## Quantum variational optimization: the role of entanglement and problem hardness

Pablo Díez-Valle (QUINFOG-IFF-CSIC)

Tuesday, January 04, 12:00

Quantum variational optimization has been posed as an alternative to solve optimization problems faster and at a larger scale than what classical methods allow. In this manuscript we study systematically the role of entanglement, the structure of the variational quantum circuit, and the structure of the optimization problem, in the success and efficiency of these algorithms. For that purpose, our study focuses on the Variational Quantum Eigensolver (VQE) algorithm, as applied to Quadratic Unconstrained Binary Optimization (QUBO) problems on random graphs with tunable density. Our numerical results indicate an advantage in adapting the distribution of entangling gates to the problem’s topology, specially for problems defined on low-dimensional graphs. Furthermore, we find evidence that applying CVaR type cost functions improves the optimization, increasing the probability of overlap with the optimal solutions. However, these techniques also improve the performance of ansatz based on product states (no entanglement), suggesting a new classical optimization method based on these could outperform existing NISQ architectures in certain regimes. Finally, our study also reveals a correlation between the hardness of a problem and the Hamming distance between the ground- and first-excited state, an idea that can be used to engineer benchmarks and understand the performance bottlenecks of optimization methods.quinfog-iff-csic

Online seminar

## ‘Impact of the external fields in topological semimetals: chiral electronics and tuning of the Fermi arcs’

Yuriko Baba D’Agostino (Universidad Complutense de Madrid)

Saturday, April 02, 12:00

Topological semimetals, such as Weyl and Dirac 3D semimetals, have attracted much interest in the last decade due to the promising new properties, especially related to their robust metallic surface states, called Fermi arcs. The effect of external perturbations such as electric fields or inversion-breaking terms enables the tuning of the surface states leading to non-trivial effects in transport properties. In this talk we will introduce the topological materials and specifically the topological semimetals. Once the basis are set, we describe the effect of external fields on Weyl semimetals. In particular, an electric field perpendicular to the surface generates a chiral dependent renormalization of the Fermi velocity in realistic low energy effective models [see Phys. Rev. B 100, 165105 (2019)]. On the other hand, the breaking of inversion symmetry produces a spin-orbit splitting that becomes non-negligible in a carefully designed sample [see New Journal of Physics 23(2) (2021)]. In a slab of topological semimetal, a substrate with heavy atoms should induce a strong and controllable Rashba spin-orbit coupling at the surface that will affect the Fermi arcs. In this case, the coupling between chiralities opens new possibilities for spin-dependent transport phenomena. Moreover, the effect of the impurities and the experimental feasibility will be discussed.

Online seminar

## Microscopy of driven ultracold atoms

Antonio Rubio (MPQ)

Sunday, April 03, 12:00

Ultracold atoms loaded in optical lattices have enabled studies in many exciting directions. On the one hand, these systems are almost ideal realizations of Hubbard models, while on the other hand, they make it possible to efficiently prepare arrays of closely spaced atoms, which can be used to tailor exotic interatomic interactions, e.g. by exciting them to Rydberg states. The opportunities for this platform have been further extended by quantum-gas microscopy, which allows the detection of site-resolved observables by using a high-resolution objective. In this talk, I will present two recent results from our bosonic quantum-gas microscope in MPQ. In the first part of the talk, I will discuss experiments on the periodically driven Bose-Hubbard model. While driven many-body systems are generically expected to heat up, at high drive frequencies these heating timescales can be extremely long, a phenomenon known as Floquet prethermalization. In our experiment, we monitor the drive-induced heating by measuring the emergence of site-resolved defects, and find evidence of an exponential-in-frequency suppression of the heating rates. The second part will focus on our recent observation of cooperative subradiance in a subwavelength array of atoms. By probing the system with a weak laser drive we are able to measure its spectral response and observe of two exciting properties: 1) a narrowing of the linewidth set by the quantum limit of the individual atoms, 2) a high reflectivity from the system, even though it is composed of only a single atomic layer.

Online seminar

## Quantum simulation of spin Hamiltonians with arrays of Rydberg atoms

Daniel Barredo (Laboratoire Charles Fabry, Institut d’Optique, CNRS Palaiseau, France. Nanomaterials and Nanotechnology Research Centre, CSIC Oviedo, Spain.)

Thursday, August 04, 12:00

Rydberg atoms in arrays of optical tweezers are among the most promising platforms for quantum simulation of many body quantum systems [1]. In this seminar, I will give a brief overview about the platform and report on our recent implementation of the antiferromagnetic Ising model with a transverse field in two different 2D geometries, a square and a triangular lattice, with up to 200 atoms [2]. By dynamically tuning the Hamiltonian we coherently drive the system across a phase transition and directly probe antiferromagnetic order. Individual control and readout of the qubits allows us to measure scalable order parameters, such as the staggered magnetization, during the dynamics. We compare these observables with state-of-the-art numerical simulations for up to 100 particles, where results are still theoretically tractable. This critical benchmark of the quantum simulation demonstrates that our platform is suitable to investigate spin models in regimes that can no longer be studied numerically, and where concepts such as geometrical frustration or spin liquids are not well understood.

Online seminar

## Coulomb Gases

Miguel Ortuño (Universidad de Murcia)

Saturday, March 04, 12:00

Coulomb glasses, also known as electron glasses, are systems with states localized by the disorder and Coulomb interactions between carriers. Localization reduces screening effects, increasing the importance of interaction effects. We review the different experimental manifestations of interactions in Coulomb glasses, as well as the numerical techniques developed for their simulations.

Online seminar

## Solving partial differential equations in quantum computers

Paula García-Molina (QUINFOG-IFF-CSIC)

Sunday, June 04, 12:00

In this work, we develop a variational quantum algorithm to solve partial differential equations (PDE’s) using a space-efficient variational ansatz that merges structured quantum circuits for coarse-graining with Fourier-based interpolation. We implement variational circuits to represent symmetrical smooth functions as the ansatz and combine them with classical optimizers that differ on the gradient calculation: no gradient, numerical gradient and analytic gradient. We apply this method to the computation of the ground state of the one-dimensional quantum harmonic oscillator and the transmon qubit. In idealized quantum computers, we show that the harmonic oscillator can be solved with an infidelity of order 10^−5 with 3 qubits and the transmon qubit with an error of order 10^−4 with 4 qubits. We find that these fidelities can be approached in real noisy quantum computers, either directly or through error mitigation techniques. However, we also find that the precision in the estimate of the eigenvalues is still sub-par with other classical methods, suggesting the need for better strategies in the optimization and the evaluation of the cost function itself.

Online seminar

## Topological quantum fluctuations and travelling wave amplifiers

Vittorio Peano (Max-Planck Institute for Light)

Friday, June 04, 12:00

It is now well-established that photonic systems can exhibit topological energy bands; similar to their electronic counterparts, this leads to the formation of chiral edge modes which can be used to transmit light in a manner that is protected against back-scattering. While it is understood how classical signals can propagate under these conditions, it is an outstanding important question how the quantum vacuum fluctuations of the electromagnetic field get modified in the presence of a topological band structure. We address this challenge by exploring a setting where a non-zero topological invariant guarantees the presence of a parametrically-unstable chiral edge mode in a system with boundaries, even though there are no bulk-mode instabilities. We show that one can exploit this to realize a topologically protected, quantum-limited travelling-wave parametric amplifier. The device is naturally protected both against internal losses and back-scattering; the latter feature is in stark contrast to standard travelling wave amplifiers. This adds a new example to the list of potential quantum devices that profit from topological transport.

Online seminar