arXiv subjects

Asa Hopkins

Publications and source records attributed to Asa Hopkins.

5 recordsLinked to original sources

arXiv2026

Numerical methods for the simulation of quantum walks and quantum annealing

It is known that Chebyshev based polynomial approximation gives a near-optimal rate of convergence for calculating a function of a Hermitian matrix. However, previous work has not discussed the option of true minimax approximation, nor the specifics of writing a high performance implementation with a rigorous analysis of errors. This work provides such an analysis and an open-source implementation of three approximation methods in C++.

math.NA↗

arXiv2025

Heuristics for multi-stage quantum walks to find Ising ground states

One way to approximate a quantum annealing schedule is to use multiple quantum walks chained together, without intermediate measurements, to produce a multi-stage quantum walk (MSQW). Previous work has shown that a MSQW is better than QAOA (quantum alternating operator ansatz) for solving optimization tasks using multiple stages [Gerblich et al, arXiv:2407.06663]. In this work, we develop an efficient heuristic for choosing the free parameters in MSQW, and use it to obtain improved scaling compared to single stage quantum walks. We show numerically that the heuristic works well for problems with a large minimum energy gap, giving a polynomial scaling in the number of stages, and leading to an overall algorithm that scales polynomially in time. For problems with a small minimum gap, the scaling breaks down such that adding more stages decreases the success probability, leading to an overall scaling that is exponential in time as expected. Our methods are general and can be applied to any optimization problem to obtain good annealing schedules.

quant-ph↗

arXiv2005

Nonlinear Quantum Dynamics

The vast majority of the literature dealing with quantum dynamics is concerned with linear evolution of the wave function or the density matrix. A complete dynamical description requires a full understanding of the evolution of measured quantum systems, necessary to explain actual experimental results. The dynamics of such systems is intrinsically nonlinear even at the level of distribution functions, both classically as well as quantum mechanically. Aside from being physically more complete, this treatment reveals the existence of dynamical regimes, such as chaos, that have no counterpart in the linear case. Here, we present a short introductory review of some of these aspects, with a few illustrative results and examples.

quant-ph↗

arXiv2004

Proposed magneto-electrostatic ring trap for neutral atoms

We propose a novel trap for confining cold neutral atoms in a microscopic ring using a magneto-electrostatic potential. The trapping potential is derived from a combination of a repulsive magnetic field from a hard drive atom mirror and the attractive potential produced by a charged disk patterned on the hard drive surface. We calculate a trap frequency of [29.7, 42.6, 62.8] kHz and a depth of [16.1, 21.8, 21.8] MHz for [133Cs, 87Rb, 40K], and discuss a simple loading scheme and a method for fabrication. This device provides a one-dimensional potential in a ring geometry that may be of interest to the study of trapped quantum degenerate one-dimensional gases.

quant-ph↗

arXiv2003

Feedback cooling of a nanomechanical resonator

Cooled, low-loss nanomechanical resonators offer the prospect of directly observing the quantum dynamics of mesoscopic systems. However, the present state of the art requires cooling down to the milliKelvin regime in order to observe quantum effects. Here we present an active feedback strategy based on continuous observation of the resonator position for the purpose of obtaining these low temperatures. In addition, we apply this to an experimentally realizable configuration, where the position monitoring is carried out by a single-electron transistor. Our estimates indicate that with current technology this technique is likely to bring the required low temperatures within reach.

cond-mat↗