arXiv subjects

Elie Bermot

Publications and source records attributed to Elie Bermot.

3 recordsLinked to original sources

arXiv2026

Log-concavity and tunneling: adiabatic quantum optimization for convex functions (with a spike)

Quantum tunneling is expected to provide a computational speedup in quantum computing, a phenomenon that Adiabatic Quantum Optimization (AQO) aims to leverage. While some academic proofs of concept have been studied, such as the "Hamming weight with a spike" (HWS) problem, the algorithmic gains of this effect remain underexplored. In this work we extend the analysis underlying HWS to more general potentials. In the first half of the work, we establish (discrete) log-concavity of the ground state as a key structural property in this context. We devise a framework for establishing log-concavity of the ground state for a large family of discrete, 1-dimensional Schr\"odinger operators. The family includes convex potentials, but also certain potentials with local minima. In the convex case, this provides a discrete version of a continuous result by Brascamp and Lieb ('76). We demonstrate the utility of our result by establishing new spectral gap bounds, going beyond related results by Jarret and Jordan ('14) for convex potentials. In the second half of the work, we use our results on log-concavity to extend the perturbative analysis of HWS by Reichardt ('04) to the larger family of potentials with log-concave ground state. As a concrete instantiation, we use our result to extend the HWS analysis from a linear potential (which is exactly solvable) to a quadratic potential (which is no longer solvable). Our result strongly suggests the broader applicability of tunneling to convex potentials with spikes

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arXiv2025

Local Rydberg blockade regimes for disk graph embedding and quantum optimization

Rydberg atom arrays are a powerful platform for solving combinatorial optimization problems, owing to the Rydberg blockade mechanism, which imposes effective constraints on simultaneous atomic excitations. These constraints have enabled the encoding of the Maximum Independent Set (MIS) problem on unit disk graphs, where atoms interact within a fixed, globally defined blockade radius. However, this restriction limits the class of addressable problems. A natural extension is to consider disk graphs, which generalize unit disk graphs by allowing arbitrary disk radii and correspond to the intersection graphs of disks in the plane. Embedding such graphs in Rydberg systems requires moving beyond the standard, globally uniform blockade model. In this work, we introduce a local Rydberg blockade regime, which emerges when local drives are applied to different pairs of atoms involved in a potential interaction. We develop a general theoretical framework for this regime and propose two novel metrics, the correlation matrix and the maximum independence violation, to quantify the quality of the embedding. Using these metrics, we demonstrate that disk graphs can be meaningfully embedded into Rydberg atom arrays under local drive schemes, thereby expanding the landscape of quantum-addressable optimization problems. Finally, when evaluating approximate solutions of the MIS problem, characterized by near-optimal independent sets, local drive approaches exhibit significantly improved performance over global ones. These results highlight the practical advantage of local blockade engineering for approximate combinatorial optimization and open a path toward leveraging the analog capabilities of Rydberg platforms beyond conventional geometric constraints.

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arXiv2023

Quantum Generative Adversarial Networks For Anomaly Detection In High Energy Physics

The standard model (SM) of particle physics represents a theoretical paradigm for the description of the fundamental forces of nature. Despite its broad applicability, the SM does not enable the description of all physically possible events. The detection of events that cannot be described by the SM, which are typically referred to as anomalous, and the related potential discovery of exotic physical phenomena is a non-trivial task. The challenge becomes even greater with next-generation colliders that will produce even more events with additional levels of complexity. The additional data complexity motivates the search for unsupervised anomaly detection methods that do not require prior knowledge about the underlying models. In this work, we develop such a technique. More explicitly, we employ a quantum generative adversarial network to identify anomalous events. The method learns the background distribution from SM data and, then, determines whether a given event is characteristic for the learned background distribution. The proposed quantum-powered anomaly detection strategy is tested on proof-of-principle examples using numerical simulations and IBM Quantum processors. We find that the quantum generative techniques using ten times fewer training data samples can yield comparable accuracy to the classical counterpart for the detection of the Graviton and Higgs particles. Additionally, we empirically compute the capacity of the quantum model and observe an improved expressivity compared to its classical counterpart.

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