Hamiltonians of Bipartite Walks
- URL: http://arxiv.org/abs/2207.01673v1
- Date: Mon, 4 Jul 2022 18:50:32 GMT
- Title: Hamiltonians of Bipartite Walks
- Authors: Qiuting Chen, Chris Godsil, Mariia Sobchuk, Harmony Zhan
- Abstract summary: We introduce a discrete quantum walk model called bipartite walks.
For the transition matrix of a quantum walk, there is a Hamiltonian associated with it.
Via the Hamiltonians, phenomena of bipartite walks lead to phenomena of continuous walks.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In this paper, we introduce a discrete quantum walk model called bipartite
walks. Bipartite walks include many known discrete quantum walk models, like
arc-reversal walks, vertex-face walks. For the transition matrix of a quantum
walk, there is a Hamiltonian associated with it. We will study the Hamiltonians
of the bipartite walks. Let $S$ be a skew-symmetric matrix. We are mainly
interested in the Hamiltonians of the form $iS$. We show that the Hamiltonian
can be written as $iS$ if and only if the adjacency matrix of the bipartite
graph is invertible. We show that arc-reversal walks and vertex-face walks are
special cases of bipartite walks. Via the Hamiltonians, phenomena of bipartite
walks lead to phenomena of continuous walks. We show in detail how we use
bipartite walks on paths to construct universal perfect state transfer in
continuous walks.
Related papers
- Quantifying non-Hermiticity using single- and many-particle quantum properties [14.37149160708975]
The non-Hermitian paradigm of quantum systems displays salient features drastically different from Hermitian counterparts.
We propose a formalism that quantifies the (dis-)similarity of these right and left ensembles, for single- as well as many-particle quantum properties.
Our findings can be instrumental in unveiling new exotic quantum phases of non-Hermitian quantum many-body systems.
arXiv Detail & Related papers (2024-06-19T13:04:47Z) - A hybrid quantum algorithm to detect conical intersections [39.58317527488534]
We show that for real molecular Hamiltonians, the Berry phase can be obtained by tracing a local optimum of a variational ansatz along the chosen path.
We demonstrate numerically the application of our algorithm on small toy models of the formaldimine molecule.
arXiv Detail & Related papers (2023-04-12T18:00:01Z) - Measurement phase transitions in the no-click limit as quantum phase
transitions of a non-hermitean vacuum [77.34726150561087]
We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians.
We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
arXiv Detail & Related papers (2023-01-18T09:26:02Z) - Periodicity of bipartite walk on biregular graphs with conditional
spectra [0.0]
We study a class of discrete quantum walks, known as bipartite walks.
Any discrete quantum walk is given by the powers of a unitary matrix $U$ indexed by arcs or edges of the underlying graph.
We apply periodicity results of bipartite walks to get a characterization of periodicity of Grover's walk on regular graphs.
arXiv Detail & Related papers (2022-11-04T21:02:30Z) - Two-level Quantum Walkers on Directed Graphs I: Universal Quantum
Computing [0.0]
We propose a model of universal quantum computation using a fermionic/bosonic multi-particle continuous-time quantum walk with two internal states.
A single-qubit is represented by the presence of a single quantum walker in either of the two parallel paths.
A physical implementation of quantum random access memory compatible with the present model will be considered in the second paper.
arXiv Detail & Related papers (2021-12-15T13:38:18Z) - Algebraic Compression of Quantum Circuits for Hamiltonian Evolution [52.77024349608834]
Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware.
We present an algorithm that compresses the Trotter steps into a single block of quantum gates.
This results in a fixed depth time evolution for certain classes of Hamiltonians.
arXiv Detail & Related papers (2021-08-06T19:38:01Z) - Persistence of Topological Phases in Non-Hermitian Quantum Walks [0.0]
We investigate the behavior of topological states in quantum walks in the presence of a lossy environment.
We show that the topological phases of the quantum walks are robust against moderate losses.
Although the topological nature persists in two-dimensional quantum walks, the $mathcalPT$-symmetric has no role to play there.
arXiv Detail & Related papers (2020-07-30T14:44:42Z) - 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) - A crossover between open quantum random walks to quantum walks [0.0]
The walk connects an open quantum random walk and a quantum walk with parameters $Min mathbbN$ controlling a decoherence effect.
We analytically show that a typical behavior of quantum walks appears even in a small gap of the parameter from the open quantum random walk.
arXiv Detail & Related papers (2020-07-02T07:42:24Z) - Projection Theorem for Discrete-Time Quantum Walks [0.0]
We make and generalize the observation that summing of probability amplitudes of a discrete-time quantum walk over partitions of the walking graph consistent with the step operator results in a unitary evolution on the reduced graph which is also a quantum walk.
We show that this is is the case for a lazy quantum walk, a walk with large coherent jumps and a walk on a circle with a twisted boundary condition.
arXiv Detail & Related papers (2020-04-03T01:51:55Z) - Quantum-Clustered Two-Photon Walks [68.8204255655161]
We demonstrate a previously unknown two-photon effect in a discrete-time quantum walk.
Two identical bosons with no mutual interactions can remain clustered together.
The two photons move in the same direction at each step due to a two-photon quantum interference phenomenon.
arXiv Detail & Related papers (2020-03-12T17:02:35Z)
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.