Self-healing of Trotter error in digital adiabatic state preparation
- URL: http://arxiv.org/abs/2209.06242v2
- Date: Thu, 10 Aug 2023 23:21:32 GMT
- Title: Self-healing of Trotter error in digital adiabatic state preparation
- Authors: Lucas K. Kovalsky, Fernando A. Calderon-Vargas, Matthew D. Grace,
Alicia B. Magann, James B. Larsen, Andrew D. Baczewski, Mohan Sarovar
- Abstract summary: We prove that the first-order Trotterization of a complete adiabatic evolution has a cumulative infidelity that scales as $mathcal O(T-2 delta t2)$ instead of $mathcal O(T2delta t2)$ expected from general Trotter error bounds.
This result suggests a self-healing mechanism and explains why, despite increasing $T$, infidelities for fixed-$delta t$ digitized evolutions still decrease for a wide variety of Hamiltonians.
- Score: 52.77024349608834
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Adiabatic time evolution can be used to prepare a complicated quantum
many-body state from one that is easier to synthesize and Trotterization can be
used to implement such an evolution digitally. The complex interplay between
non-adiabaticity and digitization influences the infidelity of this process. We
prove that the first-order Trotterization of a complete adiabatic evolution has
a cumulative infidelity that scales as $\mathcal O(T^{-2} \delta t^2)$ instead
of $\mathcal O(T^2 \delta t^2)$ expected from general Trotter error bounds,
where $\delta t$ is the time step and $T$ is the total time. This result
suggests a self-healing mechanism and explains why, despite increasing $T$,
infidelities for fixed-$\delta t$ digitized evolutions still decrease for a
wide variety of Hamiltonians. It also establishes a correspondence between the
Quantum Approximate Optimization Algorithm (QAOA) and digitized quantum
annealing.
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