The staggered quantum walk is a type of discrete-time quantum-walk model without a coin which can be generated on a graph using particular partitions of the graph nodes. We design Hamiltonians for potential realization of the staggered dynamics on a two-dimensional lattice composed of superconducting microwave resonators connected with tunable couplings. The naive generalization of the one-dimensional staggered dynamics generates two uncoupled one-dimensional quantum walks; thus more complex partitions need to be employed. However, by analyzing the coherence of the dynamics, we show that the quantumness of the evolution corresponding to two independent one-dimensional quantum walks can be elevated to the level of a single two-dimensional quantum walk, only by modifying the boundary conditions. In fact, by changing the lattice boundary conditions (or topology), we explore the walk on different surfaces such as a torus, a Klein bottle, a real projective plane, and a sphere. The coherence and the entropy reach different levels depending on the topology of the surface. We observe that the entropy captures similar information as coherence; thus we use it to explore the effects of boundaries on the dynamics of the continuous-time quantum walk and the classical random walk.The staggered quantum walk is a type of discrete-time quantum-walk model without a coin which can be generated on a graph using particular partitions of the graph nodes. We design Hamiltonians for potential realization of the staggered dynamics on a two-dimensional lattice composed of superconducting microwave resonators connected with tunable couplings. The naive generalization of the one-dimensional staggered dynamics generates two uncoupled one-dimensional quantum walks; thus more complex partitions need to be employed. However, by analyzing the coherence of the dynamics, we show that the quantumness of the evolution corresponding to two independent one-dimensional quantum walks can be elevated to the level of a single two-dimensional quantum walk, only by modifying the boundary conditions. In fact, by changing the lattice boundary conditions (or topology), we explore the walk on different surfaces such as a torus, a Klein bottle, a real projective plane, and a sphere. The coherence and the entropy reach different levels depending on the topology of the surface. We observe that the entropy captures similar information as coherence; thus we use it to explore the effects of boundaries on the dynamics of the continuous-time quantum walk and the classical random walk.

arXiv:1804.04331Physical Review AJul 18, 20185 citations

Quantum walks of interacting particles in low-dimensional lattices

Tirthaprasad Chattaraj, Roman V. Krems

Bulletin of the American Physical SocietyJun 7, 20170 citations

Decoherence in Discrete Quantum Walks

Viv M. Kendon, Ben Tregenna

arXiv:quant-ph/0301182Lecture notes in physicsDec 9, 200329 citations

Coherence evolution in two-dimensional quantum walk on lattice

Zhimin He, Zhiming Huang, Lvzhou Li +1 more

We investigate the evolution of the [Formula: see text] norm coherence in two-dimensional quantum walk on lattices for Fourier, Grover and Hadamard coins. Our study shows that the coherence of both the whole system and the position subsystem increases quadratically with the number of steps. We also analyze the influence of three kinds of noises, i.e. broken links, lattice congestion and lattice traps, on the two-dimensional quantum walk. The result shows that the increase of coherence with the number of steps gradually inclines to be linear as the probabilities of broken links and lattice congestion increase. In the quantum walk on trapped lattices, the coherence increases with the increasing time step before the crossover time [Formula: see text] and then gradually decreases after [Formula: see text].We investigate the evolution of the [Formula: see text] norm coherence in two-dimensional quantum walk on lattices for Fourier, Grover and Hadamard coins. Our study shows that the coherence of both the whole system and the position subsystem increases quadratically with the number of steps. We also analyze the influence of three kinds of noises, i.e. broken links, lattice congestion and lattice traps, on the two-dimensional quantum walk. The result shows that the increase of coherence with the number of steps gradually inclines to be linear as the probabilities of broken links and lattice congestion increase. In the quantum walk on trapped lattices, the coherence increases with the increasing time step before the crossover time [Formula: see text] and then gradually decreases after [Formula: see text].

International Journal of Quantum InformationFeb 2, 20182 citations

Discrete-Time Quantum Random Walk for Epidemiological Modeling

Serena La Manna, Nikhil Kowshik, Sudebkumar Prasant Pal

We introduce a discrete-time quantum random walk (QRW) framework for spatial epidemic modelling on a two-dimensional square lattice and compare its dynamics to classical random-walk SIR models. In our model, each infected site spawns a quantum walker whose coherent evolution (controlled by an amplitude-splitting coin and conditional shifts) can infect visited susceptible sites with probability $p$ and persists for a lifetime of $τ$ steps. We perform extensive quantum simulations on finite lattices and compute the basic reproduction number $R_0$ across a broad grid of $(p,τ)$ values. Results show that QRW dynamics interpolate between diffusive and super-diffusive regimes: at low $p$ the QRW reproduces classical-like $R_0$ , while at higher $p$ and $τ$ ballistic propagation and interference produce markedly larger $R_0$ and non-Gaussian spatial profiles. We compare the QRW $R_0$ range to empirical estimates from historical outbreaks and discuss parameter regimes where QRW offers a closer qualitative match than classical diffusion. We conclude that QRWs provide a flexible, conceptually novel toy model for exploring rapid or heavy-tailed epidemic spread.We introduce a discrete-time quantum random walk (QRW) framework for spatial epidemic modelling on a two-dimensional square lattice and compare its dynamics to classical random-walk SIR models. In our model, each infected site spawns a quantum walker whose coherent evolution (controlled by an amplitude-splitting coin and conditional shifts) can infect visited susceptible sites with probability $p$ and persists for a lifetime of $τ$ steps. We perform extensive quantum simulations on finite lattices and compute the basic reproduction number $R_0$ across a broad grid of $(p,τ)$ values. Results show that QRW dynamics interpolate between diffusive and super-diffusive regimes: at low $p$ the QRW reproduces classical-like $R_0$, while at higher $p$ and $τ$ ballistic propagation and interference produce markedly larger $R_0$ and non-Gaussian spatial profiles. We compare the QRW $R_0$ range to empirical estimates from historical outbreaks and discuss parameter regimes where QRW offers a closer qualitative match than classical diffusion. We conclude that QRWs provide a flexible, conceptually novel toy model for exploring rapid or heavy-tailed epidemic spread.

arXiv:2509.05795Sep 6, 20250 citations

Coherence of one-dimensional quantum walk on cycles

Zhimin He, Zhiming Huang, Lvzhou Li +1 more

Quantum Information ProcessingSep 27, 20178 citations

p

and persists for a lifetime of

τ

steps. We perform extensive quantum simulations on finite lattices and compute the basic reproduction number

R_0

across a broad grid of

(p,τ)

values. Results show that QRW dynamics interpolate between diffusive and super-diffusive regimes: at low

p

the QRW reproduces classical-like

R_0

, while at higher

p

and

τ

ballistic propagation and interference produce markedly larger

R_0

and non-Gaussian spatial profiles. We compare the QRW

R_0

range to empirical estimates from historical outbreaks and discuss parameter regimes where QRW offers a closer qualitative match than classical diffusion. We conclude that QRWs provide a flexible, conceptually novel toy model for exploring rapid or heavy-tailed epidemic spread.