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Related papers: Nonadaptive quantum query complexity

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We investigate the problem of quantum searching on a noisy quantum computer. Taking a 'fault-ignorant' approach, we analyze quantum algorithms that solve the task for various different noise strengths, which are possibly unknown beforehand.…

Quantum Physics · Physics 2014-07-28 Peter Vrana , David Reeb , Daniel Reitzner , Michael M. Wolf

The continuous-time query model is a variant of the discrete query model in which queries can be interleaved with known operations (called "driving operations") continuously in time. Interesting algorithms have been discovered in this…

Quantum Physics · Physics 2009-08-06 R. Cleve , D. Gottesman , M. Mosca , R. D. Somma , D. L. Yonge-Mallo

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

We compare classical and quantum query complexities of total Boolean functions. It is known that for worst-case complexity, the gap between quantum and classical can be at most polynomial. We show that for average-case complexity under the…

Quantum Physics · Physics 2009-09-25 Andris Ambainis , Ronald de Wolf

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

A typical oracle problem is finding which software program is installed on a computer, by running the computer and testing its input-output behaviour. The program is randomly chosen from a set of programs known to the problem solver. As…

Quantum Physics · Physics 2007-05-23 Giuseppe Castagnoli

In the field of quantum linear system algorithms, quantum computing has realized exponential computational advantages over classical computing. However, the focus has been on square coefficient matrices, with few quantum algorithms…

Quantum Physics · Physics 2024-09-10 Weitao Lin , Guojing Tian , Xiaoming Sun

We consider quantum learning machines -- quantum computers that modify themselves in order to improve their performance in some way -- that are trained to perform certain classical task, i.e. to execute a function which takes classical bits…

Quantum Physics · Physics 2009-12-15 Daniel Manzano , Marcin Pawlowski , Caslav Brukner

Demonstrating quantum advantage has been a pressing challenge in the field. Most claimed quantum speedups rely on a subroutine in which classical information can be accessed in a coherent quantum manner, which imposes a crucial constraint…

Quantum Physics · Physics 2025-11-04 Nhat A. Nghiem

Quantum amplitude amplification and estimation have shown quadratic speedups to unstructured search and estimation tasks. We show that a coherent combination of these quantum algorithms also provides a quadratic speedup to calculating the…

Quantum Physics · Physics 2024-12-03 Caleb Rotello

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

We present new algorithms to compute fundamental properties of a Boolean function given in truth-table form. Specifically, we give an O(N^2.322 log N) algorithm for block sensitivity, an O(N^1.585 log N) algorithm for `tree decomposition,'…

Computational Complexity · Computer Science 2007-05-23 Scott Aaronson

The standard quantum search algorithm lacks a feature, enjoyed by many classical algorithms, of having a fixed-point, i.e. a monotonic convergence towards the solution. Here we present two variations of the quantum search algorithm, which…

Quantum Physics · Physics 2007-05-23 Lov K. Grover , Apoorva Patel , Tathagat Tulsi

Solving optimisation problems is a promising near-term application of quantum computers. Quantum variational algorithms leverage quantum superposition and entanglement to optimise over exponentially large solution spaces using an…

Quantum Physics · Physics 2022-10-13 Edric Matwiejew , Jason Pye , Jingbo B. Wang

The higher than classical efficiency exhibited by some quantum algorithms is here ascribed to their non-mechanistic character, which becomes evident by joining the notions of entanglement and quantum measurement. Measurement analogically…

Quantum Physics · Physics 2007-05-23 Giuseppe Castagnoli , Dalida Monti

We show that every algorithm for testing $n$-variate Boolean functions for monotonicity must have query complexity $\tilde{\Omega}(n^{1/4})$. All previous lower bounds for this problem were designed for non-adaptive algorithms and, as a…

Computational Complexity · Computer Science 2015-11-17 Aleksandrs Belovs , Eric Blais

We investigate the power of quantum computers when they are required to return an answer that is guaranteed correct after a time that is upper-bounded by a polynomial in the worst case. In an oracle setting, it is shown that such machines…

Quantum Physics · Physics 2007-05-23 Gilles Brassard , Peter Hoyer

Grover's algorithm has achieved great success. But quantum search algorithms still are not complete algorithms because of Grover's Oracle. We concerned on this problem and present a new quantum search algorithm in adiabatic model without…

Quantum Physics · Physics 2009-09-29 Nanyang Xu , Jin Zhu , Xinhua Peng , Xianyi Zhou , Jiangfeng Du

Quantum-phase-estimation algorithms are critical subroutines in many applications for quantum computers and in quantum-metrology protocols. These algorithms estimate the unknown strength of a unitary evolution. By using coherence or…

Quantum Physics · Physics 2023-03-06 Joseph G. Smith , Crispin H. W. Barnes , David R. M. Arvidsson-Shukur

In recent years, deep learning has had a profound impact on machine learning and artificial intelligence. At the same time, algorithms for quantum computers have been shown to efficiently solve some problems that are intractable on…

Quantum Physics · Physics 2015-05-25 Nathan Wiebe , Ashish Kapoor , Krysta M. Svore