Year: 2022
Type: article
Abstract: We derive a universal nonperturbative bound on the distance between unitary evolutions generated by time-dependent Hamiltonians in terms of the difference of their integral actions. We apply our result to provide explicit error bounds for the rotating-wave approximation and generalize it beyond the qubit case. We discuss the error of the rotating-wave approximation over long time and in the presence of time-dependent amplitude modulation. We also show how our universal bound can be used to derive and to generalize other known theorems such as the strong-coupling limit, the adiabatic theorem, and product formulas, which are relevant to quantum-control strategies including the Zeno control and the dynamical decoupling. Finally, we prove generalized versions of the Trotter product formula, extending its validity beyond the standard scaling assumption.
Source: Quantum
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $215
Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Ministry of Education, Culture, Sports, Science and Technology, Regione Puglia, Istituto Nazionale di Fisica Nucleare, QuantERA, Gruppo Nazionale per la Fisica Matematica, Australian Research Council, Japan Society for the Promotion of Science
Awards: G1160787082, Quantum Measurement and Quantum Control: From Quantum Information Technologies to Foundations of Statistical Mechanics, ARC Centre of Excellence for Engineered Quantum Systems, Pushing the digital limits in quantum simulation for advanced manufacturing, Research on Dispersive Equations and Harmonic Analysis, G4883665254, G5032364540, G5998441483, G7886224254, Robust Quantum Control in the Noisy Intermediate-Scale Quantum Era, G8556958477
OpenAlex ID: W3211603258