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Alexandre Dauphin

Publications and source records attributed to Alexandre Dauphin.

At least 37 records · Page 2Linked to original sources

Characterizing out-of-distribution generalization of neural networks: application to the disordered Su-Schrieffer-Heeger model

Machine learning (ML) is a promising tool for the detection of phases of matter. However, ML models are also known for their black-box construction, which hinders understanding of what they learn from the data and makes their application to novel data risky. Moreover, the central challenge of ML is to ensure its good generalization abilities, i.e., good performance on data outside the training set. Here, we show how the informed use of an interpretability method called class activation mapping (CAM), and the analysis of the latent representation of the data with the principal component analysis (PCA) can increase trust in predictions of a neural network (NN) trained to classify quantum phases. In particular, we show that we can ensure better out-of-distribution generalization in the complex classification problem by choosing such an NN that, in the simplified version of the problem, learns a known characteristic of the phase. We show this on an example of the topological Su-Schrieffer-Heeger (SSH) model with and without disorder, which turned out to be surprisingly challenging for NNs trained in a supervised way. This work is an example of how the systematic use of interpretability methods can improve the performance of NNs in scientific problems.

quant-ph↗

Variational protocols for emulating digital gates using analog control with always-on interactions

We design variational pulse sequences tailored for neutral atom quantum simulators and show that we can engineer layers of single-qubit and multi-qubit gates. As an application, we discuss how the proposed method can be used to perform refocusing algorithms, SWAP networks, and ultimately quantum chemistry simulations. While the theoretical protocol we develop still has experimental limitations, it paves the way, with some further optimisation, for the use of analog quantum processors for variational quantum algorithms, including those not previously considered compatible with analog mode.

quant-ph↗

Amorphous quantum magnets in a two-dimensional Rydberg atom array

Amorphous solids, i.e., systems which feature well-defined short-range properties but lack long-range order, constitute an important research topic in condensed matter. While their microscopic structure is known to differ from their crystalline counterpart, there are still many open questions concerning the emergent collective behavior in amorphous materials. This is particularly the case in the quantum regime, where the numerical simulations are extremely challenging. In this article, we instead propose to explore amorphous quantum magnets with an analog quantum simulator. To this end, we first present an algorithm to generate amorphous quantum magnets, suitable for Rydberg simulators of the Ising model. Subsequently, we use semiclassical approaches to get a preliminary insight of the physics of the model. In particular, for ferromagnetic interactions, we calculate mean-field phase diagrams, and use the linear-spin-wave theory to study localization properties and dynamical structure factors of the excitations. For antiferromagnetic interactions, we show that amorphous magnets exhibit a complex classical energy landscape by means of simulated annealing. Finally, we outline an experimental proposal based on Rydberg atoms in programmable tweezer arrays, thus opening the road towards the study of amorphous quantum magnets in regimes difficult to simulate classically.

cond-mat.quant-gas↗

Optimization of Quantum Systems Emulation via a Variant of the Bandwidth Minimization Problem

This paper introduces weighted-BMP, a variant of the Bandwidth Minimization Problem (BMP), with a significant application in optimizing quantum emulation. Weighted-BMP optimizes particles ordering to reduce the emulation costs, by designing a particle interaction matrix where strong interactions are placed as close as possible to the diagonal. We formulate the problem using a Mixed Integer Linear Program (MILP) and solve it to optimality with a state of the art solver. To strengthen our MILP model, we introduce symmetry-breaking inequalities and establish a lower bound. Through extensive numerical analysis, we examine the impacts of these enhancements on the solver's performance. The introduced reinforcements result in an average CPU time reduction of 25.61 percent. Additionally, we conduct quantum emulations of realistic instances. Our numerical tests show that the weighted-BMP approach outperforms the Reverse Cuthill-McKee (RCM) algorithm, an efficient heuristic used for site ordering tasks in quantum emulation, achieving an average memory storage reduction of 24.48 percent. From an application standpoint, this study is the first to apply an exact optimization method, weighted-BMP, that considers interactions for site ordering in quantum emulation pre-processing, and shows its crucial role in cost reduction. From an algorithmic perspective, it contributes by introducing important reinforcements and lays the groundwork for future research on further enhancements, particularly on strengthening the weak linear relaxation of the MILP.

quant-ph↗

A hybrid quantum algorithm to detect conical intersections

Conical intersections are topologically protected crossings between the potential energy surfaces of a molecular Hamiltonian, known to play an important role in chemical processes such as photoisomerization and non-radiative relaxation. They are characterized by a non-zero Berry phase, which is a topological invariant defined on a closed path in atomic coordinate space, taking the value $π$ when the path encircles the intersection manifold. In this work, we show that for real molecular Hamiltonians, the Berry phase can be obtained by tracing a local optimum of a variational ansatz along the chosen path and estimating the overlap between the initial and final state with a control-free Hadamard test. Moreover, by discretizing the path into $N$ points, we can use $N$ single Newton-Raphson steps to update our state non-variationally. Finally, since the Berry phase can only take two discrete values (0 or $π$), our procedure succeeds even for a cumulative error bounded by a constant; this allows us to bound the total sampling cost and to readily verify the success of the procedure. We demonstrate numerically the application of our algorithm on small toy models of the formaldimine molecule (\ce{H2C=NH}).

quant-ph↗

Variational quantum simulation using non-Gaussian continuous-variable systems

This work introduces a novel approach to quantum simulation by leveraging continuous-variable systems within a photonic hardware-inspired framework. The primary focus is on simulating static properties of the ground state of Hamiltonians associated with infinite-dimensional systems, such as those arising in quantum field theory. We present a continuous-variable variational quantum eigensolver compatible with state-of-the-art photonic technology. The framework we introduce allows us to compare discrete and continuous variable systems without introducing a truncation of the Hilbert space, opening the possibility to investigate the scenarios where one of the two formalisms performs better. We apply it to the study of static properties of the Bose--Hubbard model and demonstrate its effectiveness and practicality, highlighting the potential of continuous-variable quantum simulations in addressing complex problems in quantum physics.

quant-ph↗

Higher-order topological Peierls insulator in a two-dimensional atom-cavity system

In this work, we investigate a two-dimensional system of ultracold bosonic atoms inside an optical cavity, and show how photon-mediated interactions give rise to a plaquette-ordered bond pattern in the atomic ground state. The latter corresponds to a 2D Peierls transition, generalizing the spontaneous bond dimmerization driven by phonon-electron interactions in the 1D Su-Schrieffer-Heeger (SSH) model. Here the bosonic nature of the atoms plays a crucial role to generate the phase, as similar generalizations with fermionic matter do not lead to a plaquette structure. Similar to the SSH model, we show how this pattern opens a non-trivial topological gap in 2D, resulting in a higher-order topological phase hosting corner states, that we characterize by means of a many-body topological invariant and through its entanglement structure. Finally, we demonstrate how this higher-order topological Peierls insulator can be readily prepared in atomic experiments through adiabatic protocols. Our work thus shows how atomic quantum simulators can be harnessed to investigate novel strongly-correlated topological phenomena beyond those observed in natural materials.

cond-mat.quant-gas↗

Retrieving space-dependent polarization transformations via near-optimal quantum process tomography

An optical waveplate rotating light polarization can be modeled as a single-qubit unitary operator, whose action can be experimentally determined via quantum process tomography. Standard approaches to tomographic problems rely on the maximum-likelihood estimation, providing the most likely transformation to yield the same outcomes as a set of experimental projective measurements. The performances of this method strongly depend on the number of input measurements and the numerical minimization routine that is adopted. Here we investigate the application of genetic and machine learning approaches to this problem, finding that both allow for accurate reconstructions and fast operations when processing a set of projective measurements very close to the minimal one. We apply these techniques to the case of space-dependent polarization transformations, providing an experimental characterization of the optical action of spin-orbit metasurfaces having patterned birefringence. Our efforts thus expand the toolbox of methodologies for optical process tomography. In particular, we find that the neural network-based scheme provides a significant speed-up, that may be critical in applications requiring a characterization in real-time. We expect these results to lay the groundwork for the optimization of tomographic approaches in more general quantum processes, including non-unitary gates and operations in higher-dimensional Hilbert spaces.

quant-ph↗

Ultra-long quantum walks via spin-orbit photonics

The possibility of fine-tuning the couplings between optical modes is a key requirement in photonic circuits for quantum simulations. In these architectures, emulating the long-time evolution of particles across large lattices requires sophisticated setups, that are often intrinsically lossy. Here we report ultra-long photonic quantum walks across several hundred optical modes, obtained by propagating a light beam through very few closely-stacked liquid-crystal metasurfaces. By exploiting spin-orbit effects, these implement space-dependent polarization transformations that mix circularly polarized optical modes carrying quantized transverse momentum. As each metasurface implements long-range couplings between distant modes, by using only a few of them we simulate quantum walks up to 320 discrete steps without any optical amplification, far beyond state-of-the-art experiments. To showcase the potential of this method, we experimentally demonstrate that in the long-time limit a quantum walk affected by dynamical disorder generates maximal entanglement between two system partitions. Our platform grants experimental access to large-scale unitary evolutions while keeping optical losses at a minimum, thereby paving the way to massive multi-photon multi-mode quantum simulations.

quant-ph↗

Topological stripe state in an extended Fermi-Hubbard model

Interaction-induced topological systems have attracted a growing interest for their exotic properties going beyond the single-particle picture of topological insulators. In particular, the interplay between strong correlations and finite doping can give rise to nonhomogeneous solutions that break the translational symmetry. In this work, we report the appearance of a topological stripe state in an interaction-induced Chern insulator around half-filling. In contrast to similar stripe phases in nontopological systems, here we observe the appearance of chiral edge states on top of the domain wall. Furthermore, we characterize their topological nature by analyzing the quantized transferred charge of the domains in a pumping scheme. Finally, we focus on aspects relevant to observing such phases in state-of-the-art quantum simulators of ultracold atoms in optical lattices. In particular, we propose an adiabatic state preparation protocol and a detection scheme of the topology of the system in real space.

cond-mat.quant-gas↗

Citizen Science to Assess Light Pollution with Mobile Phones

The analysis of the colour of artificial lights at night has an impact on diverse fields, but current data sources have either limited resolution or scarce availability of images for a specific region. In this work, we propose crowdsourced photos of streetlights as an alternative data source: for this, we designed NightUp Castelldefels, a pilot for a citizen science experiment aimed at collecting data about the colour of streetlights. In particular, we extract the colour from the collected images and compare it to an official database, showing that it is possible to classify streetlights according to their colour from photos taken by untrained citizens with their own smartphones. We also compare our findings to the results obtained from one of the current sources for this kind of study. The comparison highlights how the two approaches give complementary information about artificial lights at night in the area. This work opens a new avenue in the study of the colour of artificial lights at night with the possibility of accurate, massive and cheap data collection.

astro-ph.IM↗

Localization and multifractal properties of the long-range Kitaev chain in the presence of an Aubry-André-Harper modulation

In the presence of quasiperiodic potentials, the celebrated Kitaev chain presents an intriguing phase diagram with ergodic, localized and and multifractal states. In this work, we generalize these results by studying the localization properties of the Aubry-André-Harper model in the presence of long-range hopping and superconducting pairing amplitudes. These amplitudes decay with power-law exponents $ξ$ and $α$ respectively. To this end, we review and compare a toolbox of global and local characterization methods in order to investigate different types of transitions between ergodic, localized and multifractal states. We report energy-dependent transitions from ergodic to multifractal states for pairing terms with $α<1$ and energy-dependent transitions from ergodic to localized states with an intermediate multifractal region for $α>1$. The size of the intermediate multifractal region depends not only on the value of the superconducting pairing term $Δ$, but also on the energy band. The transitions are not described by a mobility edge, but instead we report hybridization of bands with different types of localization properties. This leads to coexisting multifractal regimes where fractal dimensions follow different distributions.

cond-mat.dis-nn↗

Revealing the topological nature of the bond order wave in a strongly correlated quantum system

We investigate the topological properties of the bond order wave phase arising in the extended Fermi-Hubbard model. In particular, we uncover a topological sector, which remained elusive in previous finite-size numerical studies due to boundary effects. We first show that, for an infinite system, the bond order wave regime is characterized by two degenerate bulk states corresponding to the trivial and topological sectors. The latter turns out to be indeed characterized by an even degeneracy of the entanglement spectrum and longe-range order of a string correlation function. For finite size systems, we show that the topological sector can be stabilized by imposing a suitable border potential. This therefore provides a concrete protocol for the observation of topologically protected degenerate edge modes in finite-size systems. Furthermore, we show that the bulk of the system is characterized by exotic solitonic solutions interpolating between the trivial and topological sectors. Finally, we propose an implementation and detection scheme of this strongly-correlated topological phase in a quantum simulator based on dipolar Fermi gases in optical lattices.

cond-mat.quant-gas↗

Accessing the topological Mott insulator in cold atom quantum simulators with realistic Rydberg dressing

The interplay between many-body interactions and the kinetic energy gives rise to rich phase diagrams hosting, among others, interaction-induced topological phases. These phases are characterized by both a local order parameter and a global topological invariant, and can exhibit exotic ground states such as self-trapped polarons and interaction-induced edge states. In this work, we investigate a realistic scenario for the quantum simulation of such systems using cold Rydberg-dressed atoms in optical lattices. We consider spinless fermions on a checkerboard lattice, interacting via the tunable-range effective potential induced by the Rydberg dressing. We perform a detailed analysis of the phase diagram at half- and incommensurate fillings, in the mean-field approximation. We furthermore study the stability of the phases with respect to temperature within the mean-field approximation and with respect to quantum fluctuations using the density matrix renormalization group method. Finally, we propose an implementation protocol, and in particular identify attainable regimes of experimental parameters in which the topological properties of the model become accessible. Our work, thereby, opens a realistic pathway to the outstanding experimental observation of this predicted phase in state-of-the-art cold atom quantum simulators.

cond-mat.quant-gas↗

Linking topological features of the Hofstadter model to optical diffraction figures

In two, three and even four spatial dimensions, the transverse responses experienced by a charged particle on a lattice in a uniform magnetic field are fully controlled by topological invariants called Chern numbers, which characterize the energy bands of the underlying Hofstadter Hamiltonian. These remarkable features, solely arising from the magnetic translational symmetry, are captured by Diophantine equations which relate the fraction of occupied states, the magnetic flux and the Chern numbers of the system bands. Here we investigate the close analogy between the topological properties of Hofstadter Hamiltonians and the diffraction figures resulting from optical gratings. In particular, we show that there is a one-to-one relation between the above mentioned Diophantine equation and the Bragg condition determining the far-field positions of the optical diffraction peaks. As an interesting consequence of this mapping, we discuss how the robustness of diffraction figures to structural disorder in the grating is a direct analogue of the robustness of transverse conductance in the Quantum Hall effect.

cond-mat.mes-hall↗

Quadratic Unconstrained Binary Optimisation via Quantum-Inspired Annealing

We present a classical algorithm to find approximate solutions to instances of quadratic unconstrained binary optimisation. The algorithm can be seen as an analogue of quantum annealing under the restriction of a product state space, where the dynamical evolution in quantum annealing is replaced with a gradient-descent based method. This formulation is able to quickly find high-quality solutions to large-scale problem instances, and can naturally be accelerated by dedicated hardware such as graphics processing units. We benchmark our approach for large scale problem instances with tuneable hardness and planted solutions. We find that our algorithm offers a similar performance to current state of the art approaches within a comparably simple gradient-based and non-stochastic setting.

quant-ph↗

Hessian-based toolbox for reliable and interpretable machine learning in physics

Machine learning (ML) techniques applied to quantum many-body physics have emerged as a new research field. While the numerical power of this approach is undeniable, the most expressive ML algorithms, such as neural networks, are black boxes: The user does neither know the logic behind the model predictions nor the uncertainty of the model predictions. In this work, we present a toolbox for interpretability and reliability, agnostic of the model architecture. In particular, it provides a notion of the influence of the input data on the prediction at a given test point, an estimation of the uncertainty of the model predictions, and an extrapolation score for the model predictions. Such a toolbox only requires a single computation of the Hessian of the training loss function. Our work opens the road to the systematic use of interpretability and reliability methods in ML applied to physics and, more generally, science.

quant-ph↗

Cold atoms meet lattice gauge theory

The central idea of this review is to consider quantum field theory models relevant for particle physics and replace the fermionic matter in these models by a bosonic one. This is mostly motivated by the fact that bosons are more ``accessible'' and easier to manipulate for experimentalists, but this ``substitution'' also leads to new physics and novel phenomena. It allows us to gain new information about among other things confinement and the dynamics of the deconfinement transition. We will thus consider bosons in dynamical lattices corresponding to the bosonic Schwinger or Z$_2$ Bose-Hubbard models. Another central idea of this review concerns atomic simulators of paradigmatic models of particle physics theory such as the Creutz-Hubbard ladder, or Gross-Neveu-Wilson and Wilson-Hubbard models. Finally, we will briefly describe our efforts to design experimentally friendly simulators of these and other models relevant for particle physics.

cond-mat.quant-gas↗