Sequency Hierarchy Truncation (SeqHT) for Adiabatic State Preparation and Time Evolution in Quantum Simulations

Zhiyao Li; Dorota M. Grabowska; Martin J. Savage

doi:10.22331/q-2025-09-29-1865

Sequency Hierarchy Truncation (SeqHT) for Adiabatic State Preparation and Time Evolution in Quantum Simulations

Zhiyao Li, Dorota M. Grabowska, and Martin J. Savage

InQubator for Quantum Simulation (IQuS), Department of Physics, University of Washington, Seattle, WA 98195

Published:	2025-09-29, volume 9, page 1865
Editor:	Fabio Anza
Eprint:	arXiv:2407.13835v2
Doi:	https://doi.org/10.22331/q-2025-09-29-1865
Citation:	Quantum 9, 1865 (2025).

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Abstract

We introduce the Sequency Hierarchy Truncation (SeqHT) scheme for reducing the resources required for state preparation and time evolution in quantum simulations, based upon a truncation in sequency. For the $\lambda\phi^4$ interaction in scalar field theory, or any interaction with a polynomial expansion, upper bounds on the contributions of operators of a given sequency are derived. For the systems we have examined, observables computed in sequency-truncated wavefunctions, including quantum correlations as measured by magic, are found to step-wise converge to their exact values with increasing cutoff sequency. The utility of SeqHT is demonstrated in the adiabatic state preparation of the $\lambda\phi^4$ anharmonic oscillator ground state using IBM's quantum computer $\texttt{ibm_sherbrooke}$. Using SeqHT, the depth of the required quantum circuits is reduced by $\sim 30\%$, leading to significantly improved determinations of observables in the quantum simulations. More generally, SeqHT is expected to lead to a reduction in required resources for quantum simulations of systems with a hierarchy of length scales.

Featured image: As quantum computers continue to advance and more resources become available, more and more sequency modes can be systematically included to improve precision of quantum simulations.

Popular summary

The Sequency Hierarchy Truncation (SeqHT) technique is introduced to reduce the resource requirements of quantum simulations of physical systems to a specified level of precision. The digital counterpart of applying a momentum cutoff to the frequency components in a physical system’s wavefunction, SeqHT performs a sequency truncation on quantum circuits used to prepare and evolve wavefunctions. As the sequency cutoff is increased, physical wavefunctions systematically approach their exact digitized form. As a demonstration, we apply SeqHT to the anharmonic oscillator with quartic self-interactions mapped to a register of qubits, adiabatically preparing the interacting ground state on IBM’s quantum computers. The required quantum resources are found to be reducible by up to 30%.

► BibTeX data

@article{Li2025sequencyhierarchy,
  doi = {10.22331/q-2025-09-29-1865},
  url = {https://doi.org/10.22331/q-2025-09-29-1865},
  title = {Sequency {H}ierarchy {T}runcation ({S}eq{HT}) for {A}diabatic {S}tate {P}reparation and {T}ime {E}volution in {Q}uantum {S}imulations},
  author = {Li, Zhiyao and Grabowska, Dorota M. and Savage, Martin J.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1865},
  month = sep,
  year = {2025}
}

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