Dynamical decoupling sequences for multi-qubit dephasing suppression and long-time quantum memory

TL;DR

This paper develops a comprehensive framework for multi-qubit dephasing control using dynamical decoupling sequences, enabling high-order error suppression and long-time quantum memory by exploiting a novel displacement anti-symmetry property.

Contribution

It introduces an exact transfer filter-function framework for multi-qubit dephasing, constructing sequences that optimize error suppression and enable long-term quantum memory.

Findings

Multi-qubit sequences with high-order error suppression are constructed.

Sequences can be exponentially more efficient than existing methods.

Long-time quantum memory is achievable through sequence repetition and fidelity plateau conditions.

Abstract

We consider a class of multi-qubit dephasing models that combine classical noise sources and linear coupling to a bosonic environment, and are controlled by arbitrary sequences of dynamical decoupling pulses. Building on a general transfer filter-function framework for open-loop control, we provide an exact representation of the controlled dynamics for arbitrary stationary non-Gaussian classical and quantum noise statistics, with analytical expressions emerging when all dephasing sources are Gaussian. This exact characterization is used to establish two main results. First, we construct multi-qubit sequences that ensure maximum high-order error suppression in both the time and frequency domain and that can be exponentially more efficient than existing ones in terms of total pulse number. Next, we show how long-time multi-qubit storage may be achieved by meeting appropriate conditions for the emergence of a fidelity plateau under sequence repetition, thereby generalizing recent results for single-qubit memory under Gaussian dephasing. In both scenarios, the key step is to endow multi-qubit sequences with a suitable displacement anti-symmetry property, which is of independent interest for applications ranging from environment-assisted entanglement generation to multi-qubit noise spectroscopy protocols.