Why and how to add direction to a quantum walk
- URL: http://arxiv.org/abs/2203.13857v1
- Date: Fri, 25 Mar 2022 18:51:23 GMT
- Title: Why and how to add direction to a quantum walk
- Authors: Rodrigo Chaves, Bruno Oliveira Chagas, Gabriel Coutinho
- Abstract summary: We formalize the treatment of directed (or chiral) quantum walks using Hermitian adjacency matrices.
This leads to a construction of a new type of quantum phenomenon: zero transfer between pairs of sites in a connected coupled network.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We formalize the treatment of directed (or chiral) quantum walks using
Hermitian adjacency matrices, bridging two developing fields of research in
quantum information and spectral graph theory. We display results and
simulations which highlight the conceptual differences between having
directions encoded in the Hamiltonians or not. This leads to a construction of
a new type of quantum phenomenon: zero transfer between pairs of sites in a
connected coupled network, which is only possible in the directed model we
study. Our main result is a description of several families of directed cycles
that admit zero transfer.
Related papers
- Lee-Yang theory of quantum phase transitions with neural network quantum
states [0.0]
We show that neural network quantum states can be combined with a Lee-Yang theory of quantum phase transitions to predict the critical points of strongly-correlated spin lattices.
Our results provide a starting point for determining the phase diagram of more complex quantum many-body systems.
arXiv Detail & Related papers (2023-01-24T11:10:37Z) - Quantum State Transfer: Interplay between Gate and Readout Errors [0.0]
We simulate quantum state transfer between two nodes connected in a linear geometry through other nodes.
We find that the nominal success probability is not necessarily a monotonic function of the two error rates.
arXiv Detail & Related papers (2022-09-15T03:22:40Z) - Operator and Graph Theoretic Techniques for Distinguishing Quantum
States via One-Way LOCC [0.0]
We bring together some of the main results and applications from our recent works in quantum information theory.
We investigate the topic of distinguishability of sets of quantum states in quantum communication.
We derive a new graph-theoretic description of distinguishability in the case of a single qubit sender.
arXiv Detail & Related papers (2021-10-14T18:26:40Z) - Quantum phase transition dynamics in the two-dimensional
transverse-field Ising model [0.0]
The quantum Kibble-Zurek mechanism (QKZM) predicts universal dynamical behavior near the quantum phase transitions (QPTs)
We study the dynamical crossing of the QPT in the paradigmatic Ising model by a joint effort of modern state-of-the-art numerical methods.
We also note that, upon traversing further into the ferromagnetic regime, deviations from the QKZM prediction appear.
arXiv Detail & Related papers (2021-06-16T18:00:04Z) - The Hintons in your Neural Network: a Quantum Field Theory View of Deep
Learning [84.33745072274942]
We show how to represent linear and non-linear layers as unitary quantum gates, and interpret the fundamental excitations of the quantum model as particles.
On top of opening a new perspective and techniques for studying neural networks, the quantum formulation is well suited for optical quantum computing.
arXiv Detail & Related papers (2021-03-08T17:24:29Z) - Enhancing nonclassical bosonic correlations in a Quantum Walk network
through experimental control of disorder [50.591267188664666]
We experimentally realize a controllable inhomogenous Quantum Walk dynamics.
We observe two photon states which exhibit an enhancement in the quantum correlations between two modes of the network.
arXiv Detail & Related papers (2021-02-09T10:57:00Z) - Information Scrambling in Computationally Complex Quantum Circuits [56.22772134614514]
We experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor.
We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate.
arXiv Detail & Related papers (2021-01-21T22:18:49Z) - Floquet engineering of continuous-time quantum walks: towards the
simulation of complex and next-to-nearest neighbor couplings [0.0]
We apply the idea of Floquet engineering in the context of continuous-time quantum walks on graphs.
We define periodically-driven Hamiltonians which can be used to simulate the dynamics of certain target quantum walks.
Our work provides explicit simulation protocols that may be used for directing quantum transport, engineering the dispersion relation of one-dimensional quantum walks or investigating quantum dynamics in highly connected structures.
arXiv Detail & Related papers (2020-12-01T12:46:56Z) - Quantum information spreading in a disordered quantum walk [50.591267188664666]
We design a quantum probing protocol using Quantum Walks to investigate the Quantum Information spreading pattern.
We focus on the coherent static and dynamic disorder to investigate anomalous and classical transport.
Our results show that a Quantum Walk can be considered as a readout device of information about defects and perturbations occurring in complex networks.
arXiv Detail & Related papers (2020-10-20T20:03:19Z) - Unraveling the topology of dissipative quantum systems [58.720142291102135]
We discuss topology in dissipative quantum systems from the perspective of quantum trajectories.
We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
arXiv Detail & Related papers (2020-07-12T11:26:02Z) - Exploring complex graphs using three-dimensional quantum walks of
correlated photons [52.77024349608834]
We introduce a new paradigm for the direct experimental realization of excitation dynamics associated with three-dimensional networks.
This novel testbed for the experimental exploration of multi-particle quantum walks on complex, highly connected graphs paves the way towards exploiting the applicative potential of fermionic dynamics in integrated quantum photonics.
arXiv Detail & Related papers (2020-07-10T09:15:44Z)
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.