Floquet-ADAPT-VQE: A Quantum Algorithm to Simulate Non-Equilibrium Physics in Periodically Driven Systems

Abhishek Kumar; Karunya Shirali; Nicholas J. Mayhall; Sophia E. Economou; Edwin Barnes

doi:10.22331/q-2026-10-23-2247

Floquet-ADAPT-VQE: A Quantum Algorithm to Simulate Non-Equilibrium Physics in Periodically Driven Systems

Abhishek Kumar^1,2, Karunya Shirali^1,2, Nicholas J. Mayhall^3,2, Sophia E. Economou^1,2, and Edwin Barnes^1,2

¹Department of Physics, Virginia Tech, Blacksburg, VA 24061, USA
²Virginia Tech Center for Quantum Information Science and Engineering, Blacksburg, VA 24061, USA
³Department of Chemistry, Virginia Tech, Blacksburg, VA 24061, USA

Published:	2026-10-23, volume 10, page 2247
Editor:	Di Fang
Eprint:	arXiv:2503.11613v3
Doi:	https://doi.org/10.22331/q-2026-10-23-2247
Citation:	Quantum 10, 2247 (2026).

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Abstract

Periodically driven quantum systems exhibit many fascinating phenomena absent in equilibrium systems, but their simulation is more challenging than that of static systems. Consequently, quantum simulation of these systems offers greater opportunity for achieving quantum advantage. To build the foundation for simulating time-periodic Hamiltonians, we utilize the Floquet-Hilbert space formalism to transform the Hamiltonian into a time-independent form and provide its Pauli decomposition. Within this formalism, we develop a hybrid quantum-classical algorithm, Floquet-ADAPT-VQE, that produces three key quantities that govern periodically driven quantum dynamics: the quasienergy, the associated Floquet eigenstates, and expectation values of observables with respect to these eigenstates. The latter is achieved by applying a fixed-depth quantum circuit to an initial Floquet eigenstate—an efficient construction made possible by the Floquet-Hilbert space formalism. We also identify a suitable auxiliary initial state whose squared Floquet energy is independent of the number of auxiliary qubits as well as the driving frequency, which leads to better convergence with fewer ADAPT iterations. We demonstrate our algorithm by performing numerical simulations on a periodically driven XYZ model with a magnetic field. We also explore potential applications of our algorithm for studying various non-equilibrium phenomena in periodically driven systems.

Popular summary

Quantum simulation offers a promising route to efficiently solving classically intractable problems in interacting many-body systems. Periodically driven many-body systems are particularly exciting: a repeating external drive can create phenomena absent in equilibrium, including time crystals and unusual topological phases. Their rich and challenging dynamics make them promising targets for quantum advantage.

In this work, we develop a framework for studying periodically driven systems using quantum computing tools designed for time-independent problems. Using the Floquet–Hilbert space formalism, we encode the periodic time dependence in an auxiliary quantum register, transforming the problem into a time-independent Hamiltonian in an extended space (Floquet–Hilbert space). We provide a systematic Pauli decomposition of this extended Floquet Hamiltonian, making it suitable for implementation on qubit-based quantum computers.

Building on this framework, we introduce Floquet-ADAPT-VQE, a hybrid quantum–classical algorithm that adaptively constructs circuits to calculate quasienergies—the counterparts of energies in driven systems—and prepare the associated Floquet states. Once an extended Floquet state is prepared, our framework also gives access to its micromotion, the dynamics within each driving cycle, and time-dependent observable expectation values using circuits whose depth does not grow with time. We also demonstrate the approach through numerical simulations of a periodically driven interacting spin model in a magnetic field.

In conclusion, our work establishes a foundation for adapting quantum algorithms for static systems to simulate periodically driven systems. It also demonstrates the benefits of using Floquet–Hilbert space. These contributions also pave the way for future algorithm development in this direction.

► BibTeX data

@article{Kumar2026floquetadaptvqe,
  doi = {10.22331/q-2026-10-23-2247},
  url = {https://doi.org/10.22331/q-2026-10-23-2247},
  title = {Floquet-{ADAPT}-{VQE}: {A} {Q}uantum {A}lgorithm to {S}imulate {N}on-{E}quilibrium {P}hysics in {P}eriodically {D}riven {S}ystems},
  author = {Kumar, Abhishek and Shirali, Karunya and Mayhall, Nicholas J. and Economou, Sophia E. and Barnes, Edwin},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {10},
  pages = {2247},
  month = oct,
  year = {2026}
}

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