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We study search by quantum walk on a finite two dimensional grid. The algorithm of Ambainis, Kempe, Rivosh (quant-ph/0402107) takes O(\sqrt{N log N}) steps and finds a marked location with probability O(1/log N) for grid of size \sqrt{N} *…

Quantum Physics · Physics 2011-12-15 Andris Ambainis , Arturs Backurs , Nikolajs Nahimovs , Raitis Ozols , Alexander Rivosh

One of the significant breakthroughs in quantum computation is Grover's algorithm for unsorted database search. Recently, the applications of Grover's algorithm to solve global optimization problems have been demonstrated, where unknown…

Quantum Physics · Physics 2017-11-22 Yan Wang

We show that quantum search can be used to compute the hardness to round an elementary function, that is, to determine the minimum working precision required to compute the values of an elementary function correctly rounded to a target…

Quantum Physics · Physics 2026-01-21 Stefanos Kourtis

Hitting the exit node from the entrance node faster on a graph is one of the properties that quantum walk algorithms can take advantage of to outperform classical random walk algorithms. Especially, continuous-time quantum walks on…

Application-specific quantum computers offer the most efficient means to tackle problems intractable by classical computers. Realizing these architectures necessitates a deep understanding of quantum circuit properties and their…

Quantum walk search may exhibit phenomena beyond the intuition from a conventional random walk theory. One of such examples is exceptional configuration phenomenon -- it appears that it may be much harder to find any of two or more marked…

Quantum Physics · Physics 2021-01-13 Adam Glos , Nikolajs Nahimovs , Konstantin Balakirev , Kamil Khadiev

In quantum computing, the connectivity of qubits placed on two-dimensional chips limits the scalability and functionality of solid-state quantum computers. This paper presents two approaches to constructing complex quantum networks from…

Quantum Physics · Physics 2024-05-28 Yu-Hang Dang , Shyam Dhamapurkar , Xiao-Long Zhu , Zheng-Yang Zhou , Hao-Yu Guan , Xiu-Hao Deng

Since the final quantum state in the Grover search algorithm is the normalized marked quantum state from the Gram-Schmidt process, Abrams and Lloyd [1] has shown that we can generate this vector by using a non-unitary gate. Following their…

Quantum Physics · Physics 2025-08-22 Ammar Daskin

Quantum Random Walks, which have drawn much attention over the past few decades for their distinctly non-classical behavior, is a promising subfield within Quantum Computing. Theoretical framework and applications for these walks have seen…

Quantum Physics · Physics 2021-01-25 Daniel Koch , Michael Samodurov , Andrew Projansky , Paul M. Alsing

We analyse the eigenvalue and eigenvector structure of the flip-flop quantum walk on regular graphs, explicitly demonstrating how it is quadratically faster than the classical random walk. Then we use it in a controlled spatial search…

Quantum Physics · Physics 2018-12-18 Abhijith J. , Apoorva Patel

We present a novel methodological framework for quantum spatial search, generalising the Childs & Goldstone ($\mathcal{CG}$) algorithm via alternating applications of marked-vertex phase shifts and continuous-time quantum walks. We…

Quantum Physics · Physics 2021-09-30 S. Marsh , J. B. Wang

Quantum walks are at the heart of modern quantum technologies. They allow to deal with quantum transport phenomena and are an advanced tool for constructing novel quantum algorithms. Quantum walks on graphs are fundamentally different from…

Quantum Physics · Physics 2019-12-18 Alexey A. Melnikov , Leonid E. Fedichkin , Alexander Alodjants

Quantum walks, both discrete and continuous, serve as fundamental tools in quantum information processing with diverse applications. This work introduces a hybrid quantum walk model that integrates the coin mechanism of discrete walks with…

Quantum Physics · Physics 2025-09-12 Tianen Chen , Yun Shang

We introduce a new tool for quantum algorithms called quantum fast-forwarding (QFF). The tool uses quantum walks as a means to quadratically fast-forward a reversible Markov chain. More specifically, with $P$ the Markov chain transition…

Quantum Physics · Physics 2019-01-24 Simon Apers , Alain Sarlette

Quantum walks provide a versatile framework for probing the structural and dynamical properties of complex systems ranging from biological networks to synthetic materials. However, their realization on current noisy pre-fault-tolerant…

Quantum walks on graphs are ubiquitous in quantum computing finding a myriad of applications. Likewise, random walks on graphs are a fundamental building block for a large number of algorithms with diverse applications. While the…

Quantum Physics · Physics 2020-12-09 Matheus G. Andrade , Franklin Marquezino , Daniel R. Figueiredo

Graph representations are a powerful concept for solving complex problems across natural science, as patterns of connectivity can give rise to a multitude of emergent phenomena. Graph-based approaches have proven particularly fruitful in…

Implementing quantum algorithms on realistic hardware requires translating high-level global operations into sequences of native elementary gates, a process known as quantum compiling. Physical limitations, such as constraints in…

Quantum walks have been employed widely to develop new tools for quantum information processing recently. A natural quantum walk dynamics of interacting particles can be used to implement efficiently the universal quantum computation. In…

Quantum Physics · Physics 2016-10-04 Alexey A. Melnikov , Leonid E. Fedichkin

Rydberg atoms provide a highly promising platform for quantum computation, leveraging their strong tunable interactions to encode and manipulate information in the electronic states of individual atoms. Key advantages of Rydberg atoms…

Quantum Physics · Physics 2025-07-29 Gabriel Almeida , Raul Santos , Lara Janiurek , Yasser Omar