Self-healing of Trotter error in digital adiabatic state preparation

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 proce...

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Bibliographic Details
Published in:arXiv.org 2023-08
Main Authors: Kovalsky, Lucas K, Calderon-Vargas, Fernando A, Grace, Matthew D, Magann, Alicia B, Larsen, James B, Baczewski, Andrew D, Mohan Sarovar
Format: Article
Language:English
Subjects:
Adiabatic flow
Algorithms
Digitization
Evolution
Optimization
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2209.06242