The Coming Decades of Quantum Simulation

Contemporary quantum technologies face major difficulties in fault tolerant quantum computing with error correction, and focus instead on various shades of quantum simulation (Noisy Intermediate Scale Quantum, NISQ) devices, analogue and digital quantum simulators and quantum annealers. There is a clear need and quest for such systems that, without necessarily simulating quantum dynamics of some physical systems, can generate massive, controllable, robust, entangled, and superposition states. This will, in particular, allow the control of decoherence, enabling the use of these states for quantum communications (e.g. to achieve efficient transfer of information in a safer and quicker way), quantum metrology, sensing and diagnostics (e.g. to precisely measure phase shifts of light fields, or to diagnose quantum materials). In this Chapter we present a vision of the golden future of quantum simulators in the decades to come

Qubit-environment entanglement outside of pure decoherence: hyperfine interaction

In spin-based architectures of quantum devices, the hyperfine interaction between the electron spin qubit and the nuclear spin environment remains one of the main sources of decoherence. This paper provides a short review of the current advances in the theoretical description of the qubit decoherence dynamics. Next, we study the qubit-environment entanglement using negativity as its measure. For an initial maximally mixed state of the environment, we study negativity dynamics as a function of environment size, changing the numbers of environmental nuclei and the total spin of the nuclei. Furthermore, we study the effect of the magnetic field on qubit-environment disentangling time scales

Bounds on the capacity and power of quantum batteries

Quantum batteries, composed of quantum cells, are expected to outperform their classical analogs. The origin of such advantages lies in the role of quantum correlations, which may arise during the charging and discharging processes performed on the battery. In this theoretical work, we introduce a systematic characterization of the relevant quantities of quantum batteries, i.e., the capacity and the power, in relation to such correlations. For these quantities, we derive upper bounds for batteries that are a collection of non-interacting quantum cells with fixed Hamiltonians. The capacity, that is, a bound on the stored or extractable energy, is derived with the help of the energy-entropy diagram, and this bound is respected as long as the charging and discharging processes are entropy preserving. While studying power, we consider a geometric approach for the evolution of the battery state in the energy eigenspace of the battery Hamiltonian. Then, an upper bound for power is derived for arbitrary charging process, in terms of the Fisher information and the energy variance of the battery. The former quantifies the speed of evolution, and the latter encodes the non-local character of the battery state. Indeed, due to the fact that the energy variance is bounded by the multipartite entanglement properties of batteries composed of qubits, we establish a fundamental bound on power imposed by quantum entanglement. We also discuss paradigmatic models for batteries that saturate the bounds both for the stored energy and the power. Several experimentally realizable quantum batteries, based on integrable spin chains, the Lipkin-Meshkov-Glick and the Dicke models, are also studied in the light of these newly introduced bounds.We acknowledge the Spanish Ministry MINECO (National Plan 15 Grant: FISICATEAMO No. FIS2016-79508- P, SEVERO OCHOA No. SEV-2015-0522, FPI), European Social Fund, Fundació Cellex, Generalitat de Catalunya (AGAUR Grant No. 2017 SGR 1341 and CERCA/Program), EU FEDER, ERC AdG OSYRIS, EU FETPRO QUIC, and the National Science Centre, Poland-Symfonia Grant No. 2016/20/W/ST4/00314. M.N.B. gratefully acknowledges financial supports from Max-Planck Institute fellowship and from SERB-DST, Government of India, and A.R. thanks supports from CELLEX-ICFO-MPQ fellowship. We also thank M. Polini for fruitful discussions and for drawing our attention to Ref. [34], and an anonymous referee for motivating the finding of Corollary.Postprint (author's final draft

Simulating twistronics without a twist

We propose a scheme to emulate the essence of twisted bilayer graphene by exploiting ultracold atoms in an optical lattice. In our scheme, no bilayer nor twist are directly realized. Instead, two synthetic layers are produced exploiting coherently-coupled internal atomic states, and a supercell structure is generated via a spatially-dependent Raman coupling. We show that this system displays a band structure similar to that of magic angle twisted bilayer graphene, and explain its origin by deriving underlying effective Hamiltonians via perturbative approaches. Our proposal can be implemented using state-of-the-art experimental techniques, and opens the route towards the controlled study of strongly-correlated flat band accompanied by hybridization physics akin to magic angle bilayer graphene in cold atom quantum simulators.Comment: 9 pages, 8 figures, includes supplementary materia

Synthetic dimensions for topological and quantum phases: Perspective

In this Perspective article we report on recent progress on studies of synthetic dimensions, mostly, but not only, based on the research realized around the Barcelona groups (ICFO, UAB), Donostia (DIPC), Pozna\'n (UAM), Krak\'ow (UJ), and Allahabad (HRI). The concept of synthetic dimensions works particularly well in atomic physics, quantum optics, and photonics, where the internal degrees of freedom (Zeeman sublevels of the ground state, metastable excited states, or motional states for atoms, and angular momentum states or transverse modes for photons) provide the synthetic space. We describe our attempts to design quantum simulators with synthetic dimensions, to mimic curved spaces, artificial gauge fields, lattice gauge theories, twistronics, quantum random walks, and more

Theoretical models for quantum simulators of novel materials and devices

(English) Over the past three decades, optically trapped ultra-cold atoms have served as a versatile platform for controlled exploration of numerous condensed matter phenomena. The successful fabrication of magic angle twisted bi-layer graphene (MATBG) has introduced a for condensed matter physicists, while concurrently posing a novel challenge for the quantum simulation community. This thesis is devoted to addressing this problem, focusing mainly on the simulation of MATBG structures using ultra-cold atoms within its initial three chapters. To overcome the issue of unit cell expansion resulting from rotation misalignment, in the first chapter we propose the concept of "twist-less twistronics” (twistronics, a term coined from twist and electronics). This innovative notion involves replacing the physical rotation of one layer with a light-modulated hopping amplitude between the layers. Enabled by the architecture of ultra-cold atoms, this approach yields quasi-flat bands, a pivotal ingredient for collective phenomena observed in Magic-Angle Twisted Bilayer Graphene (MATBG), achieved at significantly reduced unit cell sizes. The opening chapter also presents a suitable experimental set-up. Moreover, it provides a comprehensive theoretical framework, including tight-binding calculations and effective models derived from perturbative analysis. The second chapter delves into the topological properties of an analogous system, emphasizing the energy separation between the quasi-flat bands and the resulting spectrum. We demonstrate Quantum Anomalous Hall Effect across diverse parameter regimes, accompanied by an exhaustive phase diagram with respect to tunable parameters. In the third chapter, we extend our investigation to encompass onsite, density-density attractive interactions between lattice atoms. Employing the Hartree-Fock-Bogoliubov mean-field approximation, we consider all feasible interaction channels within/between layers and spins. This chapter aims to elucidate the relationship between band flattening, a fully controlled parameter in our system, and the emergence/size of a superconductive gap. Notably, we uncover a substantial enhancement in the critical (Kosterlitz-Thouless) temperature within the quasi-flat band regime at quarter filling, along with a comprehensive diagram illustrating superconducting order parameters corresponding to each interaction channel. The fourth chapter marks a departure from condensed matter simulations, delving into "special purpose quantum computing" within the context of quantum batteries. These devices, analogous to their classical counterparts, store and release energy on demand, a process inherently governed by the battery Hamiltonian. Our work establishes a novel framework for assessing quantum battery performance and setting fundamental bounds on two key attributes: power and capacity. We investigate the essential Hamiltonian terms of a for achieving quantum speed-up in battery charging. The last, fifth chapter describes the theoretical tools, that have been used to support the first experimental realisation of the Extended Bose Hubbard model with dipolar excitons. We discuss the parameters of interests and important observables, such as a structure factor and discuss both the exact diagonalization and mean-field methods, which were necessary to verify the observation of strongly correlated phases at half and unit filling.(Català) Durant les últimes tres dècades, els àtoms ultrafreds atrapats òpticament han servit com a plataforma versàtil per a l'exploració controlada de nombrosos fenòmens de matèria condensada. L'èxit de la fabricació del grafè de bicapes rotades en angle màgic (magic angle twisted bi-layer graphene, MATBG) n’ha introduït una per als físics de matèria condensada, mentre que al mateix temps planteja un nou repte per a la comunitat en simulació quàntica. Aquesta tesi es dedica a abordar aquest problemàtica dins dels seus tres capítols inicials, centrant-se principalment en la simulació de les estructures MATBG utilitzant àtoms ultrafreds. Per superar la qüestió de l'expansió de la cel·la unitària resultant de la desalineació de la rotació, en el primer capítol proposem el concepte de "twist-less twistronics ". Aquesta noció innovadora implica substituir la rotació física d'una capa per salts en l’amplitud de llum modulada entre les capes. Aquest enfocament produeix bandes quasi planes activades per l'arquitectura d'àtoms ultrafreds, un ingredient fonamental per als fenòmens col·lectius observats en MATBG, aconseguit a mides per les cel·les unitàries significativament reduïdes. El capítol inicial també presenta la configuració experimental adequada. A més, proporciona un marc teòric exhaustiu, que inclou càlculs d'unió estreta i models efectius derivats de l'anàlisi pertorbativa. El segon capítol s'aprofundeix en les propietats topològiques d'un sistema anàleg, emfatitzant la separació d'energia entre les bandes quasi planes i l'espectre resultant. Demostrem l'efecte Hall quàntic anòmal a través de diversos règims de paràmetres, acompanyats d'un diagrama de fases exhaustiu respecte als paràmetres sintonitzables. En el tercer capítol, estenem la nostra investigació per incloure interaccions atractives densitat-densitat entre els àtoms de reticles in-situ. Utilitzant l'aproximació de camp mitjà Hartree-Fock-Bogoliubov, considerem tots els canals d'interacció factibles dins/entre capes i espins. Aquest capítol pretén dilucidar la relació entre l'aplanament de banda, un paràmetre totalment controlat en el nostre sistema, i l'aparició/mida d'un buit superconductiu. Notablement, descobrim una millora substancial en la temperatura crítica (Kosterlitz-Thouless) dins del règim de banda quasi plana a ompliment d’un quart, juntament amb un diagrama exhaustiu que il·lustra els paràmetres d'ordre superconductor corresponents a cada canal d'interacció. El quart capítol marca un desviament de les simulacions de matèria condensada, aprofundint en la "informàtica quàntica de propòsit especial" dins del context de les bateries quàntiques. Aquests dispositius, anàlegs als seus homòlegs clàssics, emmagatzemen i alliberen energia sota demanda, un procés inherentment governat per la bateria hamiltoniana. El nostre treball estableix un nou marc per avaluar el rendiment quàntic de la bateria i establir límits fonamentals en dos atributs clau: potència i capacitat. Investiguem els termes hamiltonians essencials per aconseguir l'acceleració quàntica en la càrrega de la bateria. L'últim capítol, cinquè, descriu les eines teòriques, que s'han utilitzat per donar suport a la primera realització experimental del model de Bose-Hubbard ampliat amb excitons dipolars. Es discuteixen els paràmetres d'interessos i els observables importants, com ara un factor d'estructura, i es discuteix tant la diagonalització exacta com els mètodes del camp mitjà, que eren necessaris per verificar l'observació de fases fortament correlacionades per la meitat i l'ompliment i onpliment complert