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We introduce quantized bipartite walks, compute their spectra, generalize the algorithms of Grover \cite{g} and Ambainis \cite{amb03} and interpret them as quantum walks with memory. We compare the performance of walk based classical and…

Quantum Physics · Physics 2007-05-23 Mario Szegedy

We investigate quantum walks in multiple dimensions with different quantum coins. We augment the model by assuming that at each step the amplitudes of the coin state are multiplied by random phases. This model enables us to study in detail…

Quantum Physics · Physics 2009-11-13 Jozef Kosik , Vladimir Buzek , Mark Hillery

A transition of quantum walk induced by classical randomness changes the probability distribution of the walker from a two-peak structure to a single-peak one when the random parameter exceeds a critical value. We first establish the…

Quantum Physics · Physics 2023-10-02 Christopher Mastandrea , Chih-Chun Chien

A powerful strategy to accelerate quantum-walk-based search algorithms leverages on resetting protocols, where a detector monitors a target site and the evolution of the walker is restarted if no detection occurs within a fixed time…

Quantum Physics · Physics 2025-11-03 Sayan Roy , Shamik Gupta , Giovanna Morigi

Quantum walks have been shown to be fruitful tools in analysing the dynamic properties of quantum systems. This article proposes to use quantum walks as an approach to Quantum Neural Networks (QNNs). QNNs replace binary McCulloch-Pitts…

Quantum Physics · Physics 2014-04-02 Maria Schuld , Ilya Sinayskiy , Francesco Petruccione

We investigate a quantum walk on a ring represented by a directed triangle graph with complex edge weights and monitored at a constant rate until the quantum walker is detected. To this end, the first hitting time statistics is recorded…

Quantum Physics · Physics 2024-04-11 Qingyuan Wang , Silin Ren , Ruoyu Yin , Klaus Ziegler , Eli Barkai , Sabine Tornow

Quantum walks, the quantum analogue of the classical random walk, have been shown to underpin quantum algorithms for fluid dynamics. We propose the quantum half-adder gate method for quantum walks as a good benchmark algorithm, specifically…

Quantum Physics · Physics 2026-04-17 Steph Foulds , Viv Kendon

Quantum walks have emerged as an interesting approach to quantum information processing, exhibiting many unique properties compared to the analogous classical random walk. Here we introduce a model for a discrete-time quantum walk with…

Quantum Physics · Physics 2013-05-08 Peter P. Rohde , Gavin K. Brennen , Alexei Gilchrist

Recently, several groups have investigated quantum analogues of random walk algorithms, both on a line and on a circle. It has been found that the quantum versions have markedly different features to the classical versions. Namely, the…

Quantum Physics · Physics 2009-11-07 B. C. Travaglione , G. J. Milburn

We make use of the Open Quantum Random Walk setting due to S. Attal, F. Petruccione, C. Sabot and I. Sinayskiy [J. Stat. Phys. (2012) 147:832-852] in order to discuss hitting times and a quantum version of the Mean Hitting Time Formula from…

Mathematical Physics · Physics 2017-01-04 Carlos F. Lardizabal

Repeatedly-monitored quantum walks with a rate $1/\tau$ yield discrete-time trajectories which are inherently random. With these paths the first-hitting time with sharp restart is studied. We find an instability in the optimal mean hitting…

Statistical Mechanics · Physics 2024-06-28 Ruoyu Yin , Qingyuan Wang , Eli Barkai

Quantum walks exhibit many unique characteristics compared to classical random walks. In the classical setting, self-avoiding random walks have been studied as a variation on the usual classical random walk. Classical self-avoiding random…

Quantum Physics · Physics 2015-01-08 Elizabeth Camilleri , Peter P. Rohde , Jason Twamley

Quantum versions of random walks on the line and the cycle show a quadratic improvement over classical random walks in their spreading rates and mixing times respectively. Non-unitary quantum walks can provide a useful optimisation of these…

Quantum Physics · Physics 2008-03-25 Viv Kendon , Olivier Maloyer

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

Fast computational algorithms are in constant demand, and their development has been driven by advances such as quantum speedup and classical acceleration. This paper intends to study search algorithms based on quantum walks in quantum…

Quantum Physics · Physics 2026-01-06 Yazhen Wang

Recently, it has been shown that one-dimensional quantum walks can mix more quickly than classical random walks, suggesting that quantum Monte Carlo algorithms can outperform their classical counterparts. We study two quantum walks on the…

Quantum Physics · Physics 2007-05-23 Cristopher Moore , Alexander Russell

Quantum Stochastic Walks (QSW) allow for a generalization of both quantum and classical random walks by describing the dynamic evolution of an open quantum system on a network, with nodes corresponding to quantum states of a fixed basis. We…

Quantum Physics · Physics 2020-03-31 Nicola Dalla Pozza , Filippo Caruso

The quantum switch, a process enabling a coherent superposition of different orders of quantum channels, has garnered significant attention due to its ability to enable noiseless communications through noisy channels, such as…

Quantum Physics · Physics 2026-01-13 Claudio Pellitteri , Marcello Caleffi , Angela Sara Cacciapuoti

We investigate the splitting probability of a monitored continuous-time quantum walk with two targets and show that, in stark contrast to a classical random walk, it exhibits a nonanalytic, phase-transition-like behavior controlled by the…

Statistical Mechanics · Physics 2026-01-23 Prashant Singh , David A. Kessler , Eli Barkai

Quantum walk acts obviously different from its classical counterpart, but decoherence will lessen and close the gap between them. To understand this process, it is necessary to investigate the evolution of quantum walk under different…

Quantum Physics · Physics 2015-06-04 Peng Xue , Yongsheng Zhang