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

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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>&amp;#x03BB;</mml:mi><mml:msup><mml:mi>&amp;#x03D5;</mml:mi><mml:mn>4</mml:mn></mml:msup></mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>&amp;#x03BB;</mml:mi><mml:msup><mml:mi>&amp;#x03D5;</mml:mi><mml:mn>4</mml:mn></mml:msup></mml:math> anharmonic oscillator ground state using IBM's quantum computer <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow class="MJX-TeXAtom-ORD"><mml:mtext mathvariant="monospace">ibm_sherbrooke</mml:mtext></mml:mrow></mml:math>. Using SeqHT, the depth of the required quantum circuits is reduced by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>&amp;#x223C;</mml:mo><mml:mn>30</mml:mn><mml:mi mathvariant="normal">&amp;#x0025;</mml:mi></mml:math>, 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.