Analytical and experimental study of center line miscalibrations in M\o lmer-S\o rensen gates

TL;DR

This paper provides an analytical and experimental analysis of how center line miscalibrations affect the fidelity of Mølmer-Sørensen gates in trapped ion quantum computers, aiding in improved calibration for high-fidelity operations.

Contribution

It introduces a systematic perturbative approach using Magnus expansion to predict the effects of miscalibrations on gate performance, validated by experimental benchmarks.

Findings

Analytical model accurately predicts gate errors due to miscalibrations.

Experimental results confirm the model's predictions.

Method aids in designing better calibration protocols for quantum gates.

Abstract

A major challenge for the realisation of useful universal quantum computers is achieving high fidelity two-qubit entangling gate operations. However, calibration errors can affect the quantum gate operations and limit their fidelity. To reduce such errors it is desirable to have an analytical understanding and quantitative predictions of the effects that miscalibrations of gate parameters have on the gate performance. In this work, we study a systematic perturbative expansion in miscalibrated parameters of the Molmer-Sorensen entangling gate, which is widely used in trapped ion quantum processors. Our analytical treatment particularly focuses on systematic center line detuning miscalibrations. Via a unitary Magnus expansion, we compute the gate evolution operator which allows us to obtain relevant key properties such as relative phases, electronic populations, quantum state purity and fidelities. These quantities, subsequently, are used to assess the performance of the gate using the fidelity of entangled states as performance metric. We verify the predictions from our model by benchmarking them against measurements in a trapped-ion quantum processor. The method and the results presented here can help design and calibrate high-fidelity gate operations of large-scale quantum computers.