Coherent interaction of multistate quantum systems possessing the Majorana and Morris-Shore dynamic symmetries with pulse trains

TL;DR

This paper derives exact analytic formulas for the interaction of multistate quantum systems with pulse trains, leveraging symmetries to simplify the dynamics and enabling applications in quantum gate analysis and quantum information processing.

Contribution

It introduces explicit formulas linking single-pulse and multi-pulse propagators for systems with Majorana and Morris-Shore symmetries, facilitating analysis of complex quantum interactions.

Findings

Derived explicit formulas for multi-pulse propagators

Linked single-step and multi-step quantum dynamics

Enabled applications in quantum gate error analysis

Abstract

We present exact analytic formulae which describe the interaction of multistate quantum systems possessing the Majorana and Morris-Shore dynamic symmetries with a train of pulses. The pulse train field can be viewed as repeated interactions of the quantum system with the same field and hence the overall propagator is expressed as the matrix power of the single-pulse propagator. Because of the Majorana and Morris-Shore symmetries the multistate dynamics is characterised by intrinsic two-state features, described by one or more pairs of complex-valued Cayley-Klein parameters. This facilitates the derivation of explicit formulae linking the single-step and multi-step propagators. The availability of such analytic relations opens the prospects for a variety of applications, e.g., analytic description of coherent pulse train interactions, or coherent amplification of quantum gate errors for accurate quantum gate tomography for ensembles of qubits, qutrits and generally qudits.