Related papers: Uniform Mixing in Chiral Quantum Walks

Uniform Mixing in Chiral Quantum Walks

URL: http://arxiv.org/abs/2605.04414v1
Date: Wed, 06 May 2026 02:12:09 GMT
Title: Uniform Mixing in Chiral Quantum Walks
Abstract summary: We show that for some unitary signing $$ the complete graph $K_n$ has probabilistic uniform mixing.<n>In contrast, it is known em no complete graph has uniform mixing except for $K$, $K_3$, and $K_4$.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: This paper studies uniform mixing in continuous-time quantum walks. We show that for some unitary signing $σ$ the complete graph $K^σ_n$ has probabilistic uniform mixing. In contrast, it is known {\em no} complete graph has uniform mixing except for $K_2$, $K_3$, and $K_4$. Our technique is based on a stopping rule for quantum walks which reduces global to local uniform mixing. As a special case, we found an orientation of $H(n,4)$ that mixes to uniform faster than any other Hamming graphs. We also show that there are infinite families of oriented circulants with {\em average} uniform mixing. This is a chiral violation of Godsil's {\em No-Go} theorem which states that no graph has average uniform mixing except for $K_2$.

Related papers

Arithmetic of Bohr Frequencies Governs Uniform Mixing in Randomly Timed Quantum Spin Chains [0.0]
Randomizing the readout time averages the mode interference in a quantum walk.<n>We ask when this makes the site populations of a uniformly coupled $XY$ chain exactly uniform for every initial site.<n>We classify these parity collisions using vanishing sums of roots of unity and prove existence in the positive cases through a phase distribution on a torus.
arXiv Detail & Related papers (2026-09-13T12:14:12Z)
Uniform mixing and $ε$-uniform mixing on cycles [6.617487928813374]
We study continuous-time quantum walks on cycles.<n>For every prime $p2$, we show that the cycle $C_p2$ admits $$-uniform mixing.
arXiv Detail & Related papers (2026-07-05T09:56:05Z)
Slow Mixing of Quantum Gibbs Samplers [47.373245682678515]
We present a quantum generalization of these tools through a generic bottleneck lemma.<n>This lemma focuses on quantum measures of distance, analogous to the classical Hamming distance but rooted in uniquely quantum principles.<n>We show how to lift classical slow mixing results in the presence of a transverse field using Poisson Feynman-Kac techniques.
arXiv Detail & Related papers (2024-11-06T22:51:27Z)
Quantum walks advantage on the dihedral group for uniform sampling problem [0.0]
This paper advances the general understanding of quantum walk mixing on Cayley graphs.<n>It highlights the improved mixing time achieved by continuous-time quantum walks on $D_2n$.<n>This work has potential applications in algorithms for a class of sampling problems based on non-abelian groups.
arXiv Detail & Related papers (2023-12-25T11:21:55Z)
$ε$-Uniform Mixing in Discrete Quantum Walks [0.0]
We study whether the probability distribution of a discrete quantum walk can get arbitrarily close to uniform. We establish a characterization of this phenomenon on regular non-bipartite graphs in terms of their adjacency eigenvalues and eigenprojections.
arXiv Detail & Related papers (2023-11-30T18:43:38Z)
Quantum connection, charges and virtual particles [65.268245109828]
A quantum bundle $L_hbar$ is endowed with a connection $A_hbar$ and its sections are standard wave functions $psi$ obeying the Schr"odinger equation. We will lift the bundles $L_Cpm$ and connection $A_hbar$ on them to the relativistic phase space $T*R3,1$ and couple them to the Dirac spinor bundle describing both particles and antiparticles.
arXiv Detail & Related papers (2023-10-10T10:27:09Z)
A Unified Framework for Uniform Signal Recovery in Nonlinear Generative Compressed Sensing [68.80803866919123]
Under nonlinear measurements, most prior results are non-uniform, i.e., they hold with high probability for a fixed $mathbfx*$ rather than for all $mathbfx*$ simultaneously. Our framework accommodates GCS with 1-bit/uniformly quantized observations and single index models as canonical examples. We also develop a concentration inequality that produces tighter bounds for product processes whose index sets have low metric entropy.
arXiv Detail & Related papers (2023-09-25T17:54:19Z)
Constructions of $k$-uniform states in heterogeneous systems [65.63939256159891]
We present two general methods to construct $k$-uniform states in the heterogeneous systems for general $k$. We can produce many new $k$-uniform states such that the local dimension of each subsystem can be a prime power.
arXiv Detail & Related papers (2023-05-22T06:58:16Z)
Uncertainties in Quantum Measurements: A Quantum Tomography [52.77024349608834]
The observables associated with a quantum system $S$ form a non-commutative algebra $mathcal A_S$. It is assumed that a density matrix $rho$ can be determined from the expectation values of observables. Abelian algebras do not have inner automorphisms, so the measurement apparatus can determine mean values of observables.
arXiv Detail & Related papers (2021-12-14T16:29:53Z)
Constructions of $k$-uniform states from mixed orthogonal arrays [18.378398718548016]
We study $k$-uniform states in heterogeneous systems whose local dimensions are mixed. We present two constructions of $2$-uniform states in heterogeneous systems. We show that some $k$-uniform bases can not be distinguished by local operations and classical communications.
arXiv Detail & Related papers (2020-06-07T08:35:22Z)
Quantum Coupon Collector [62.58209964224025]
We study how efficiently a $k$-element set $Ssubseteq[n]$ can be learned from a uniform superposition $|Srangle of its elements. We give tight bounds on the number of quantum samples needed for every $k$ and $n$, and we give efficient quantum learning algorithms.
arXiv Detail & Related papers (2020-02-18T16:14:55Z)

This list is automatically generated from the titles and abstracts of the papers in this site.