Variational counterdiabatic driving of the Hubbard model for ground-state preparation

• URL: http://arxiv.org/abs/2206.07597v2
• Date: Mon, 20 Jun 2022 15:55:16 GMT
• Title: Variational counterdiabatic driving of the Hubbard model for ground-state preparation
• Authors: Q Xie, Kazuhiro Seki and Seiji Yunoki
• Abstract summary: Counterdiabatic protocols enable fast driving of quantum states by invoking an auxiliary adiabatic gauge potential (AGP) We show that the optimal variational parameters in the approximated AGP satisfy a set of linear equations whose coefficients are given by the squared Frobenius norms of these commutators. We then examine the CD driving of the one-dimensional Hubbard model up to $L = 14 sites with driving order $l leqslant 3$.
• Score: 0.7734726150561086
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Counterdiabatic (CD) protocols enable fast driving of quantum states by invoking an auxiliary adiabatic gauge potential (AGP) that suppresses transitions to excited states throughout the driving process. Usually, the full spectrum of the original unassisted Hamiltonian is a prerequisite for constructing the exact AGP, which implies that CD protocols are extremely difficult for many-body systems. Here, we apply a variational CD protocol recently proposed by P. W. Claeys et al. [Phys. Rev. Lett. 123, 090602 (2019)] to a two-component fermionic Hubbard model in one spatial dimension. This protocol engages an approximated AGP expressed as a series of nested commutators. We show that the optimal variational parameters in the approximated AGP satisfy a set of linear equations whose coefficients are given by the squared Frobenius norms of these commutators. We devise an exact algorithm that escapes the formidable iterative matrix-vector multiplications and evaluates the nested commutators and the CD Hamiltonian in analytic representations. We then examine the CD driving of the one-dimensional Hubbard model up to $L = 14$ sites with driving order $l \leqslant 3$. Our results demonstrate the usefulness of the variational CD protocol to the Hubbard model and permit a possible route towards fast ground-state preparation for many-body systems.

Related papers

• Improving variational counterdiabatic driving with weighted actions and computer algebra [0.0]
  Variational counterdiabatic (CD) driving is a disciplined and widely used method to robustly control quantum many-body systems.<n>Here, we reveal that introducing a new degree of freedom into the theory of the AGP can significantly improve variational CD driving.<n>We develop an efficient numerical algorithm to compute the refined driving protocol using computer algebra.
  arXiv  Detail & Related papers  (2025-05-23T20:51:51Z)
• Approximation of diffeomorphisms for quantum state transfers [49.1574468325115]
  We seek to combine two emerging standpoints in control theory. We numerically find control laws driving state transitions in a bilinear Schr"odinger PDE posed on the torus.
  arXiv  Detail & Related papers  (2025-03-18T17:28:59Z)
• Programming optical-lattice Fermi-Hubbard quantum simulators [39.58317527488534]
  We develop ground-state preparation algorithms for different fermionic models.<n>In particular, we first design variational, pre-compiled quantum circuits to prepare the ground state of the native Fermi-Hubbard model.<n>We discuss how to approximate the imaginary-time evolution using variational fermionic circuits.
  arXiv  Detail & Related papers  (2025-02-07T16:40:58Z)
• Can Transformers Do Enumerative Geometry? [44.99833362998488]
  We introduce a new paradigm in computational enumerative geometry in analyzing the $psi$-class intersection numbers on the moduli space of curves. We develop a Transformer-based model for computing $psi$-class intersection numbers based on the underlying quantum Airy structure. We go beyond merely computing intersection numbers and explore the enumerative "world-model" of the Transformers.
  arXiv  Detail & Related papers  (2024-08-27T09:44:01Z)
• Scalable approach to monitored quantum dynamics and entanglement phase transitions [0.0]
  Measurement-induced entanglement phase transitions in monitored quantum circuits have stimulated activity in a diverse research community. We present a solution by introducing a scalable protocol in $U(1)$ symmetric circuits.
  arXiv  Detail & Related papers  (2024-06-27T09:59:58Z)
• Bayesian Circular Regression with von Mises Quasi-Processes [57.88921637944379]
  In this work we explore a family of expressive and interpretable distributions over circle-valued random functions. For posterior inference, we introduce a new Stratonovich-like augmentation that lends itself to fast Gibbs sampling. We present experiments applying this model to the prediction of wind directions and the percentage of the running gait cycle as a function of joint angles.
  arXiv  Detail & Related papers  (2024-06-19T01:57:21Z)
• Noise-aware variational eigensolvers: a dissipative route for lattice gauge theories [40.772310187078475]
  We propose a novel variational ansatz for the ground-state preparation of the $mathbbZ$ lattice gauge theory (LGT) in quantum simulators. It combines dissipative and unitary operations in a completely deterministic scheme with a circuit depth that does not scale with the size of the considered lattice. We find that, with very few variational parameters, the ansatz can achieve $>!99%$ precision in energy in both the confined and deconfined phase of the $mathbbZ$ LGT.
  arXiv  Detail & Related papers  (2023-08-07T14:23:00Z)
• A hybrid quantum algorithm to detect conical intersections [39.58317527488534]
  We show that for real molecular Hamiltonians, the Berry phase can be obtained by tracing a local optimum of a variational ansatz along the chosen path. We demonstrate numerically the application of our algorithm on small toy models of the formaldimine molecule.
  arXiv  Detail & Related papers  (2023-04-12T18:00:01Z)
• Dissipative preparation and stabilization of many-body quantum states in a superconducting qutrit array [55.41644538483948]
  We present and analyze a protocol for driven-dissipatively preparing and stabilizing a manifold of quantum manybody entangled states. We perform theoretical modeling of this platform via pulse-level simulations based on physical features of real devices. Our work shows the capacity of driven-dissipative superconducting cQED systems to host robust and self-corrected quantum manybody states.
  arXiv  Detail & Related papers  (2023-03-21T18:02:47Z)
• Rotated ansatz for approximate counterdiabatic driving [0.0]
  We introduce a novel variational rotated ansatz (RA) to systematically generate experimentally accessible approximate CD protocols. We numerically benchmark our approach on state preparation and adiabatic quantum computing algorithms, and find that using RA protocols significantly enhances their performances.
  arXiv  Detail & Related papers  (2022-07-07T20:00:09Z)
• Algebraic Compression of Quantum Circuits for Hamiltonian Evolution [52.77024349608834]
  Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. We present an algorithm that compresses the Trotter steps into a single block of quantum gates. This results in a fixed depth time evolution for certain classes of Hamiltonians.
  arXiv  Detail & Related papers  (2021-08-06T19:38:01Z)
• Deep Gaussian Process Emulation using Stochastic Imputation [0.0]
  We propose a novel deep Gaussian process (DGP) inference method for computer model emulation using imputation. Byally imputing the latent layers, the approach transforms the DGP into the linked GP, a state-of-the-art surrogate model formed by linking a system of feed-forward coupled GPs.
  arXiv  Detail & Related papers  (2021-07-04T10:46:23Z)
• Scalable Variational Gaussian Processes via Harmonic Kernel Decomposition [54.07797071198249]
  We introduce a new scalable variational Gaussian process approximation which provides a high fidelity approximation while retaining general applicability. We demonstrate that, on a range of regression and classification problems, our approach can exploit input space symmetries such as translations and reflections. Notably, our approach achieves state-of-the-art results on CIFAR-10 among pure GP models.
  arXiv  Detail & Related papers  (2021-06-10T18:17:57Z)
• Floquet Engineering of Lie Algebraic Quantum Systems [13.939388417767136]
  We propose a Floquet engineering' formalism to systematically design a periodic driving protocol. The formalism is applicable to quantum systems which have an underlying closed Lie-algebraic structure.
  arXiv  Detail & Related papers  (2021-03-29T19:57:10Z)
• Analytic Design of Accelerated Adiabatic Gates in Realistic Qubits: General Theory and Applications to Superconducting Circuits [0.0]
  "Shortcuts to adiabaticity" is a general method for speeding up adiabatic quantum protocols. We develop an $analytic$ approach that allows one to go beyond these limitations. We show in detail how our ideas can be used to analytically design high-fidelity single-qubit "tripod" gates in a realistic superconducting fluxonium qubit.
  arXiv  Detail & Related papers  (2021-02-04T02:11:06Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.