arXiv subjects

Thibaud Louvet

Publications and source records attributed to Thibaud Louvet.

11 recordsLinked to original sources

arXiv2026

Feasibility of performing quantum chemistry calculations on quantum computers

Quantum chemistry is envisioned as an early and disruptive application for quantum computers. Yet, closer scrutiny of the proposed algorithms shows that there are considerable difficulties along the way. Here, we propose two criteria for evaluating two leading quantum approaches for finding the ground state of molecules. The first criterion applies to the variational quantum eigensolver (VQE) algorithm. It sets an upper bound to the level of imprecision/decoherence that can be tolerated in quantum hardware as a function of the targeted precision, the number of gates and the typical energy contribution from states populated by decoherence processes. We find that decoherence is highly detrimental to the accuracy of VQE and performing relevant chemistry calculations would require performances that are expected for fault-tolerant quantum computers, not mere noisy hardware, even with advanced error mitigation techniques. Physically, the sensitivity of VQE to decoherence originates from the fact that, in VQE, the spectrum of the studied molecule has no correlation with the spectrum of the quantum hardware used to perform the computation. The second criterion applies to the quantum phase estimation (QPE) algorithm, which is often presented as the go-to replacement of VQE upon availability of (noiseless) fault-tolerant quantum computers. QPE requires an input state with a large enough overlap with the sought-after ground state. We provide a criterion to estimate quantitatively this overlap based on the energy and the energy variance of said input state. Using input states from a variety of state-of-the-art classical methods, we show that the scaling of this overlap with system size does display the standard orthogonality catastrophe, namely an exponential suppression with system size. This in turns leads to an exponentially reduced QPE success probability.

quant-ph↗

arXiv2026

Topological Lasing from Thouless Pumping in Bilayer Photonic Crystal

Topological lasing leverages concepts from topological physics to achieve single-mode light amplification within topological bandgaps, offering robustness against fabrication imperfections. Recent advances in microelectromechanical systems (MEMSs) and phase-change materials (PCMs) at the subwavelength scale promise new avenues for dynamically reconfigurable topological lasers, enabling robust and tunable nanoscale light sources. Here, we numerically demonstrate a dynamically reconfigurable lasing action at telecom wavelengths in a bilayer photonic crystal through the mechanisms of Thouless pumping. By designing two competing periodic potentials -- one slowly translating photonic grating atop another stationary one -- we observe a transition between a topological pumping regime and conventional mode oscillation. A carefully engineered heterojunction between these phases supports a robust lasing mode that can be dynamically tuned via MEMSs or reversible PCMs. Our work establishes bilayer photonic crystals as a programmable platform for achieving topological light sources, showcasing a potential pathway for merging topological photonics with reconfigurable photonic devices.

physics.optics↗

arXiv2025

Solving the Gross-Pitaevskii equation on multiple different scales using the quantics tensor train representation

Solving partial differential equations of highly featured problems represents a formidable challenge, where reaching high precision across multiple length scales can require a prohibitive amount of computer memory or computing time. However, the solutions to physics problems typically have structures operating on different length scales, and as a result exhibit a high degree of compressibility. Here, we use the quantics tensor train representation to build a solver for the time-dependent Gross-Pitaevskii equation. We demonstrate that the quantics approach generalizes well to the presence of the non-linear term in the equation. We show that we can resolve phenomena across length scales separated by seven orders of magnitude in one dimension within one hour on a single core in a laptop, greatly surpassing the capabilities of more naive methods. We illustrate our methodology with various modulated optical trap potentials presenting features at vastly different length scales, including solutions to the Gross-Pitaevskii equation on two-dimensional grids above a trillion points ($2^{20} \times 2^{20}$). This quantum-inspired methodology can be readily extended to other partial differential equations combining spatial and temporal evolutions, providing a powerful method to solve highly featured differential equations at unprecedented length scales.

quant-ph↗

arXiv2024

Learning tensor networks with tensor cross interpolation: new algorithms and libraries

The tensor cross interpolation (TCI) algorithm is a rank-revealing algorithm for decomposing low-rank, high-dimensional tensors into tensor trains/matrix product states (MPS). TCI learns a compact MPS representation of the entire object from a tiny training data set. Once obtained, the large existing MPS toolbox provides exponentially fast algorithms for performing a large set of operations. We discuss several improvements and variants of TCI. In particular, we show that replacing the cross interpolation by the partially rank-revealing LU decomposition yields a more stable and more flexible algorithm than the original algorithm. We also present two open source libraries, xfac in Python/C++ and TensorCrossInterpolation.jl in Julia, that implement these improved algorithms, and illustrate them on several applications. These include sign-problem-free integration in large dimension, the superhigh-resolution quantics representation of functions, the solution of partial differential equations, the superfast Fourier transform, the computation of partition functions, and the construction of matrix product operators.

physics.comp-ph↗

arXiv2022

A density-matrix renormalization group algorithm for simulating quantum circuits with a finite fidelity

We develop a density-matrix renormalization group (DMRG) algorithm for the simulation of quantum circuits. This algorithm can be seen as the extension of time-dependent DMRG from the usual situation of hermitian Hamiltonian matrices to quantum circuits defined by unitary matrices. For small circuit depths, the technique is exact and equivalent to other matrix product state (MPS) based techniques. For larger depths, it becomes approximate in exchange for an exponential speed up in computational time. Like an actual quantum computer, the quality of the DMRG results is characterized by a finite fidelity. However, unlike a quantum computer, the fidelity depends strongly on the quantum circuit considered. For the most difficult possible circuit for this technique, the so-called "quantum supremacy" benchmark of Google Inc. , we find that the DMRG algorithm can generate bit strings of the same quality as the seminal Google experiment on a single computing core. For a more structured circuit used for combinatorial optimization (Quantum Approximate Optimization Algorithm or QAOA), we find a drastic improvement of the DMRG results with error rates dropping by a factor of 100 compared with random quantum circuits. Our results suggest that the current bottleneck of quantum computers is their fidelities rather than the number of qubits.

quant-ph↗

arXiv2021

Quantized Berry winding from an emergent $\mathcal{PT}$ symmetry

Linear crossing of energy bands occur in a wide variety of materials. In this paper we address the question of the quantization of the Berry winding characterizing the topology of these crossings in dimension $D=2$. Based on the historical example of $2$-bands crossing occuring in graphene, we propose to relate these Berry windings to the topological Chern number of a $D=3$ dimensional extension of these crossings. This dimensional embedding is obtained through a choice of a gap-opening potential. We show that the presence of an (emergent) $\mathcal{PT}$ symmetry, local in momentum and antiunitary, allows us to relate $D=3$ Chern numbers to $D=2$ Berry windings quantized as multiple of $π$. We illustrate this quantization mechanism on a variety of three-band crossings.

cond-mat.mes-hall↗

arXiv2017

Signature of the Chiral Anomaly in Ballistic Magneto-Transport

We compute the magneto-conductance of a short junction made out of a Weyl semi-metal. We show that it displays quantum oscillations at low magnetic field and low temperature, before reaching a universal high-field regime where it increases linearly with the field. Besides identifying a new characterization of the physics of materials with Weyl singularities in their energy spectrum, this ballistic regime corresponds to the simplest setup to study and understand the manifestation of the so-called chiral anomaly of massless relativistic particles in condensed matter. At low fields the algebraic in field magneto-conductance incorporates contributions besides the anomalous chiral current while the linear conductance at higher fields constitutes an unambiguous signature of the chiral anomaly in a Weyl conductor. Finally, we study the dependence of the ballistic magneto-conductance on the chemical potential, and discuss the cross-over towards the diffusive regime when elastic scattering is present.

cond-mat.mes-hall↗

arXiv2016

On the disorder-driven quantum transition in three-dimensional relativistic metals

The Weyl semimetals are topologically protected from a gap opening against weak disorder in three dimensions. However, a strong disorder drives this relativistic semimetal through a quantum transition towards a diffusive metallic phase characterized by a finite density of states at the band crossing. This transition is usually described by a perturbative renormalization group in $d=2+\varepsilon$ of a $U(N)$ Gross-Neveu model in the limit $N \to 0$. Unfortunately, this model is not multiplicatively renormalizable in $2+\varepsilon$ dimensions: An infinite number of relevant operators are required to describe the critical behavior. Hence its use in a quantitative description of the transition beyond one-loop is at least questionable. We propose an alternative route, building on the correspondence between the Gross-Neveu and Gross-Neveu-Yukawa models developed in the context of high energy physics. It results in a model of Weyl fermions with a random non-Gaussian imaginary potential which allows one to study the critical properties of the transition within a $d=4-\varepsilon$ expansion. We also discuss the characterization of the transition by the multifractal spectrum of wave functions.

cond-mat.dis-nn↗

arXiv2016

New Quantum Transition in Weyl Semimetals with Correlated Disorder

A Weyl semimetal denotes an electronic phase of solids in which two bands cross linearly. In this paper we study the effect of a spatially correlated disorder on such a phase. Using a renormalization group analysis, we show that in three dimensions, three scenarios are possible depending on the disorder correlations. A standard transition is recovered for short range correlations. For disorder decaying slower than $1/r^{2}$, the Weyl semimetal is unstable to any weak disorder and no transition persists. In between, a new phase transition occurs. This transition still separates a disordered metal from a semi-metal, but with a new critical behavior that we analyze to two-loop order.

cond-mat.mes-hall↗

arXiv2015

Minimal conductivity, topological Berry winding and duality in three-band semimetals

The physics of massless relativistic quantum particles has recently arisen in the electronic properties of solids following the discovery of graphene. Around the accidental crossing of two energy bands, the electronic excitations are described by a Weyl equation initially derived for ultra-relativistic particles. Similar three and four band semimetals have recently been discovered in two and three dimensions. Among the remarkable features of graphene are the characterization of the band crossings by a topological Berry winding, leading to an anomalous quantum Hall effect, and a finite minimal conductivity at the band crossing while the electronic density vanishes. Here we show that these two properties are intimately related: this result paves the way to a direct measure of the topological nature of a semi-metal. By considering three band semimetals with a flat band in two dimensions, we find that only few of them support a topological Berry phase. The same semimetals are the only ones displaying a non vanishing minimal conductivity at the band crossing. The existence of both a minimal conductivity and a topological robustness originates from properties of the underlying lattice, which are encoded not by a symmetry of their Bloch Hamiltonian, but by a duality.

cond-mat.mes-hall↗

arXiv2013

Broken Symmetries, Zero-Energy Modes, and Quantum Transport in Disordered Graphene: From Supermetallic to Insulating Regimes

The role of defect-induced zero-energy modes on charge transport in graphene is investigated using Kubo and Landauer transport calculations. By tuning the density of random distributions of monovacancies either equally populating the two sublattices or exclusively located on a single sublattice, all conduction regimes are covered from direct tunneling through evanescent modes to mesoscopic transport in bulk disordered graphene. Depending on the transport measurement geometry, defect density, and broken sublattice-symmetry, the Dirac point conductivity is either exceptionally robust against disorder (supermetallic state) or suppressed through a gap opening or by algebraic localization of zero-energy modes, whereas weak localization and the Anderson insulating regime are obtained for higher energies. These findings clarify the contribution of zero-energy modes to transport at the Dirac point, hitherto controversial.

cond-mat.mes-hall↗