Giuseppe Di Molfetta

Physical Review B 106 (10), 104309

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

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

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]

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Physical Review A 105 (6), 062420

Geodesic quantum walks with Victor Deng

We propose a new family of discrete-spacetime quantum walks capable to propagate on any arbitrary triangulations. Moreover we also extend and generalise the duality principle introduced in~\cite{arrighi2019curved}, linking continuous local deformations of a given triangulation and the inhomogeneity of the local unitaries that guide the quantum walker. We proved that in the formal continuous limit, in both space and time, this new family of quantum walks converges to the (1+2)D massless Dirac equation on curved manifolds. We believe that this result has relevance in both modelling/simulating quantum transport on discrete curved structures, such as fullerene molecules or dynamical causal triangulation, and in addressing fast and efficient optimization problems in the context of the curved space optimization methods.

[arXiv]

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A relativistic discrete spacetime formulation of 3+ 1 QED with Nathanael Eon, Giuseppe Magnifico and Pablo Arrighi

We propose a new family of discrete-spacetime quantum walks capable to propagate on any arbitrary triangulations. Moreover we also extend and generalise the duality principle introduced in~\cite{arrighi2019curved}, linking continuous local deformations of a given triangulation and the inhomogeneity of the local unitaries that guide the quantum walker. We proved that in the formal continuous limit, in both space and time, this new family of quantum walks converges to the (1+2)D massless Dirac equation on curved manifolds. We believe that this result has relevance in both modelling/simulating quantum transport on discrete curved structures, such as fullerene molecules or dynamical causal triangulation, and in addressing fast and efficient optimization problems in the context of the curved space optimization methods.

[arXiv]

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Scientific reports 12 (1), 1-9

A discrete relativistic spacetime formalism for 1+ 1-QED with continuum limits with Kevissen Sellapillay and Pablo Arrighi

We build a quantum cellular automaton (QCA) which coincides with 1+1 QED on its known continuum limits. It consists in a circuit of unitary gates driving the evolution of particles on a one dimensional lattice, and having them interact with the gauge field on the links. The particles are massive fermions, and the evolution is exactly U(1) gauge-invariant. We show that, in the continuous-time discrete-space limit, the QCA converges to the Kogut–Susskind staggered version of  1+1 QED. We also show that, in the continuous spacetime limit and in the free one particle sector, it converges to the Dirac equation—a strong indication that the model remains accurate in the relativistic regime.

[arXiv]

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