Related papers: Strong dispersion property for the quantum walk on the hypercube

Related papers

Quantum Speedups for Stochastic Optimization with Heavy-Tailed Noise [49.730496294398726]
We develop a novel quantum mean estimator for heavy-tailed random variables.<n>We derive stronger lower bounds for tail index>4/3$, showing that a nontrivial dependence on a dimension is unavoidable.<n>For a convex objective function, we propose a quantum projected gradient descent method.
arXiv Detail & Related papers (2026-07-28T09:29:37Z)
Near-Optimal Clustering in Mixture of Markov Chains [74.3828414695655]
We study the problem of clustering $T$ trajectories of length $H$, each generated by one of $K$ unknown ergodic Markov chains over a finite state space of size $S$.<n>We derive an instance-dependent, high-probability lower bound on the clustering error rate, governed by the weighted KL divergence between the transition kernels of the chains.<n>We then present a novel two-stage clustering algorithm.
arXiv Detail & Related papers (2025-06-02T05:10:40Z)
Complexity Analysis of Normalizing Constant Estimation: from Jarzynski Equality to Annealed Importance Sampling and beyond [40.79840141270367]
Given an unnormalized probability density $piproptomathrme-V$, estimating its normalizing constant $Z=int_mathbbRdmathrme-V(x)mathrmdx$ or free energy $F=-log Z$ is a crucial problem in Bayesian statistics, statistical mechanics, and machine learning.<n>We propose a new algorithm based on reverse diffusion samplers, establish a framework for analyzing its complexity, and empirically demonstrate its efficiency in tackling multimodality.
arXiv Detail & Related papers (2025-02-07T00:05:28Z)
Efficient unitary designs and pseudorandom unitaries from permutations [35.66857288673615]
We show that products exponentiated sums of $S(N)$ permutations with random phases match the first $2Omega(n)$ moments of the Haar measure. The heart of our proof is a conceptual connection between the large dimension (large-$N$) expansion in random matrix theory and the method.
arXiv Detail & Related papers (2024-04-25T17:08:34Z)
Robust spectral $\pi$ pairing in the random-field Floquet quantum Ising model [44.84660857803376]
We study level pairings in the many-body spectrum of the random-field Floquet quantum Ising model. The robustness of $pi$ pairings against longitudinal disorder may be useful for quantum information processing.
arXiv Detail & Related papers (2024-01-09T20:37:48Z)
The quantum beam splitter with many partially indistinguishable photons: multiphotonic interference and asymptotic classical correspondence [44.99833362998488]
We present the analysis of the quantum two-port interferometer in the $n rightarrow infty$ limit of $n$ partially indistinguishable photons. Our main result is that the output distribution is dominated by the $O(sqrtn)$ channels around a certain $j*$ that depends on the degree of indistinguishability. The form is essentially the doubly-humped semi-classical envelope of the distribution that would arise from $2 j*$ indistinguishable photons, and which reproduces the corresponding classical intensity distribution.
arXiv Detail & Related papers (2023-12-28T01:48:26Z)
Quantum walks advantage on the dihedral group for uniform sampling problem [0.0]
Mixing through walks is the process for a Markov chain to approximate a stationary distribution for a group. Quantum walks have shown potential advantages in mixing time over the classical case but lack general proof in the finite group case. This work has potential applications in algorithms for sampling non-abelian groups, graph isomorphism tests, etc.
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)
The scaling law of the arrival time of spin systems that present pretty good transmission [49.1574468325115]
The pretty good transmission scenario implies that the probability of sending one excitation from one extreme of a spin chain to the other can reach values arbitrarily close to the unity just by waiting a time long enough. Some works suggest that the time $t_varepsilon$ at which the pretty good transmission takes place scales as $1/(|varepsilon|)f(N)$. We show that the exponent is not a simple function of the chain length but a power law of the number of linearly independent irrational eigenvalues of the one-excitation block of the Hamiltonian
arXiv Detail & Related papers (2023-09-05T13:13:00Z)
Moments, Random Walks, and Limits for Spectrum Approximation [40.43008834125277]
We show that there are distributions on $[-1,1]$ that cannot be approximated to accuracy $epsilon$ in Wasserstein-1 distance. No algorithm can compute an $epsilon$-accurate approximation to the spectrum of a normalized graph adjacency matrix with constant probability.
arXiv Detail & Related papers (2023-07-02T05:03:38Z)
A Nearly Tight Bound for Fitting an Ellipsoid to Gaussian Random Points [50.90125395570797]
This nearly establishes a conjecture ofciteSaundersonCPW12, within logarithmic factors. The latter conjecture has attracted significant attention over the past decade, due to its connections to machine learning and sum-of-squares lower bounds for certain statistical problems.
arXiv Detail & Related papers (2022-12-21T17:48:01Z)
The uniform measure for quantum walk on hypercube: a quantum Bernoulli noises approach [6.855885246744849]
We present a quantum Bernoulli noises approach to quantum walks on hypercubes. We introduce a discrete-time quantum walk model on a general hypercube. We establish two limit theorems showing that the averaged probability distribution of the walk even converges to the uniform probability distribution.
arXiv Detail & Related papers (2022-11-15T07:24:02Z)
Random quantum circuits are approximate unitary $t$-designs in depth $O\left(nt^{5+o(1)}\right)$ [0.0]
We show that random quantum circuits generate approximate unitary $t$-designs in depth $O(nt5+o(1))$. Our techniques involve Gao's quantum union bound and the unreasonable effectiveness of the Clifford group.
arXiv Detail & Related papers (2022-03-30T18:02:08Z)
Parameter Estimation with Reluctant Quantum Walks: a Maximum Likelihood approach [0.0]
A coin action is presented, with the real parameter $theta$ to be estimated. For $k$ large, we show that the likelihood is sharply peaked at a displacement determined by the ratio $d/k$.
arXiv Detail & Related papers (2022-02-24T00:51:17Z)
Random quantum circuits transform local noise into global white noise [118.18170052022323]
We study the distribution over measurement outcomes of noisy random quantum circuits in the low-fidelity regime. For local noise that is sufficiently weak and unital, correlations (measured by the linear cross-entropy benchmark) between the output distribution $p_textnoisy$ of a generic noisy circuit instance shrink exponentially. If the noise is incoherent, the output distribution approaches the uniform distribution $p_textunif$ at precisely the same rate.
arXiv Detail & Related papers (2021-11-29T19:26:28Z)
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)
On the Almost Sure Convergence of Stochastic Gradient Descent in Non-Convex Problems [75.58134963501094]
This paper analyzes the trajectories of gradient descent (SGD) We show that SGD avoids saddle points/manifolds with $1$ for strict step-size policies.
arXiv Detail & Related papers (2020-06-19T14:11:26Z)

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