Digital state preparation error in the adiabatic regime

Presenting Author: Lucas Kocia, Sandia National Laboratories
Contributing Author(s): Fernando A. Calderon-Vargas, Matthew D. Grace, Alicia B. Magann, James B. Larsen, Andrew D. Baczewski, Mohan Sarovar

Adiabatic time evolution can be used to prepare a complicated quantum many-body state from one that is easier to synthesize. The digitization of such an evolution introduces an additional structured contribution. We prove that the first-order Trotterization of an adiabatic evolution produces cumulative infidelity that scales as O(δt^2/T^2) instead of O(Tδt) expected from general Trotter bounds, where δt is the timestep and T is the total time. This greatly reduces the required circuit depth for adiabatic digital quantum simulation algorithms and explains why, despite increasing T, infidelities for constant-timestep digitized evolutions still decrease for a wide variety of Hamiltonians. As a consequence, this result resolves an open problem relating these evolutions to the quantum approximate optimization algorithm.

(Session 5 : Thursday from 5:00 pm - 7:00 pm)


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