Dynamical Quantum Error Correction of Unitary Operations with Bounded Controls

TL;DR

This paper extends dynamical quantum error correction techniques to ensure decoherence suppression during generic quantum gate operations using only bounded controls, with explicit constructions and numerical validation.

Contribution

It develops a framework for achieving decoherence-protected quantum gates with bounded controls, including explicit constructions for relevant error models and numerical validation.

Findings

Effective fidelity performance in non-Markovian spin-bath models

Robustness against systematic control errors in perturbative regimes

Explicit constructions for linear decoherence and pure dephasing models

Abstract

Dynamically corrected gates were recently introduced [Khodjasteh and Viola, Phys. Rev. Lett. 102, 080501 (2009)] as a tool to achieve decoherence-protected quantum gates based on open-loop Hamiltonian engineering. Here, we further expand the framework of dynamical quantum error correction, with emphasis on elucidating under what conditions decoherence suppression can be ensured while performing a generic target quantum gate, using only available bounded-strength control resources. Explicit constructions for physically relevant error models are detailed, including arbitrary linear decoherence and pure dephasing on qubits. The effectiveness of dynamically corrected gates in an illustrative non-Markovian spin-bath setting is investigated numerically, confirming the expected fidelity performance in a wide parameter range. Robutness against a class of systematic control errors is automatically incorporated in the perturbative error regime.