Reducing sequencing complexity in dynamical quantum error suppression by Walsh modulation

TL;DR

This paper introduces Walsh dynamical decoupling sequences that simplify quantum error suppression by reducing sequencing complexity, leveraging digital-compatible Walsh functions for efficient, flexible, and robust quantum control.

Contribution

It develops a unifying Walsh-based framework for dynamical decoupling sequences, enhancing error suppression efficiency and enabling digital-compatible quantum error correction methods.

Findings

Walsh sequences include many known and new dynamical decoupling protocols.

The number of Rademacher functions determines error suppression effectiveness.

Walsh modulation can protect nontrivial quantum logic gates.

Abstract

We study dynamical error suppression from the perspective of reducing sequencing complexity, in order to facilitate efficient semi-autonomous quantum-coherent systems. With this aim, we focus on digital sequences where all interpulse time periods are integer multiples of a minimum clock period and compatibility with simple digital classical control circuitry is intrinsic, using so-called em Walsh functions as a general mathematical framework. The Walsh functions are an orthonormal set of basis functions which may be associated directly with the control propagator for a digital modulation scheme, and dynamical decoupling (DD) sequences can be derived from the locations of digital transitions therein. We characterize the suite of the resulting Walsh dynamical decoupling (WDD) sequences, and identify the number of periodic square-wave (Rademacher) functions required to generate a Walsh function as the key determinant of the error-suppressing features of the relevant WDD sequence. WDD forms a unifying theoretical framework as it includes a large variety of well-known and novel DD sequences, providing significant flexibility and performance benefits relative to basic quasi-periodic design. We also show how Walsh modulation may be employed for the protection of certain nontrivial logic gates, providing an implementation of a dynamically corrected gate. Based on these insights we identify Walsh modulation as a digital-efficient approach for physical-layer error suppression.