Higher-order Zeno sequences

TL;DR

This paper introduces higher-order Zeno sequences that significantly improve the convergence rate of quantum Zeno dynamics, enabling faster and more efficient quantum control through advanced measurement and control techniques.

Contribution

The authors develop a novel framework relating higher-order Zeno sequences to higher-order Trotter formulas, achieving improved error scaling and shorter sequences for quantum Zeno effects.

Findings

Achieved error scaling of (1/N^{2k}) with higher-order sequences.

Developed control fields that improve Zeno error scaling to second order.

Connected higher-order Zeno sequences to randomized and Uhrig dynamical decoupling.

Abstract

The quantum Zeno effect typically refers to freezing the dynamics of a quantum system through frequent observations. In general, quantum Zeno dynamics is obtained with an error of order $\mathcal{O}(1/N)$, where $N$ is the number of projective measurements performed within a fixed evolution time. In this work, we develop higher-order Zeno sequences that achieve faster convergence to Zeno dynamics, yielding an improved error scaling of $\mathcal{O}(1/N^{2k})$, where $k$ describes the order of the Zeno sequence. This is achieved by relating higher-order Zeno sequences to higher-order Trotter formulas that achieve similar convergence behavior. We leverage this relation to develop higher-order Zeno sequences for different manifestations of the quantum Zeno effect, including frequent projective measurements and unitary kicks. We go on to discuss achieving quantum Zeno dynamics through periodic control fields of high frequency. We explicitly develop control fields that yield a second-order type improvement in the Zeno error scaling and present shorter Zeno sequences. Finally, we discuss the connection to randomized and Uhrig dynamical decoupling to develop more efficient implementations in the weak coupling regime.