# Robust Quantum Control against Clock Noises in Multi-Qubit Systems

## TL;DR

This paper addresses the challenge of clock noise in multi-qubit quantum control by deriving an error estimation formula, proposing optimization algorithms for robustness, and demonstrating their effectiveness through simulations.

## Contribution

It introduces a quantitative measure for control robustness against clock noises and develops two optimization algorithms, homotopic and b-GRAPE, to enhance robustness in quantum control.

## Key findings

- Both algorithms significantly improve robustness against clock noises.
- Homotopic algorithm converges faster.
- b-GRAPE achieves more robust controls.

## Abstract

High-precision manipulation of multi-qubit quantum systems requires strictly clocked and synchronized multi-channel control signals. However, practical Arbitrary Waveform Generators (AWGs) always suffer from random signal jitters and channel latencies that induces non-ignorable state or gate operation errors. In this paper, we analyze the average gate error caused by clock noises, from which an estimation formula is derived for quantifying the control robustness against clock noises. This measure is then employed for finding robust controls via a homotopic optimization algorithm. We also introduce our recently proposed stochastic optimization algorithm, b-GRAPE, for training robust controls via randomly generated clock noise samples. Numerical simulations on a two-qubit example demonstrate that both algorithms can greatly improve the control robustness against clock noises. The homotopic algorithm converges much faster than the b-GRAPE algorithm, but the latter can achieve more robust controls against clock noises.