Browse
Submit Data
Databases
API
Help

Dataset Information

0 Views

0 Connections

0 Citations

0 Reanalyses

0 Downloads

Omics score: 0

Observing ground-state properties of the Fermi-Hubbard model using a scalable algorithm on a quantum computer

ABSTRACT: The famous, yet unsolved, Fermi-Hubbard model for strongly-correlated electronic systems is a prominent target for quantum computers. However, accurately representing the Fermi-Hubbard ground state for large instances may be beyond the reach of near-term quantum hardware. Here we show experimentally that an efficient, low-depth variational quantum algorithm with few parameters can reproduce important qualitative features of medium-size instances of the Fermi-Hubbard model. We address 1 × 8 and 2 × 4 instances on 16 qubits on a superconducting quantum processor, substantially larger than previous work based on less scalable compression techniques, and going beyond the family of 1D Fermi-Hubbard instances, which are solvable classically. Consistent with predictions for the ground state, we observe the onset of the metal-insulator transition and Friedel oscillations in 1D, and antiferromagnetic order in both 1D and 2D. We use a variety of error-mitigation techniques, including symmetries of the Fermi-Hubbard model and a recently developed technique tailored to simulating fermionic systems. We also introduce a new variational optimisation algorithm based on iterative Bayesian updates of a local surrogate model. The Fermi-Hubbard model represents one of the benchmarks for testing quantum computational methods for condensed matter. Here, the authors are able to reproduce qualitative properties of the model on 1 × 8 and 2 × 4 lattices, by running a VQE-based algorithm on a superconducting quantum processor.

SUBMITTER: Stanisic S

PROVIDER: S-EPMC9553922 | biostudies-literature | 2022 Jan

REPOSITORIES: biostudies-literature

ACCESS DATA

Json Xml

Similar Datasets

Observing non-ergodicity due to kinetic constraints in tilted Fermi-Hubbard chains.

Project description:The thermalization of isolated quantum many-body systems is deeply related to fundamental questions of quantum information theory. While integrable or many-body localized systems display non-ergodic behavior due to extensively many conserved quantities, recent theoretical studies have identified a rich variety of more exotic phenomena in between these two extreme limits. The tilted one-dimensional Fermi-Hubbard model, which is readily accessible in experiments with ultracold atoms, emerged as an intriguing playground to study non-ergodic behavior in a clean disorder-free system. While non-ergodic behavior was established theoretically in certain limiting cases, there is no complete understanding of the complex thermalization properties of this model. In this work, we experimentally study the relaxation of an initial charge-density wave and find a remarkably long-lived initial-state memory over a wide range of parameters. Our observations are well reproduced by numerical simulations of a clean system. Using analytical calculations we further provide a detailed microscopic understanding of this behavior, which can be attributed to emergent kinetic constraints.

| S-EPMC8302618 | biostudies-literature

Long distance entanglement and high-dimensional quantum teleportation in the Fermi-Hubbard model.

Project description:The long distance entanglement in finite size open Fermi-Hubbard chains, together with the end-to-end quantum teleportation are investigated. We show the peculiarity of the ground state of the Fermi-Hubbard model to support maximum long distance entanglement, which allows it to operate as a quantum resource for high fidelity long distance quantum teleportation. We determine the physical properties and conditions for creating scalable long distance entanglement and analyze its stability under the effect of the Coulomb interaction and the hopping amplitude. Furthermore, we show that the choice of the measurement basis in the protocol can drastically affect the fidelity of quantum teleportation and we argue that perfect information transfer can be attained by choosing an adequate basis reflecting the salient properties of the quantum channel, i.e. Hubbard projective measurements.

| S-EPMC9849208 | biostudies-literature

Improved machine learning algorithm for predicting ground state properties.

Project description:Finding the ground state of a quantum many-body system is a fundamental problem in quantum physics. In this work, we give a classical machine learning (ML) algorithm for predicting ground state properties with an inductive bias encoding geometric locality. The proposed ML model can efficiently predict ground state properties of an n-qubit gapped local Hamiltonian after learning from only [Formula: see text] data about other Hamiltonians in the same quantum phase of matter. This improves substantially upon previous results that require [Formula: see text] data for a large constant c. Furthermore, the training and prediction time of the proposed ML model scale as [Formula: see text] in the number of qubits n. Numerical experiments on physical systems with up to 45 qubits confirm the favorable scaling in predicting ground state properties using a small training dataset.

| S-EPMC10828424 | biostudies-literature

Semiempirical Quantum-Chemical Orthogonalization-Corrected Methods: Benchmarks for Ground-State Properties.

Project description:The semiempirical orthogonalization-corrected OMx methods (OM1, OM2, and OM3) go beyond the standard MNDO model by including additional interactions in the electronic structure calculation. When augmented with empirical dispersion corrections, the resulting OMx-Dn approaches offer a fast and robust treatment of noncovalent interactions. Here we evaluate the performance of the OMx and OMx-Dn methods for a variety of ground-state properties using a large and diverse collection of benchmark sets from the literature, with a total of 13035 original and derived reference data. Extensive comparisons are made with the results from established semiempirical methods (MNDO, AM1, PM3, PM6, and PM7) that also use the NDDO (neglect of diatomic differential overlap) integral approximation. Statistical evaluations show that the OMx and OMx-Dn methods outperform the other methods for most of the benchmark sets.

| S-EPMC4785506 | biostudies-literature

Detecting quantum critical points in the t-[Formula: see text] Fermi-Hubbard model via complex network theory.

Project description:A considerable success in phenomenological description of [Formula: see text] superconductors has been achieved within the paradigm of Quantum Critical Point (QCP)-a parental state of a variety of exotic phases that is characterized by dense entanglement and absence of well-defined quasiparticles. However, the microscopic origin of the critical regime in real materials remains an open question. On the other hand, there is a popular view that a single-band t-[Formula: see text] Hubbard model is the minimal model to catch the main relevant physics of superconducting compounds. Here, we suggest that emergence of the QCP is tightly connected with entanglement in real space and identify its location on the phase diagram of the hole-doped t-[Formula: see text] Hubbard model. To detect the QCP we study a weighted graph of inter-site quantum mutual information within a four-by-four plaquette that is solved by exact diagonalization. We demonstrate that some quantitative characteristics of such a graph, viewed as a complex network, exhibit peculiar behavior around a certain submanifold in the parametric space of the model. This method allows us to overcome difficulties caused by finite size effects and to identify precursors of the transition point even on a small lattice, where long-range asymptotics of correlation functions cannot be accessed.

| S-EPMC7686386 | biostudies-literature

Experimental realization of an extended Fermi-Hubbard model using a 2D lattice of dopant-based quantum dots.

Project description:The Hubbard model is an essential tool for understanding many-body physics in condensed matter systems. Artificial lattices of dopants in silicon are a promising method for the analog quantum simulation of extended Fermi-Hubbard Hamiltonians in the strong interaction regime. However, complex atom-based device fabrication requirements have meant emulating a tunable two-dimensional Fermi-Hubbard Hamiltonian in silicon has not been achieved. Here, we fabricate 3 × 3 arrays of single/few-dopant quantum dots with finite disorder and demonstrate tuning of the electron ensemble using gates and probe the many-body states using quantum transport measurements. By controlling the lattice constants, we tune the hopping amplitude and long-range interactions and observe the finite-size analogue of a transition from metallic to Mott insulating behavior. We simulate thermally activated hopping and Hubbard band formation using increased temperatures. As atomically precise fabrication continues to improve, these results enable a new class of engineered artificial lattices to simulate interactive fermionic models.

| S-EPMC9652469 | biostudies-literature

Quantum Chemistry Dataset with Ground- and Excited-state Properties of 450 Kilo Molecules.

Project description:Due to rapid advancements in deep learning techniques, the demand for large-volume high-quality datasets grows significantly in chemical research. We developed a quantum-chemistry database that includes 443,106 small organic molecules with sizes up to 10 heavy atoms including C, N, O, and F. Ground-state geometry optimizations and frequency calculations of all compounds were performed at the B3LYP/6-31G* level with the BJD3 dispersion correction, while the excited-state single-point calculations were conducted at the ωB97X-D/6-31G* level. Totally twenty-seven molecular properties, such as geometric, thermodynamic, electronic and energetic properties, were gathered from these calculations. Meanwhile, we also established a comprehensive protocol for the construction of a high-volume quantum-chemistry dataset. Our QCDGE (Quantum Chemistry Dataset with Ground- and Excited-State Properties) dataset contains a substantial volume of data, exhibits high chemical diversity, and most importantly includes excited-state information. This dataset, along with its construction protocol, is expected to have a significant impact on the broad applications of machine learning studies across different fields of chemistry, especially in the area of excited-state research.

| S-EPMC11362161 | biostudies-literature

Realizing the symmetry-protected Haldane phase in Fermi-Hubbard ladders.

Project description:Topology in quantum many-body systems has profoundly changed our understanding of quantum phases of matter. The model that has played an instrumental role in elucidating these effects is the antiferromagnetic spin-1 Haldane chain1,2. Its ground state is a disordered state, with symmetry-protected fourfold-degenerate edge states due to fractional spin excitations. In the bulk, it is characterized by vanishing two-point spin correlations, gapped excitations and a characteristic non-local order parameter3,4. More recently it has been understood that the Haldane chain forms a specific example of a more general classification scheme of symmetry-protected topological phases of matter, which is based on ideas connected to quantum information and entanglement5-7. Here, we realize a finite-temperature version of such a topological Haldane phase with Fermi-Hubbard ladders in an ultracold-atom quantum simulator. We directly reveal both edge and bulk properties of the system through the use of single-site and particle-resolved measurements, as well as non-local correlation functions. Continuously changing the Hubbard interaction strength of the system enables us to investigate the robustness of the phase to charge (density) fluctuations far from the regime of the Heisenberg model, using a novel correlator.

| S-EPMC9200636 | biostudies-literature

Advantages of Unfair Quantum Ground-State Sampling.

Project description:The debate around the potential superiority of quantum annealers over their classical counterparts has been ongoing since the inception of the field. Recent technological breakthroughs, which have led to the manufacture of experimental prototypes of quantum annealing optimizers with sizes approaching the practical regime, have reignited this discussion. However, the demonstration of quantum annealing speedups remains to this day an elusive albeit coveted goal. We examine the power of quantum annealers to provide a different type of quantum enhancement of practical relevance, namely, their ability to serve as useful samplers from the ground-state manifolds of combinatorial optimization problems. We study, both numerically by simulating stoquastic and non-stoquastic quantum annealing processes, and experimentally, using a prototypical quantum annealing processor, the ability of quantum annealers to sample the ground-states of spin glasses differently than thermal samplers. We demonstrate that (i) quantum annealers sample the ground-state manifolds of spin glasses very differently than thermal optimizers (ii) the nature of the quantum fluctuations driving the annealing process has a decisive effect on the final distribution, and (iii) the experimental quantum annealer samples ground-state manifolds significantly differently than thermal and ideal quantum annealers. We illustrate how quantum annealers may serve as powerful tools when complementing standard sampling algorithms.

| S-EPMC5430793 | biostudies-literature

Two-dimensional ground-state mapping of a Mott-Hubbard system in a flexible field-effect device.

Project description:A Mott insulator sometimes induces unconventional superconductivity in its neighbors when doped and/or pressurized. Because the phase diagram should be strongly related to the microscopic mechanism of the superconductivity, it is important to obtain the global phase diagram surrounding the Mott insulating state. However, the parameter available for controlling the ground state of most Mott insulating materials is one-dimensional owing to technical limitations. Here, we present a two-dimensional ground-state mapping for a Mott insulator using an organic field-effect device by simultaneously tuning the bandwidth and bandfilling. The observed phase diagram showed many unexpected features such as an abrupt first-order superconducting transition under electron doping, a recurrent insulating phase in the heavily electron-doped region, and a nearly constant superconducting transition temperature in a wide parameter range. These results are expected to contribute toward elucidating one of the standard solutions for the Mott-Hubbard model.

| S-EPMC6510553 | biostudies-literature

OmicsDI is part of the ELIXIR infrastructure

OmicsDI is an Elixir interoperability service. Learn more ›

Tweets

OmicsDI Databases

PRIDE
PeptideAtlas
MassIVE
JPOST Repository
Physiome Model Repository

EGA
EVA
ENA
LINCS
PAXDB
Cell Collective

MetaboLights
Metabolomics Workbench
MetabolomeExpress
GNPS
BioModels
FAIRDOMHub

ArrayExpress
dbGaP
ExpressionAtlas
GEO
NODE

Information

Databases
Help
API
Contact us
Code on GitHub
Terms of use
Submit Data