Self-Healing of Trotter Error in Digital Adiabatic State Preparation.

Autor:	Kovalsky LK; Quantum Algorithms and Applications Collaboratory, Sandia National Laboratories, Livermore, California 94550, USA., Calderon-Vargas FA; Quantum Algorithms and Applications Collaboratory, Sandia National Laboratories, Livermore, California 94550, USA., Grace MD; Quantum Algorithms and Applications Collaboratory, Sandia National Laboratories, Livermore, California 94550, USA., Magann AB; Quantum Algorithms and Applications Collaboratory, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA., Larsen JB; Quantum Algorithms and Applications Collaboratory, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA.; Department of Mathematics, Brigham Young University, Provo, Utah 84602, USA., Baczewski AD; Quantum Algorithms and Applications Collaboratory, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA., Sarovar M; Quantum Algorithms and Applications Collaboratory, Sandia National Laboratories, Livermore, California 94550, USA.
Jazyk:	angličtina
Zdroj:	Physical review letters [Phys Rev Lett] 2023 Aug 11; Vol. 131 (6), pp. 060602.
DOI:	10.1103/PhysRevLett.131.060602
Abstrakt:	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 nonadiabaticity 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 O(T^{-2}δt^{2}) instead of O(T^{2}δt^{2}) expected from general Trotter error bounds, where δt 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-δt digitized evolutions still decrease for a wide variety of Hamiltonians. It also establishes a correspondence between the quantum approximate optimization algorithm and digitized quantum annealing.
Databáze:	MEDLINE
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