Quantum computing Floquet energy spectra
arXiv:2112.04276 · doi:10.22331/q-2023-07-20-1063
Abstract
Quantum systems can be dynamically controlled using time-periodic external fields, leading to the concept of Floquet engineering, with promising technological applications. Computing Floquet energy spectra is harder than only computing ground state properties or single time-dependent trajectories, and scales exponentially with the Hilbert space dimension. Especially for strongly correlated systems in the low frequency limit, classical approaches based on truncation break down. Here, we present two quantum algorithms to determine effective Floquet modes and energy spectra. We combine the defining properties of Floquet modes in time and frequency domains with the expressiveness of parametrized quantum circuits to overcome the limitations of classical approaches. We benchmark our algorithms and provide an analysis of the key properties relevant for near-term quantum hardware.
arXiv comment21 pages, 7 figures
References in corpus (70)
- Quantum Computing in the NISQ era and beyond
- Photonic Floquet Topological Insulators
- Variational Quantum Algorithms
- Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
- Nonequilibrium dynamics of closed interacting quantum systems
- Experimental realisation of the topological Haldane model
- Many-body localization, thermalization, and entanglement
- Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
- Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
- Observation of Floquet-Bloch states on the surface of a topological insulator
- Atomic quantum gases in periodically driven optical lattices
- Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices
- Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
- Floquet Engineering of Quantum Materials
- Hamiltonian Simulation by Qubitization
- Electrodynamics of Correlated Electron Materials
- Simulating Hamiltonian dynamics with a truncated Taylor series
- Towards Practical Quantum Variational Algorithms
- High-frequency approximation for periodically driven quantum systems from a Floquet-space perspective
- Long-time behavior of periodically driven isolated interacting lattice systems
- Floquet scattering theory of quantum pumps
- Variational Quantum Computation of Excited States
- Theory of variational quantum simulation
- Semiclassical Fourier Transform for Quantum Computation
- A random compiler for fast Hamiltonian simulation
- Effective Hamiltonians, prethermalization and slow energy absorption in periodically driven many-body systems
- The Expressive Power of Parameterized Quantum Circuits
- Hybrid Quantum-Classical Approach to Quantum Optimal Control
- Simulating quantum many-body dynamics on a current digital quantum computer
- Many-body energy localization transition in periodically driven systems
- Ultrafast and reversible control of the exchange interaction in Mott insulators
- Classification of Interacting Topological Floquet Phases in One Dimension
- Variational Fast Forwarding for Quantum Simulation Beyond the Coherence Time
- Efficient Symmetry-Preserving State Preparation Circuits for the Variational Quantum Eigensolver Algorithm
- Topology and Broken Symmetry in Floquet Systems
- Arbitrary accuracy iterative phase estimation algorithm as a two qubit benchmark
- Correlated electron systems periodically driven out of equilibrium: Floquet + DMFT formalism
- Tailoring quantum gases by Floquet engineering
- Dissipative Floquet Topological Systems
- Controlled Population of Floquet-Bloch States via Coupling to Bose and Fermi Baths
- Faster quantum simulation by randomization
- Nonequilibrium steady states and transient dynamics of conventional superconductors under phonon driving
- Gate-efficient simulation of molecular eigenstates on a quantum computer
- Time evolution of a quantum many-body system: transition from integrability to ergodicity in thermodynamic limit
- Nonequilibrium Steady State of Photoexcited Correlated Electrons in the Presence of Dissipation
- Simulation of Nonequilibrium Dynamics on a Quantum Computer
- An efficient quantum algorithm for the time evolution of parameterized circuits
- Ergodic properties of a generic non-integrable quantum many-body system in thermodynamic limit
- Heating and many-body resonances in a periodically driven two-band system
- Dynamical Stability of a Many-body Kapitza Pendulum
- Optimal quantum circuits for general phase estimation
- Non-equilibrium electronic transport in a one-dimensional Mott insulator
- Classification and characterization of nonequilibrium Higgs modes in unconventional superconductors
- Evaluating the noise resilience of variational quantum algorithms
- Quantum-optimal-control-inspired ansatz for variational quantum algorithms
- Coherent Control of Bond Making
- Floquet Perturbation Theory: Formalism and Application to Low-Frequency Limit
- Scaling of variational quantum circuit depth for condensed matter systems
- Avoided level crossing spectroscopy with dressed matter waves
- Dimensional Expressivity Analysis of Parametric Quantum Circuits
- Nonequilibrium steady states of the electric-field-driven Mott insulator: Thermalization, emergent Wannier-Stark ladder, and dielectric breakdown
- Digital Quantum Simulation of Non-Equilibrium Quantum Many-Body Systems
- Detecting superconductivity out-of-equilibrium
- Noise-Resilient Quantum Dynamics Using Symmetry-Preserving Ansatzes
- Dynamical properties of a driven dissipative dimerized chain
- Spectral functions of a time-periodically driven Falicov-Kimball model: real-space Floquet DMFT study
- Laser pulse driven control of charge and spin order in the two-dimensional Kondo lattice
- Ultrafast Laser Driven Many-Body Dynamics and Kondo Coherence Collapse
- Momentum-resolved analysis of condensate dynamic and Higgs oscillations in quenched superconductors with tr-ARPES
- Estimating heating times in periodically driven quantum many-body systems via avoided crossing spectroscopy
Cited by in corpus (7)
- Large-scale simulations of Floquet physics on near-term quantum computers
- Noise-Robust Detection of Quantum Phase Transitions
- Randomised benchmarking for universal qudit gates
- Entanglement-informed Construction of Variational Quantum Circuits
- Quantum Software Ecosystem Design
- Probabilistic imaginary-time evolution in state-vector-based and shot-based simulations and on quantum devices
- Critical Scaling of the Quantum Wasserstein Distance