English
Related papers

Related papers: Amplitude amplification and estimation require inv…

200 papers

Grover's quantum search and its generalization, quantum amplitude amplification, provide quadratic advantage over classical algorithms for a diverse set of tasks, but are tricky to use without knowing beforehand what fraction $\lambda$ of…

Quantum Physics · Physics 2014-11-26 Theodore J. Yoder , Guang Hao Low , Isaac L. Chuang

Quantum search is among the most important algorithms in quantum computing. At its core is quantum amplitude amplification, a technique that achieves a quadratic speedup over classical search by combining two global reflections: the oracle,…

Quantum Physics · Physics 2026-05-05 John Burke , Ciaran McGoldrick

We study some extensions of Grover's quantum searching algorithm. First, we generalize the Grover iteration in the light of a concept called amplitude amplification. Then, we show that the quadratic speedup obtained by the quantum searching…

Quantum Physics · Physics 2017-01-03 Gilles Brassard , Peter Hoyer , Alain Tapp

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

Quantum amplitude estimation is a key sub-routine of a number of quantum algorithms with various applications. We propose an adaptive algorithm for interval estimation of amplitudes. The quantum part of the algorithm is based only on…

Quantum Physics · Physics 2022-06-20 Yunpeng Zhao , Haiyan Wang , Kuai Xu , Yue Wang , Ji Zhu , Feng Wang

We give a natural problem over input quantum oracles $U$ which cannot be solved with exponentially many black-box queries to $U$ and $U^\dagger$, but which can be solved with constant many queries to $U$ and $U^*$, or $U$ and…

Quantum Physics · Physics 2026-05-11 Ewin Tang , John Wright , Mark Zhandry

In this work, we show the characterization of quantum iterations that would generally construct quantum amplitude amplification algorithms with a quadratic speedup, namely, quantum amplitude amplification operators (QAAOs). Exact quantum…

Quantum Physics · Physics 2021-12-30 Hyeokjea Kwon , Joonwoo Bae

Amplitude amplification is a central tool used in Grover's quantum search algorithm and has been used in various forms in numerous quantum algorithms since then. It has been shown to completely eliminate one-sided error of quantum search…

Computational Complexity · Computer Science 2016-05-09 Debajyoti Bera

Amplitude amplification is one of primary tools in building algorithms for quantum computers. This technique generalizes key ideas of the Grover search algorithm. Potentially useful modifications are connected with changing phases in the…

Quantum Physics · Physics 2018-07-04 Alexey E. Rastegin

Grover's search algorithm was a groundbreaking advancement in quantum algorithms, displaying a quadratic speed-up of querying for items. Since the creation of this algorithm it has been utilized in various ways, including in preparing…

Quantum Physics · Physics 2024-01-18 Andrew Vlasic , Salvatore Certo , Anh Pham

Quantum search/amplitude amplification algorithms are designed to be able to amplify the amplitude in the target state linearly with the number of operations. Since the probability is the square of the amplitude, this results in the success…

Quantum Physics · Physics 2008-06-03 Lov K. Grover

Grover's algorithm is a primary algorithm offered as evidence that quantum computers can provide an advantage over classical computers. It involves an "oracle" specified for a given application whose structure is not part of the formal…

Quantum Physics · Physics 2024-11-14 E. M. Stoudenmire , Xavier Waintal

With reference to a search in a database of size N, Grover states: "What is the reason that one would expect that a quantum mechanical scheme could accomplish the search in O(square root of N) steps? It would be insightful to have a simple…

Quantum Physics · Physics 2009-11-13 Giuseppe Castagnoli

We propose an algorithm using a modified variant of amplitude amplification to solve combinatorial optimization problems via the use of a subdivided phase oracle. Instead of dividing input states into two groups and shifting the phase…

Quantum Physics · Physics 2023-09-07 Naphan Benchasattabuse , Takahiko Satoh , Michal Hajdušek , Rodney Van Meter

We present a full implementation and simulation of a novel quantum reinforcement learning method. Our work is a detailed and formal proof of concept for how quantum algorithms can be used to solve reinforcement learning problems and shows…

Quantum Physics · Physics 2023-11-10 Simon Wiedemann , Daniel Hein , Steffen Udluft , Christian Mendl

Quantum state preparation is an important ingredient for other higher-level quantum algorithms, such as Hamiltonian simulation, or for loading distributions into a quantum device to be used e.g. in the context of optimization tasks such as…

Quantum Physics · Physics 2022-08-10 Johannes Bausch

Amplitude estimation algorithms are based on Grover's algorithm: alternating reflections about the input state and the desired outcome. But what if we are given the ability to perform arbitrary rotations, instead of just reflections? In…

Quantum Physics · Physics 2023-03-08 Patrick Rall , Bryce Fuller

In recent years, quantum-enhanced machine learning has emerged as a particularly fruitful application of quantum algorithms, covering aspects of supervised, unsupervised and reinforcement learning. Reinforcement learning offers numerous…

Quantum Physics · Physics 2022-08-03 A. Hamann , V. Dunjko , S. Wölk

In this paper, we present an algorithm for preparing quantum states of the form $\sum_{i=0}^{n-1} \alpha_i |i\rangle$, where the coefficients $\alpha_i$ are specified by a quantum oracle. Our method achieves this task twice as fast as the…

Quantum Physics · Physics 2025-06-17 Artem Chernikov , Karina Zakharova , Sergey Sysoev

In previous works, we showed that an optimal quantum algorithm can always be seen as a sum over classical histories in each of which the problem solver knows in advance one of the possible halves of the solution she will read in the future…

Quantum Physics · Physics 2017-06-28 Giuseppe Castagnoli
‹ Prev 1 2 3 10 Next ›