Time-optimal synthesis of unitary transformations in coupled fast and slow qubit system

TL;DR

This paper develops a canonical decomposition of SU(4) tailored for coupled qubit systems with different time scales, enabling efficient time-optimal control algorithms for quantum transformations.

Contribution

It introduces a new canonical decomposition of SU(4) for coupled qubits with disparate time scales, facilitating time-optimal control synthesis.

Findings

Canonical decomposition of SU(4) for coupled qubits

Time-optimal control algorithms for unitary synthesis

Application to electron-nuclear spin systems

Abstract

In this paper, we study time-optimal control problems related to system of two coupled qubits where the time scales involved in performing unitary transformations on each qubit are significantly different. In particular, we address the case where unitary transformations produced by evolutions of the coupling take much longer time as compared to the time required to produce unitary transformations on the first qubit but much shorter time as compared to the time to produce unitary transformations on the second qubit. We present a canonical decomposition of SU(4) in terms of the subgroup SU(2)xSU(2)xU(1), which is natural in understanding the time-optimal control problem of such a coupled qubit system with significantly different time scales. A typical setting involves dynamics of a coupled electron-nuclear spin system in pulsed electron paramagnetic resonance experiments at high fields. Using the proposed canonical decomposition, we give time-optimal control algorithms to synthesize various unitary transformations of interest in coherent spectroscopy and quantum information processing.