Work

On Strong Bounds for Trotter and Zeno Product Formulas with Bosonic Applications

Year: 2024

Type: article

Abstract: The Trotter product formula and the quantum Zeno effect are both indispensable tools for constructing time-evolutions using experimentally feasible building blocks. In this work, we discuss assumptions under which quantitative bounds can be proven in the strong operator topology on Banach spaces and provide natural bosonic examples. Specially, we assume the existence of a continuously embedded Banach space, which relatively bounds the involved generators and creates an invariant subspace of the limiting semigroup with a stable restriction. The slightly stronger assumption of admissible subspaces is well-recognized in the realm of hyperbolic evolution systems (time-dependent semigroups), to which the results are extended. By assuming access to a hierarchy of continuously embedded Banach spaces, Suzuki-higher-order bounds can be demonstrated. In bosonic applications, these embedded Banach spaces naturally arise through the number operator, leading to a diverse set of examples encompassing notable instances such as the Ornstein-Uhlenbeck semigroup and multi-photon driven dissipation used in bosonic error correction.

Source: Quantum

DOI: 10.22331/q-2024-07-25-1424

Author: Tim Möbus

Institutions: Munich Center for Quantum Science and Technology, Technical University of Munich

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $215

Funders: Deutsche Forschungsgemeinschaft, Eberhard Karls Universität Tübingen