Large-scale simulations of Floquet physics on near-term quantum computers

Abstract

Periodically driven quantum systems exhibit a diverse set of phenomena but are more challenging to simulate than their equilibrium counterparts. Here, we introduce the Quantum High-Frequency Floquet Simulation (QHiFFS) algorithm as a method to simulate fast-driven quantum systems on quantum hardware. Central to QHiFFS is the concept of a kick operator which transforms the system into a basis where the dynamics is governed by a time-independent effective Hamiltonian. This allows prior methods for time-independent simulation to be lifted to simulate Floquet systems. We use the periodically driven biaxial next-nearest neighbor Ising (BNNNI) model, a natural test bed for quantum frustrated magnetism and criticality, as a case study to illustrate our algorithm. We implemented a 20-qubit simulation of the driven two-dimensional BNNNI model on Quantinuum's trapped ion quantum computer. Our error analysis shows that QHiFFS exhibits not only a cubic advantage in driving frequency $\omega$ but also a linear advantage in simulation time $t$ compared to~Trotterization.

13 + 21 pages, 5 + 7 figures

References in corpus (25)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Quantum computational advantage using photons
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Simulating Hamiltonian dynamics with a truncated Taylor series
• Connecting ansatz expressibility to gradient magnitudes and barren plateaus
• Training variational quantum algorithms is NP-hard
• Observation of Time-Crystalline Eigenstate Order on a Quantum Processor
• Beyond Barren Plateaus: Quantum Variational Algorithms Are Swamped With Traps
• Observation of a many-body-localized discrete time crystal with a programmable spin-based quantum simulator
• Tailoring quantum gases by Floquet engineering
• Quantum circuits for strongly correlated quantum systems
• Equivalence of quantum barren plateaus to cost concentration and narrow gorges
• Barren plateaus preclude learning scramblers
• Observation of a symmetry-protected topological time crystal with superconducting qubits
• An efficient quantum algorithm for the time evolution of parameterized circuits
• Realizing a dynamical topological phase in a trapped-ion quantum simulator
• Variational Hamiltonian simulation for translational invariant systems via classical pre-processing
• Quantum simulation of three-body interactions in weakly driven quantum systems
• Algebraic Bethe Circuits
• Digital Quantum Simulation of Non-Equilibrium Quantum Many-Body Systems
• Dynamical simulation via quantum machine learning with provable generalization
• Reaching the equilibrium state of frustrated triangular Ising magnet Ca3Co2O6
• Quantum computing Floquet energy spectra
• Inducing and controlling superconductivity in Hubbard honeycomb model using an electromagnetic drive
• Real-time simulation of light-driven spin chains on quantum computers

Cited by in corpus (5)

• QFactor: A Domain-Specific Optimizer for Quantum Circuit Instantiation
• Time-dependent Hamiltonian Simulation via Magnus Expansion: Algorithm and Superconvergence
• Simulating Floquet scrambling circuits on trapped-ion quantum computers
• Shot-noise reduction for lattice Hamiltonians
• Generalized pulse design in Floquet engineering: Application to interacting spin systems