https://doi.org/10.1140/epjp/s13360-025-06261-9
Regular Article
Aspects of complexity in quantum evolutions on the Bloch sphere
1
Department of Nanoscale Science and Engineering, University at Albany-SUNY, 12222, Albany, NY, USA
2
Department of Physics, University at Albany-SUNY, 12222, Albany, NY, USA
Received:
23
January
2025
Accepted:
25
March
2025
Published online:
30
April
2025
We enhance our quantitative comprehension of the complexity associated with both time-optimal and time sub-optimal quantum Hamiltonian evolutions that connect arbitrary source and target states on the Bloch sphere, as recently presented in Cafaro (Nucl Phys B 1010: 116755, 2025). Initially, we examine each unitary Schrödinger quantum evolution selected through various metrics, such as path length, geodesic efficiency, speed efficiency, and the curvature coefficient of the corresponding quantum-mechanical trajectory that connects the source state to the target state on the Bloch sphere. Subsequently, we evaluate the selected evolutions using our proposed measure of complexity, as well as in relation to the concept of complexity length scale. The choice of both time-optimal and time sub-optimal evolutions, along with the selection of source and target states, enables us to conduct pertinent sanity checks that seek to validate the physical relevance of the framework supporting our proposed complexity measure. Our research suggests that, in general, efficient quantum evolutions possess a lower complexity than their inefficient counterparts. However, it is important to recognize that complexity is not solely determined by length; in fact, longer trajectories that are adequately curved may exhibit a complexity that is less than or equal to that of shorter trajectories with a lower curvature coefficient.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
