Protection of quantum systems by nested dynamical decoupling

TL;DR

This paper introduces a nested Uhrig dynamical decoupling (NUDD) scheme that efficiently protects multi-qubit quantum systems from decoherence using only single-qubit operations, with polynomially increasing control pulses.

Contribution

The paper presents a novel NUDD scheme that achieves arbitrary decoupling orders for multi-qubit systems with finite-amplitude pulses, expanding dynamical decoupling capabilities.

Findings

NUDD can protect multi-qubit systems to arbitrary order.

The number of control pulses grows polynomially with decoupling order.

Implementation is feasible with finite-amplitude pulses, with errors up to second order.

Abstract

Based on a theorem we establish on dynamical decoupling of time-dependent systems, we present a scheme of nested Uhrig dynamical decoupling (NUDD) to protect multi-qubit systems in generic quantum baths to arbitrary decoupling orders, using only single-qubit operations. The number of control pulses in NUDD increases polynomially with the decoupling order. For general multi-level systems, this scheme can preserve a set of unitary Hermitian system operators which mutually either commute or anti-commute, and hence all operators in the Lie algebra generated from this set of operators, generating an effective symmetry group for the system up to a given order of precision. NUDD can be implemented with pulses of finite amplitude, up to an error in the second order of the pulse durations.