Stronger resilience to disorder in 2D quantum walks than in 1D
- URL: http://arxiv.org/abs/2312.16076v1
- Date: Tue, 26 Dec 2023 14:53:35 GMT
- Title: Stronger resilience to disorder in 2D quantum walks than in 1D
- Authors: Amrita Mandal and Ujjwal Sen
- Abstract summary: We study the response of spreading behavior, of two-dimensional discrete-time quantum walks, to glassy disorder in the jump length.
We find that the ballistic spreading of the clean walk is inhibited in presence of disorder, and the walk becomes sub-ballistic but remains super-diffusive.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We study the response of spreading behavior, of two-dimensional discrete-time
quantum walks, to glassy disorder in the jump length. We consider different
discrete probability distributions to mimic the disorder, and three types of
coin operators, viz., Grover, Fourier, and Hadamard, to analyze the scale
exponent of the disorder-averaged spreading. We find that the ballistic
spreading of the clean walk is inhibited in presence of disorder, and the walk
becomes sub-ballistic but remains super-diffusive. The resilience to
disorder-induced inhibition is stronger in two-dimensional walks, for all the
considered coin operations, in comparison to the same in one dimension. The
quantum advantage of quantum walks is therefore more secure in two dimensions
than in one.
Related papers
- Observation of disorder-free localization and efficient disorder averaging on a quantum processor [117.33878347943316]
We implement an efficient procedure on a quantum processor, leveraging quantum parallelism, to efficiently sample over all disorder realizations.
We observe localization without disorder in quantum many-body dynamics in one and two dimensions.
arXiv Detail & Related papers (2024-10-09T05:28:14Z) - Multipartite Entanglement in the Measurement-Induced Phase Transition of
the Quantum Ising Chain [77.34726150561087]
External monitoring of quantum many-body systems can give rise to a measurement-induced phase transition.
We show that this transition extends beyond bipartite correlations to multipartite entanglement.
arXiv Detail & Related papers (2023-02-13T15:54:11Z) - Quantum walks in two dimensions: controlling directional spreading with
entangling coins and tunable disordered step operator [0.0]
We show that considering a given disorder in one direction, it is possible to control the degree of spreading and entanglement in the other direction.
This observation helps assert that the random quantum walks of this ilk serve as a controllable decoherence channel.
arXiv Detail & Related papers (2022-09-13T18:13:22Z) - Characterization of anomalous diffusion in one-dimensional quantum walks [1.9551668880584971]
Homogeneous and accelerated quantum walks display superdiffusive behavior, whereas uncorrelated static and dynamic disorders induce strong and weak localization of the particle.
We employ two reliable measures of coherence for conclusively establishing the role of quantum interference as the driving force behind the anomalous diffusive behavior in the dynamics of quantum walks.
arXiv Detail & Related papers (2021-12-29T15:49:17Z) - Response to glassy disorder in coin on spread of quantum walker [0.0]
We analyze the response to glassy disorder in the coin operation of a discrete-time quantum walk in one dimension.
We find that the ballistic spread of the disorder-free quantum walker is inhibited by the insertion of disorder.
The falloff from ballistic spread can be slow (Gaussian) or fast (parabolic) for different disorders, when the strength of the disorder is still weak.
arXiv Detail & Related papers (2021-11-18T17:51:28Z) - Continuous-time dynamics and error scaling of noisy highly-entangling
quantum circuits [58.720142291102135]
We simulate a noisy quantum Fourier transform processor with up to 21 qubits.
We take into account microscopic dissipative processes rather than relying on digital error models.
We show that depending on the dissipative mechanisms at play, the choice of input state has a strong impact on the performance of the quantum algorithm.
arXiv Detail & Related papers (2021-02-08T14:55:44Z) - Controlling many-body dynamics with driven quantum scars in Rydberg atom
arrays [41.74498230885008]
We experimentally investigate non-equilibrium dynamics following rapid quenches in a many-body system composed of 3 to 200 strongly interacting qubits in one and two spatial dimensions.
We discover that scar revivals can be stabilized by periodic driving, which generates a robust subharmonic response akin to discrete time-crystalline order.
arXiv Detail & Related papers (2020-12-22T19:00:02Z) - Continuous and time-discrete non-Markovian system-reservoir
interactions: Dissipative coherent quantum feedback in Liouville space [62.997667081978825]
We investigate a quantum system simultaneously exposed to two structured reservoirs.
We employ a numerically exact quasi-2D tensor network combining both diagonal and off-diagonal system-reservoir interactions with a twofold memory for continuous and discrete retardation effects.
As a possible example, we study the non-Markovian interplay between discrete photonic feedback and structured acoustic phononovian modes, resulting in emerging inter-reservoir correlations and long-living population trapping within an initially-excited two-level system.
arXiv Detail & Related papers (2020-11-10T12:38:35Z) - Quantum dynamics and relaxation in comb turbulent diffusion [91.3755431537592]
Continuous time quantum walks in the form of quantum counterparts of turbulent diffusion in comb geometry are considered.
Operators of the form $hatcal H=hatA+ihatB$ are described.
Rigorous analytical analysis is performed for both wave and Green's functions.
arXiv Detail & Related papers (2020-10-13T15:50:49Z) - Topological delocalization in the completely disordered two-dimensional
quantum walk [0.0]
We investigate the effect of spatial disorder on two-dimensional split-step discrete-time quantum walks with two internal "coin" states.
We find that spatial disorder of the most general type, i.e., position-dependent Haar random coin operators, does not lead to Anderson localization but to a diffusive spread instead.
This is a delocalization, which happens because disorder places the quantum walk to a critical point between different anomalous Floquet-Anderson insulating topological phases.
arXiv Detail & Related papers (2020-05-01T03:57:37Z) - Second-order topological insulator in a coinless discrete-time quantum
walk [3.7528520149256006]
We construct a two-dimensional coinless quantum walk to simulate second-order topological insulator with zero-dimensional corner states.
We show that both of the corner and edge states can be observed through the probability distribution of the walker.
We propose a possible experimental implementation to realize this discrete-time quantum walk in a three-dimensional integrated photonic circuits.
arXiv Detail & Related papers (2020-03-19T09:07:34Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.