Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 25 min ago
Peer-reviewedCC BY 4.0Quantum

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

  • Abhishek Kumar1,2
  • Karunya Shirali1,2
  • Nicholas J. Mayhall3,2
  • Sophia E. Economou1,2
  • Edwin Barnes1,2
  1. 1Department of Physics, Virginia Tech, Blacksburg, VA 24061, USA
  2. 2Virginia Tech Center for Quantum Information Science and Engineering, Blacksburg, VA 24061, USA
  3. 3Department of Chemistry, Virginia Tech, Blacksburg, VA 24061, USA
Open at sourcePDFDOICite

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.

Related

  1. Floquet analysis of coherence in periodically driven diamond NV ensemble systems
    Cuong M. Nguyen, Uijin Ko, Seong-Joo Lee +3
    arXivPreprintCC BY-NC-SA 4.0Full textQuantum physics & quantum informationarXiv
  2. Generating pairwise entanglement in periodically driven quantum spin chains with stochastic resetting
    Sinchan Ghosh, Manas Kulkarni, K. Sengupta +1
    Physical Review BPeer-reviewedLicence not statedAtomic, molecular & optical physicsHAL
  3. Quantum communication and Bell nonlocality require infinite classical communication to simulate
    Carlos de Gois, Thyago S. R. Santos, Carlos Vieira
    arXivPreprintarXiv licenceFull textQuantum physics & quantum informationarXiv
  4. Quality-of-Transmission Estimation in Quantum Networks: Compute, Simulate, or Learn?
    Anis Bekri, Amar Abane, Van Sy Mai +2
    arXivPreprintarXiv licenceFull textQuantum physics & quantum informationarXiv
  5. What Does It Cost to Simulate a Quantum Sentence Classifier? An Energy and Compute Perspective on Near-Term QNLP
    Kishlay Kashyap, Sandipan Ganguly
    arXivPreprintCC BY-NC-ND 4.0Full textQuantum physics & quantum informationarXiv

Cite

BibTeXRIS
BibTeX
@article{kumar2026floquetadaptvqe,
  title = {{Floquet-ADAPT-VQE: A Quantum Algorithm to Simulate Non-Equilibrium Physics in Periodically Driven Systems}},
  author = {Abhishek Kumar and Karunya Shirali and Nicholas J. Mayhall and Sophia E. Economou and Edwin Barnes},
  journal = {Quantum},
  year = {2026},
  month = oct,
  doi = {10.22331/q-2026-10-23-2247},
  url = {https://quantum-journal.org/papers/q-2026-10-23-2247/},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Floquet-ADAPT-VQE: A Quantum Algorithm to Simulate Non-Equilibrium Physics in Periodically Driven Systems
AU  - Abhishek Kumar
AU  - Karunya Shirali
AU  - Nicholas J. Mayhall
AU  - Sophia E. Economou
AU  - Edwin Barnes
PY  - 2026
DA  - 2026/10/23
JO  - Quantum
DO  - 10.22331/q-2026-10-23-2247
UR  - https://quantum-journal.org/papers/q-2026-10-23-2247/
AB  - 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.
SN  - 2521-327X
ER  -