CoChat
Sign Up
Cited by 111Quantum Computing Algorithms and ArchitectureQuantum Mechanics and ApplicationsNoncommutative and Quantum Gravity Theories

The DOI matches its Crossref record; 48 of the 48 references it cites were found in a registry or an index.

Relationship between quantum walks and relativistic quantum mechanics

Open access
Chandrashekar, C. M., Banerjee, Subhashish, Srikanth, R.·2010·Physical Review A
DOI 10.1103/physreva.81.062340
Open this paper in CoChat — free accountOpen PDF

Abstract

Quantum walk models have been used as an algorithmic tool for quantum computation and to describe various physical processes. This article revisits the relationship between relativistic quantum mechanics and the quantum walks. We show the similarities of the mathematical structure of the decoupled and coupled forms of the discrete-time quantum walk to that of the Klein-Gordon and Dirac equations, respectively. In the latter case, the coin emerges as an analog of the spinor degree of freedom. Discrete-time quantum walk as a coupled form of the continuous-time quantum walk is also shown by transforming the decoupled form of the discrete-time quantum walk to the Schr\"odinger form. By showing the coin to be a means to make the walk reversible and that the Dirac-like structure is a consequence of the coin use, our work suggests that the relativistic causal structure is a consequence of conservation of information. However, decoherence (modeled by projective measurements on position space) generates entropy that increases with time, making the walk irreversible and thereby producing an arrow of time. The Lieb-Robinson bound is used to highlight the causal structure of the quantum walk to put in perspective the relativistic structure of the quantum walk, the maximum speed of walk propagation, and earlier findings related to the finite spread of the walk probability distribution. We also present a two-dimensional quantum walk model on a two-state system to which the study can be extended.

Overview

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1103/physreva.81.062340

Cites

48 of 48 references verified0 citation errors · 0 not checkable

Statistics

Verification

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Citations

Cites

Research works printed but not linked: 3

  1. G. V. Riazanov, 1958, Sov. Phys. JETP, 6, 1107
  2. A. Ambainis, 2001, Proceeding of the 33rd ACM Symposium on Theory of Computing
  3. A. M. Childs, 2003, Proceedings of the 35th ACM Symposium on Theory of Computing

Cited by

Sorted by citations

See all 111

Related

See all

Metadata

Authors
Chandrashekar, C. M., Banerjee, S., & Srikanth, R.
Affiliations
  • University of Waterloo (CA)
  • Chennai Mathematical Institute (IN)
  • Raman Research Institute (IN)
ORCID
Venue
Physical Review A
Publisher
American Physical Society (APS)
Published
2010-06-25
Volume
81
Issue
6
ISSN
  • 0556-2791 (ISSN-L)
  • 1050-2947
  • 1094-1622
DOI
10.1103/physreva.81.062340
OpenAlex
W2089766148
Cited by
109
References
48
Citations by year
2026: 1 · 2025: 5 · 2024: 7 · 2023: 1 · 2022: 9 · 2021: 10 · 2020: 11 · 2019: 12 · 2018: 9 · 2017: 4 · 2016: 7 · 2015: 5 · 2014: 6 · 2013: 8 · 2012: 8
FWCI
7.45
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review A (publishedVersion)
  • arXiv (Cornell University) (publishedVersion)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Noncommutative and Quantum Gravity Theories
Keywords
quantum walks, relativistic quantum mechanics, Klein-Gordon equation, Dirac equation, discrete-time quantum walks, continuous-time quantum walks, coin operator, reversibility, information conservation, arrow of time, decoherence, entropy (information theory), Lieb-Robinson bound, causal structure, two-dimensional quantum walk, two-level system

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review