We propose a novel quantum computing architecture that combines the engineered electromagnetic properties of quantum metamaterials with the strongly correlated electron physics of magic-angle systems. By integrating magic-angle twisted bilayer graphene (MATBG) into superconducting metamaterial waveguides, we demonstrate theoretically that the resulting hybrid system exhibits: (1) enhanced qubit coherence through geometric control of electromagnetic modes, (2) tunable qubit-qubit coupling via metamaterial dispersion engineering, and (3) topologically protected quantum states arising from the interplay of moiré band structure and metamaterial boundary conditions. Our framework provides design equations for a scalable quantum computing platform that leverages both the flat-band physics of magic-angle materials and the controllable photon-matter interactions of quantum metamaterials.
We propose a novel quantum computing architecture that combines the engineered electromagnetic properties of quantum metamaterials with the strongly correlated electron physics of magic-angle systems. By integrating magic-angle twisted bilayer graphene (MATBG) into superconducting metamaterial waveguides, we demonstrate theoretically that the resulting hybrid system exhibits: (1) enhanced qubit coherence through geometric control of electromagnetic modes, (2) tunable qubit-qubit coupling via metamaterial dispersion engineering, and (3) topologically protected quantum states arising from the interplay of moiré band structure and metamaterial boundary conditions. Our framework provides design equations for a scalable quantum computing platform that leverages both the flat-band physics of magic-angle materials and the controllable photon-matter interactions of quantum metamaterials.
Magic-angle twisted bilayer graphene (MATBG) presents a fascinating platform for investigating the effects of electron interactions in topological flat bands. The Bistritzer-MacDonald (BM) model provides a simplified quantitative description of the flat bands. Introducing long-range Coulomb interactions leads to an interacting BM (IBM) Hamiltonian, a momentum-space continuum description which offers a very natural starting point for many-body studies of MATBG. Accurate and reliable many-body computations in the IBM model are challenging, however, and have been limited mostly to special fillings or smaller lattice sizes. We employ a state-of-the-art auxiliary-field quantum Monte Carlo (AFQMC) method to study the IBM model, which constrains the sign problem to enable accurate treatment of large system sizes. We determine ground-state properties and quantify errors compared to mean-field theory calculations. Our calculations identify correlated metal states and their competition with the insulating Kramers intervalley-coherent state at both half-filling and charge neutrality. Additionally, we investigate one- and three-quarter fillings, and examine the effect of many-body corrections beyond single Slater determinant solutions. We discuss the effect that details of the IBM Hamiltonian have on the results, including different forms of double-counting corrections, and the need to establish and precisely specify many-body Hamiltonians to allow more direct and quantitative comparisons with experiments in MATBG.
Abstract At a magic relative twist angle, magic angle twisted bilayer graphene (MATBG) has an octet of flat bands that can host strong correlation physics when partially filled. A key theoretical discovery in MATBG is the existence of ferromagnetic Slater determinants as exact ground states of the corresponding flat band interacting (FBI) Hamiltonian. The FBI Hamiltonian describes the behavior of electrons that interact with each other in a high-dimensional space, and is constructed from the band structure of the non-interacting Bistritzer–MacDonald model at the chiral limit. A key property of the FBI Hamiltonian for MATBG is that it is frustration-free and can be written as a sum of non-commuting terms. In this work, we provide a complete characterization of the ground state manifold of the FBI Hamiltonian, proving that it is precisely the linear span of such ferromagnetic Slater determinants.
Moiré superlattices in twisted bilayer graphene and transition-metal dichalcogenides have emerged as a powerful tool for engineering novel band structures and quantum phases of two-dimensional quantum materials. Here we investigate Moiré physics emerging from twisting two independent hexagonal optical lattices of atomic (pseudo-)spin states (instead of bilayers) that exhibit remarkably different physics from twisted bilayer graphene. We employ a momentum-space tight-binding calculation that includes all range real-space tunnelings and show that all twist angles θ≲6° can become magic and support gapped flat bands. Because of the greatly enhanced density of states near the flat bands, the system can be driven to superfluidity by weak attractive interaction. Strikingly, the superfluid phase corresponds to a Larkin-Ovchinnikov state with finite momentum pairing that results from the interplay between flat bands and interspin interactions in the unique single-layer spin-twisted lattice. Our work may pave the way for exploring novel quantum phases and twistronics in cold atomic systems.
(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.
Recent years have seen rapid advances in our ability to harness, manipulate, or enhance quantum effects within artificial nanostructures and electronic metamaterials. Synthetic materials, including nanopatterned electronic structures, Moir´e materials, and quantum hetero-structures, can enable the bottom-up functional engineering of electronic band structure, electron-phonon interactions, thermal transport, kinetic nonlinearity, and other material properties. In turn, such functional materials engineering, when applied to superconducting nanoelectronics, can lead to enhanced functionalities and new operating regimes in devices ranging from SC qubits for quantum information science, single-photon detectors, quantum-limited parametric amplifiers, and millimeterwave quantum technologies. We propose to develop a new class of quantum-limited parametric amplifiers, based on superconducting (SC) Josephson metamaterials with strong and tailor-able nonlinearity in the microwave regime. Our innovation is in the establishment of a fundamentally new light-matter interacting system, through the unique combination of SC Josephson nonlinear metamaterials and surface magnon-polariton resonators.
Two-dimensional (2D) materials have emerged as a versatile and powerful platform for quantum technologies, offering atomic-scale control, strong quantum confinement, and seamless integration into heterogeneous device architectures. Their reduced dimensionality enables unique quantum phenomena, including optically addressable spin defects, tunable single-photon emitters, low-dimensional magnetism, gate-controlled superconductivity, and correlated states in Moiré superlattices. This Roadmap provides a comprehensive overview of recent progress and future directions in exploiting 2D materials for quantum sensing, computation, communication, and simulation. We survey advances spanning spin defects and quantum sensing, quantum emitters and nonlinear photonics, computational theory and data-driven discovery of quantum defects, spintronic and magnonic devices, cavity-engineered quantum materials, superconducting and hybrid quantum circuits, quantum dots, Moiré quantum simulators, and quantum communication platforms. Across these themes, we identify common challenges in defect control, coherence preservation, interfacial engineering, and scalable integration, alongside emerging opportunities driven by machine−learning−assisted design and integrated experiment−theory feedback loops. By connecting microscopic quantum states to mesoscopic excitations and macroscopic device architectures, this Roadmap outlines a materials-centric framework for integrating coherent quantum functionalities and positions 2D materials as foundational building blocks for next-generation quantum technologies.