Bath Dynamical Decoupling with a Quantum Channel

Abstract

Bang-bang dynamical decoupling protects an open quantum system from decoherence due to its interaction with the surrounding bath/environment. In its standard form, this is achieved by strongly kicking the system with cycles of unitary operations, which average out the interaction Hamiltonian. In this paper, we generalize the notion of dynamical decoupling to repeated kicks with a quantum channel, which is applied to the bath. We derive necessary and sufficient conditions on the employed quantum channel and find that bath dynamical decoupling works if and only if the kick is ergodic. Furthermore, we study in which circumstances CPTP kicks on a mono-partite quantum system induce quantum Zeno dynamics with its Hamiltonian cancelled out. This does not require the ergodicity of the kicks, and the absence of decoherence-free subsystems is both necessary and sufficient. While the standard unitary dynamical decoupling is essentially the same as the quantum Zeno dynamics, our investigation implies that this is not true any more in the case of CPTP kicks. To derive our results, we prove some spectral properties of ergodic quantum channels, that might be of independent interest. Our approach establishes an enhanced and unified mathematical understanding of several recent experimental demonstrations and might form the basis of new dynamical decoupling schemes that harness environmental noise degrees of freedom.

26 pages, 3 figures, 1 table

References in corpus (55)

• Quantum Computing in the NISQ era and beyond
• Keeping a Quantum Bit Alive by Optimized $\pi$-Pulse Sequences
• Optimized Dynamical Decoupling in a Model Quantum Memory
• Fault-Tolerant Quantum Dynamical Decoupling
• Quantum Zeno subspaces
• Theory of Decoherence-Free Fault-Tolerant Universal Quantum Computation
• Quantum Zeno dynamics: mathematical and physical aspects
• Unification of Dynamical Decoupling and the Quantum Zeno Effect
• From the quantum Zeno to the inverse quantum Zeno effect
• Decoherence-Free Subspaces and Subsystems
• A Unified and Generalized Approach to Quantum Error Correction
• Robust dynamical decoupling with bounded controls
• Robust dynamical decoupling for quantum computing and quantum memory
• Quenching Spin Decoherence in Diamond through Spin Bath Polarization
• Performance of Deterministic Dynamical Decoupling Schemes: Concatenated and Periodic Pulse Sequences
• Random decoupling schemes for quantum dynamical control and error suppression
• Observing bulk diamond spin coherence in high-purity nanodiamonds
• Procedures for Converting among Lindblad, Kraus and Matrix Representations of Quantum Dynamical Semigroups
• High fidelity quantum gates via dynamical decoupling
• Controlling the quantum dynamics of a mesoscopic spin bath in diamond
• Introduction to Haar Measure Tools in Quantum Information: A Beginner's Tutorial
• A Brief History of the GKLS Equation
• Preserving qubit coherence by dynamical decoupling
• Unitary designs and codes
• Theory of Initialization-Free Decoherence-Free Subspaces and Subsystems
• Ergodic and Mixing Quantum Channels in Finite Dimensions
• On Quantum Control via Encoded Dynamical Decoupling
• Enhanced Convergence and Robust Performance of Randomized Dynamical Decoupling
• A method to find quantum noiseless subsystems
• On Protected Realizations of Quantum Information
• The Generalized Lyapunov Theorem and its Application to Quantum Channels
• Quantum Zeno Dynamics from General Quantum Operations
• Principles of Control for Decoherence-Free Subsystems
• Coherent transfer of electron spin correlations assisted by dephasing noise
• Operator-Schmidt decompositions and the Fourier transform, with applications to the operator-Schmidt numbers of unitaries
• High fidelity quantum memory via dynamical decoupling: theory and experiment
• One bound to rule them all: from Adiabatic to Zeno
• Coherent control of a nuclear spin via interactions with a rare-earth ion in the solid-state
• Advantages of Randomization in Coherent Quantum Dynamical Control
• Twirling and Hamiltonian Engineering via Dynamical Decoupling for GKP Quantum Computing
• On period, cycles and fixed points of a quantum channel
• Uniqueness of steady states of Gorini-Kossakowski-Sudarshan-Lindblad equations: a simple proof
• Asymptotics of quantum channels
• Criteria for Davies Irreducibility of Markovian Quantum Dynamics
• A continuous-time diffusion limit theorem for dynamical decoupling and intrinsic decoherence
• Quantum Zeno effect generalized
• Unification of Random Dynamical Decoupling and the Quantum Zeno Effect
• Randomized Dynamical Decoupling Techniques for Coherent Quantum Control
• Optimal convergence rate in the quantum Zeno effect for open quantum systems in infinite dimensions
• Concatenating quantum error-correcting codes with decoherence-free subspaces and vice versa
• Number of steady states of quantum evolutions
• On the Liouville-von Neumann equation for unbounded Hamiltonians
• On Strong Bounds for Trotter and Zeno Product Formulas with Bosonic Applications
• Asymptotic Dynamics of Open Quantum Systems and Modular Theory
• Product formulas in the framework of mean ergodic theorems