  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.
