Rigorous Bounds for Optimal Dynamical Decoupling

Abstract

We present rigorous performance bounds for the optimal dynamical decoupling pulse sequence protecting a quantum bit (qubit) against pure dephasing. Our bounds apply under the assumption of instantaneous pulses and of bounded perturbing environment and qubit-environment Hamiltonians. We show that if the total sequence time is fixed the optimal sequence can be used to make the distance between the protected and unperturbed qubit states arbitrarily small in the number of applied pulses. If, on the other hand, the minimum pulse interval is fixed and the total sequence time is allowed to scale with the number of pulses, then longer sequences need not always be advantageous. The rigorous bound may serve as testbed for approximate treatments of optimal decoupling in bounded models of decoherence.

11 pages, 3 figures, submitted to Phys Rev A

References in corpus (20)

• Dynamical Decoupling of Open Quantum Systems
• Dynamical suppression of decoherence in two-state quantum systems
• Keeping a Quantum Bit Alive by Optimized $\pi$-Pulse Sequences
• Optimized Dynamical Decoupling in a Model Quantum Memory
• Fault-Tolerant Quantum Dynamical Decoupling
• Symmetrizing Evolutions
• Electron spin dynamics in quantum dots and related nanostructures due to hyperfine interaction with nuclei
• 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
• Experimental Uhrig Dynamical Decoupling using Trapped Ions
• Universal pulse sequence to minimize spin dephasing in the central spin decoherence problem
• Near-optimal dynamical decoupling of a qubit
• Concatenated Control Sequences based on Optimized Dynamic Decoupling
• Optimized Dynamical Decoupling for Power Law Noise Spectra
• Distance Bounds on Quantum Dynamics
• Rigorous Bounds on the Performance of a Hybrid Dynamical Decoupling-Quantum Computing Scheme
• Efficient Coherent Control by Optimized Sequences of Pulses of Finite Duration
• Towards optimized suppression of dephasing in systems subject to pulse timing constraints
• Optimized Dynamical Decoupling for Time Dependent Hamiltonians

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• Optimizing electrically controlled echo sequences for the exchange-only qubit
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• Efficient Chromatic-Number-Based Multi-Qubit Decoherence and Crosstalk Suppression
• Virtual Z gates and symmetric gate compilation
• Symmetry-Enhanced Performance of Dynamical Decoupling
• Efficiency of Dynamical Decoupling for (Almost) Any Spin-Boson Model
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