Protection of quantum systems by nested dynamical decoupling

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.

11 pages, fully rewritten from version 1, some corrections made from version 2

References in corpus (14)

• Optimized Dynamical Decoupling in a Model Quantum Memory
• Fault-Tolerant Quantum Dynamical Decoupling
• Performance of Deterministic Dynamical Decoupling Schemes: Concatenated and Periodic Pulse Sequences
• Universality of Uhrig dynamical decoupling for suppressing qubit pure dephasing and relaxation
• Exact Results on Dynamical Decoupling by $\pi$-Pulses in Quantum Information Processes
• Restoring Coherence Lost to a Slow Interacting Mesoscopic Bath
• Universal pulse sequence to minimize spin dephasing in the central spin decoherence problem
• Preserving qubit coherence by dynamical decoupling
• Performance comparison of dynamical decoupling sequences for a qubit in a rapidly fluctuating spin-bath
• Concatenated Control Sequences based on Optimized Dynamic Decoupling
• Optimization of Short Coherent Control Pulses
• Protecting unknown two-qubit entangled states by nesting Uhrig's dynamical decoupling sequences
• Advantages of Randomization in Coherent Quantum Dynamical Control
• Generalization of short coherent control pulses: extension to arbitrary rotations

Cited by in corpus (10)

• Multiqubit Spectroscopy of Gaussian Quantum Noise
• Preserving entanglement and nonlocality in solid-state qubits by dynamical decoupling
• Protecting and Enhancing Spin Squeezing via Continuous Dynamical Decoupling
• Concatenated dynamical decoupling with virtual pulses
• Spin-echo entanglement protection from random telegraph noise
• No-go theorem and optimization of dynamical decoupling against noise with soft cutoff
• Uhrig Dynamical Control of a Three-Level System Via Non-Markovian Quantum State Diffusion
• Extending quantum control of time-independent systems to time-dependent systems
• Dynamical Decoupling in Common Environment
• Short coherent control pulse with small random errors in its direction