Rigorous Performance Bounds for Quadratic and Nested Dynamical Decoupling

TL;DR

This paper establishes rigorous bounds on the effectiveness of quadratic and nested dynamical decoupling sequences in protecting qubits from decoherence, demonstrating that increasing pulses improves fidelity under realistic assumptions.

Contribution

It provides the first rigorous performance bounds for quadratic and nested dynamical decoupling sequences applicable to multi-qubit systems with bounded environment interactions.

Findings

Trace-norm distance can be made arbitrarily small with more pulses

Bounds apply under realistic assumptions of instantaneous pulses and bounded Hamiltonians

Protection effectiveness increases with the number of pulses

Abstract

We present rigorous performance bounds for the quadratic dynamical decoupling (QDD) pulse sequence which protects a qubit from general decoherence, and for its nested generalization to an arbitrary number of qubits. Our bounds apply under the assumption of instantaneous pulses and of bounded perturbing environment and qubit-environment Hamiltonians such as those realized by baths of nuclear spins in quantum dots. We prove that if the total sequence time is fixed then the trace-norm distance between the unperturbed and protected system states can be made arbitrarily small by increasing the number of applied pulses.