Second-order shaped pulses for solid-state quantum computation

TL;DR

This paper introduces highly optimized second-order shaped pulses for solid-state quantum computing, enabling improved qubit control and error correction through detailed analytical and numerical analysis.

Contribution

It provides a systematic construction and analysis method for self-refocusing pulse shapes up to second order, enhancing quantum control techniques.

Findings

Optimized pulse shapes reduce errors in quantum rotations.

Analytical tools predict pulse performance in complex sequences.

Numerical methods complement analytical analysis for higher-order effects.

Abstract

We present the constructon and detailed analysis of highly-optimized self-refocusing pulse shapes for several rotation angles. We characterize the constructed pulses by the coefficients appearing in the Magnus expansion up to second order. This allows a semi-analytical analysis of the performance of the constructed shapes in sequences and composite pulses by computing the corresponding leading-order error operators. Higher orders can be analyzed with the numerical technique suggested by us previously. We illustrate the technique by analysing several composite pulses designed to protect against pulse amplitude errors, and on decoupling sequences for potentially long chains of qubits with on-site and nearest-neighbor couplings.