Perturbative Framework for Engineering Arbitrary Floquet Hamiltonian

• URL: http://arxiv.org/abs/2410.10467v2
• Date: Thu, 26 Dec 2024 10:22:22 GMT
• Title: Perturbative Framework for Engineering Arbitrary Floquet Hamiltonian
• Authors: Yingdan Xu, Lingzhen Guo,
• Abstract summary: We develop a systematic perturbative framework to engineer an arbitrary target Hamiltonian in the Floquet phase space. The high-order errors in the engineered Floquet Hamiltonian are mitigated by adding high-order driving potentials perturbatively.
• Score: 0.0
• License:
• Abstract: We develop a systematic perturbative framework to engineer an arbitrary target Hamiltonian in the Floquet phase space of a periodically driven oscillator based on Floquet-Magnus expansion. The high-order errors in the engineered Floquet Hamiltonian are mitigated by adding high-order driving potentials perturbatively. We introduce a transformation method that allows us to obtain an analytical expression of the leading-order correction drive for engineering a target Hamiltonian with discrete rotational and chiral symmetries in phase space. We also provide a numerically efficient procedure to calculate high-order correction drives and apply it to engineer the target Hamiltonian with degenerate eigenstates of multi-component cat states that are important for fault-tolerant hardware-efficiency bosonic quantum computation.

Related papers

• Multichromatic Floquet engineering of quantum dissipation [0.0]
  monochromatic driving of a quantum system is a successful technique in quantum simulations. We show that the time coarse-grained dynamics of such a driven closed quantum system is encapsulated in an effective Master equation. As an application, we emulate the dissipation induced by phase noise and incoherent emission/absorption processes in the bichromatic driving of a two-level system.
  arXiv  Detail & Related papers  (2023-06-02T16:51:28Z)
• Higher-Order Methods for Hamiltonian Engineering Pulse Sequence Design [0.0]
  We introduce a framework for designing Hamiltonian engineering pulse sequences that accounts for the effects of higher-order contributions to the Floquet-Magnus expansion. Our techniques result in simple, intuitive decoupling rules, despite the higher-order contributions naively involving complicated, non-local-in-time commutators.
  arXiv  Detail & Related papers  (2023-03-13T18:00:11Z)
• Engineering Arbitrary Hamiltonians in Phase Space [0.0]
  We introduce a general method to engineer arbitrary Hamiltonians in the Floquet phase space of a periodically driven oscillator. We establish the relationship between an arbitrary target Floquet Hamiltonian in phase space and the periodic driving potential in real space. Our protocol can be realised in a range of experimental platforms for nonclassical states generation and bosonic quantum computation.
  arXiv  Detail & Related papers  (2023-02-08T18:49:02Z)
• Non-perturbative Floquet engineering of the toric-code Hamiltonian and its ground state [0.0]
  We develop a hybrid continuous-digital strategy that exploits the commutativity of different terms in the target Hamiltonian. A proof-of-principle implementation of a topological device and its use to simulate the topological phase transition are also discussed.
  arXiv  Detail & Related papers  (2022-11-17T17:51:56Z)
• Simulating the Mott transition on a noisy digital quantum computer via Cartan-based fast-forwarding circuits [62.73367618671969]
  Dynamical mean-field theory (DMFT) maps the local Green's function of the Hubbard model to that of the Anderson impurity model. Quantum and hybrid quantum-classical algorithms have been proposed to efficiently solve impurity models. This work presents the first computation of the Mott phase transition using noisy digital quantum hardware.
  arXiv  Detail & Related papers  (2021-12-10T17:32:15Z)
• Analytical and experimental study of center line miscalibrations in M\o lmer-S\o rensen gates [51.93099889384597]
  We study a systematic perturbative expansion in miscalibrated parameters of the Molmer-Sorensen entangling gate. We compute the gate evolution operator which allows us to obtain relevant key properties. We verify the predictions from our model by benchmarking them against measurements in a trapped-ion quantum processor.
  arXiv  Detail & Related papers  (2021-12-10T10:56:16Z)
• Rotating Majorana Zero Modes in a disk geometry [75.34254292381189]
  We study the manipulation of Majorana zero modes in a thin disk made from a $p$-wave superconductor. We analyze the second-order topological corner modes that arise when an in-plane magnetic field is applied. We show that oscillations persist even in the adiabatic phase because of a frequency independent coupling between zero modes and excited states.
  arXiv  Detail & Related papers  (2021-09-08T11:18:50Z)
• Designing Kerr Interactions for Quantum Information Processing via Counterrotating Terms of Asymmetric Josephson-Junction Loops [68.8204255655161]
  static cavity nonlinearities typically limit the performance of bosonic quantum error-correcting codes. Treating the nonlinearity as a perturbation, we derive effective Hamiltonians using the Schrieffer-Wolff transformation. Results show that a cubic interaction allows to increase the effective rates of both linear and nonlinear operations.
  arXiv  Detail & Related papers  (2021-07-14T15:11:05Z)
• Benchmarking Embedded Chain Breaking in Quantum Annealing [0.0]
  The embedded Hamiltonian may violate the principles of adiabatic evolution and generate excitations that correspond to errors in the computed solution. We empirically benchmark the probability of chain breaks and identify sweet spots for solving a suite of embedded Hamiltonians.
  arXiv  Detail & Related papers  (2021-04-07T17:05:57Z)
• Simulating nonnative cubic interactions on noisy quantum machines [65.38483184536494]
  We show that quantum processors can be programmed to efficiently simulate dynamics that are not native to the hardware. On noisy devices without error correction, we show that simulation results are significantly improved when the quantum program is compiled using modular gates.
  arXiv  Detail & Related papers  (2020-04-15T05:16:24Z)
• Operator-algebraic renormalization and wavelets [62.997667081978825]
  We construct the continuum free field as the scaling limit of Hamiltonian lattice systems using wavelet theory. A renormalization group step is determined by the scaling equation identifying lattice observables with the continuum field smeared by compactly supported wavelets.
  arXiv  Detail & Related papers  (2020-02-04T18:04:51Z)

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.