Symmetry-Enhanced Performance of Dynamical Decoupling

Abstract

We consider a system with general decoherence and a quadratic dynamical decoupling sequence (QDD) for the coherence control of a qubit coupled to a bath of spins. We investigate the influence of the geometry and of the initial conditions of the bath on the performance of the sequence. The overall performance is quantified by a distance norm $d$. It is expected that $d$ scales with $T$, the total duration of the sequence, as $T^{\min \{N_x,N_z\}+1}$, where $N_x$ and $N_z$ are the number of pulses of the outer and of the inner sequence, respectively. We show both numerically and analytically that the state of the bath can boost the performance of QDD under certain conditions: The scaling of QDD for a given number of pulses can be enhanced by a factor of 2 if the bath is prepared in a highly symmetric state and if the system Hamiltonian is SU(2) invariant.

9 pages, 4 figures, published version

References in corpus (18)

• Optimized Dynamical Decoupling in a Model Quantum Memory
• Fault-Tolerant Quantum Dynamical Decoupling
• How to Enhance Dephasing Time in Superconducting Qubits
• Universality of Uhrig dynamical decoupling for suppressing qubit pure dephasing and relaxation
• Exact Results on Dynamical Decoupling by $\pi$-Pulses in Quantum Information Processes
• Universal pulse sequence to minimize spin dephasing in the central spin decoherence problem
• Exact dynamics in the inhomogeneous central-spin model
• Optimal pulse spacing for dynamical decoupling in the presence of a purely-dephasing spin-bath
• Performance comparison of dynamical decoupling sequences for a qubit in a rapidly fluctuating spin-bath
• Concatenated Control Sequences based on Optimized Dynamic Decoupling
• Protection of quantum systems by nested dynamical decoupling
• Distance Bounds on Quantum Dynamics
• Limits on Preserving Quantum Coherence using Multi-Pulse Control
• Rigorous Bounds for Optimal Dynamical Decoupling
• The Intrinsic Origin of Spin Echoes in Dipolar Solids Generated by Strong Pi Pulses
• Spin- and entanglement-dynamics in the central spin model with homogeneous couplings
• Wavefunction considerations for the central spin decoherence problem in a nuclear spin bath
• Generalization of short coherent control pulses: extension to arbitrary rotations

Cited by in corpus (1)

• Rigorous Performance Bounds for Quadratic and Nested Dynamical Decoupling