Giuseppe Di Molfetta

Physical Review A 110, 042418 (2024)

Dirac quantum walk on tetrahedra with Ugo Nzongani, Nathanaël Eon, Iván Márquez-Martín, Armando Pérez and Pablo Arrighi

Discrete-time quantum walks (QWs) are transportation models of single quantum particles over a lattice. Their evolution is driven through causal and local unitary operators. QWs are a powerful tool for quantum simulation of fundamental physics, as some of them have a continuum limit converging to well-known physics partial differential equations, such as the Dirac or the Schrödinger equation. In this paper, we show how to recover the Dirac equation in (3+1) dimensions with a QW evolving in a tetrahedral space. This paves the way to simulate the Dirac equation on a curved space-time. This also suggests an ordered scheme for propagating matter over a spin network, of interest in loop quantum gravity, where matter propagation has remained an open problem.

[arXiv]

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European Physical Journal D 77:80 (2023)

Twisted quantum walks, generalised Dirac equation and Fermion doubling with Nicolas Jolly

Quantum discrete-time walkers have since their introduction demonstrated applications in algo- rithmics and to model and simulate a wide range of transport phenomena. They have long been considered the discrete-time and discrete space analogue of the Dirac equation and have been used as a primitive to simulate quantum field theories precisely because of some of their internal symmetries. In this paper we introduce a new family of quantum walks, said twisted, which admits, as continuous limit, a generalised Dirac operator equipped with a dispersion term. Moreover, this quadratic term in the energy spectrum acts as an effective mass, leading to a regularization of the well-known Fermion doubling problem.

[arXiv]

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Physical Review B 106 (10), 104309  (2022)

Entanglement dynamics and ergodicity breaking in a quantum cellular automaton with Kevissen Sellapillay and Alberto Verga

Ergodicity breaking is observed in the blockade regime of Rydberg atom arrays, in the form of low entanglement eigenstates known as scars, which fail to thermalize. The signature of these states persists in periodically driven systems, where they coexist with an extensive number of chaotic states. Here we investigate a quantum cellular automaton based on the classical rule that updates a site if its two neighbors are in the lower state. We show that the breaking of ergodicity extends to chaotic states. The dynamical breaking of ergodicity is controlled by chiral quasiparticle excitations which propagate entanglement. Evidence of nonlocal entanglement is found, showing that these nonthermal chaotic states may be useful to quantum computation.

[arXiv]

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Physical Review A 106 (3), 032408 (2022)

Quantum simulations of hydrodynamics via the Madelung transformation with Julien Zylberman, Marc Brachet, Nuno F Loureiro, and Fabrice Debbasch

Developing numerical methods to simulate efficiently nonlinear fluid dynamics on universal quantum computers is a challenging problem. In this paper, a generalization of the Madelung transform is defined to solve quantum relativistic charged fluid equations interacting with external electromagnetic forces via the Dirac equation. The Dirac equation is discretized into discrete-time quantum walks which can be efficiently implemented on universal quantum computers. A variant of this algorithm is proposed to implement simulations using current noisy intermediate scale quantum (NISQ) devices in the case of homogeneous external forces. 

[arXiv]

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Uncertainty in Artificial Intelligence, 1697-1706 (2022)

Quantum perceptron revisited: Computational-statistical tradeoffs with Hachem Kadri and Mathieu Roget

We show a quadratic improvement over the classical perceptron in both the number of samples and the margin of the data. We derive a bound on the expected error of the hypothesis returned by our algorithm, which compares favorably to the one obtained with the classical online perceptron. We use numerical experiments to illustrate the trade-off between computational complexity and statistical accuracy in quantum perceptron learning and discuss some of the key practical issues surrounding the implementation of quantum perceptron models into near-term quantum devices, whose practical implementation represents a serious challenge due to inherent noise. However, the potential benefits make correcting this worthwhile.

[arXiv]