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

TL;DR

The paper introduces SeqHT, a truncation scheme in quantum simulations that reduces resource requirements by truncating in sequency, demonstrated on a scalar field theory and IBM quantum hardware, improving efficiency and accuracy.

Contribution

SeqHT provides a novel truncation method based on sequency hierarchy, enabling resource-efficient quantum simulations with step-wise convergence of observables.

Findings

Circuit depth reduced by ~30% using SeqHT.

Observables converge step-wise with increasing sequency cutoff.

SeqHT improves resource efficiency in quantum simulations of hierarchical systems.

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 ${\textit ibm\_sherbrooke}$. 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.