantum Physics · Physics 2013-06-24 S. Iriyama , M. Ohya , I. V. Volovich

We prove a general lower bound of quantum decision tree complexity in terms of some entropy notion. We regard the computation as a communication process in which the oracle and the computer exchange several rounds of messages, each round…

Quantum Physics · Physics 2007-05-23 Yaoyun Shi

We identify "proper quantum computation" with computational processes that cannot be efficiently simulated on a classical computer. For optical quantum computation, we establish "no-go" theorems for classes of quantum optical experiments…

Quantum Physics · Physics 2007-05-23 Stephen D. Bartlett , Barry C. Sanders

Approximate Counting refers to the problem where we are given query access to a function $f : [N] \to \{0,1\}$, and we wish to estimate $K = #\{x : f(x) = 1\}$ to within a factor of $1+\epsilon$ (with high probability), while minimizing the…

Quantum Physics · Physics 2020-10-12 Ramgopal Venkateswaran , Ryan O'Donnell

We investigate the power of quantum computers when they are required to return an answer that is guaranteed to be correct after a time that is upper-bounded by a polynomial in the worst case. We show that a natural generalization of Simon's…

Quantum Physics · Physics 2017-01-04 Gilles Brassard , Peter Hoyer

In this note we investigate the relationship between worst-case quantum query complexity and average-case classical query complexity. Specifically, we show that if a quantum computer can evaluate a total Boolean function f with bounded…

Computational Complexity · Computer Science 2012-01-19 Scott Aaronson

The problem of minimizing the maximum of $N$ convex, Lipschitz functions plays significant roles in optimization and machine learning. It has a series of results, with the most recent one requiring $O(N\epsilon^{-2/3} + \epsilon^{-8/3})$…

Quantum Physics · Physics 2024-02-21 Hao Wang , Chenyi Zhang , Tongyang Li

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

Numerous conceptually important quantum algorithms rely on a black-box device known as an oracle, which is typically difficult to construct without knowing the answer to the problem that the algorithm is intended to solve. A notable example…

Quantum computation has attracted much attention since it was shown by Shor and Grover the possibility to implement quantum algorithms able to realize, respectively, factoring and searching in a faster way than any other known classical…

Quantum Physics · Physics 2007-05-23 Rubens Viana Ramos , Paulo Benicio de Sousa , David Sena Oliveira

The question of answering queries over ML predictions has been gaining attention in the database community. This question is challenging because the cost of finding high quality answers corresponds to invoking an oracle such as a human…

Databases · Computer Science 2022-11-18 Dujian Ding , Sihem Amer-Yahia , Laks VS Lakshmanan

We study optimal perfect distinguishability between a unitary and a general quantum operation. In 2-dimensional case we provide a simple sufficient and necessary condition for sequential perfect distinguishability and an analytical formula…

Quantum Physics · Physics 2010-10-13 Cheng Lu , Jianxin Chen , Runyao Duan