Unification of Random Dynamical Decoupling and the Quantum Zeno Effect

Abstract

Periodic deterministic bang-bang dynamical decoupling and the quantum Zeno effect are known to emerge from the same physical mechanism. Both concepts are based on cycles of strong and frequent kicks provoking a subdivision of the Hilbert space into independent subspaces. However, previous unification results do not capture the case of random bang-bang dynamical decoupling, which can be advantageous to the deterministic case but has an inherently acyclic structure. Here, we establish a correspondence between random dynamical decoupling and the quantum Zeno effect by investigating the average over random decoupling evolutions. This protocol is a manifestation of the quantum Zeno dynamics and leads to a unitary bath evolution. By providing a framework that we call equitability of system and bath, we show that the system dynamics under random dynamical decoupling converges to a unitary with a decoupling error that characteristically depends on the convergence speed of the Zeno limit. This reveals a unification of the random dynamical decoupling and the quantum Zeno effect.

arXiv comment31 pages, 4 figures

References in corpus (30)

• Quantum Computing in the NISQ era and beyond
• 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
• Fault-Tolerant Quantum Dynamical Decoupling
• Quantum Zeno subspaces
• Quantum Zeno dynamics: mathematical and physical aspects
• Universal Control of Decoupled Quantum Systems
• Unification of Dynamical Decoupling and the Quantum Zeno Effect
• From the quantum Zeno to the inverse quantum Zeno effect
• Robust dynamical decoupling with bounded controls
• Control of decoherence: analysis and comparison of three different strategies
• Random decoupling schemes for quantum dynamical control and error suppression
• Procedures for Converting among Lindblad, Kraus and Matrix Representations of Quantum Dynamical Semigroups
• Randomized Benchmarking with Confidence
• On Quantum Control via Encoded Dynamical Decoupling
• Enhanced Convergence and Robust Performance of Randomized Dynamical Decoupling
• Quantum Zeno Dynamics from General Quantum Operations
• Principles of Control for Decoherence-Free Subsystems
• Generalized Adiabatic Theorem and Strong-Coupling Limits
• Operator-Schmidt decompositions and the Fourier transform, with applications to the operator-Schmidt numbers of unitaries
• One bound to rule them all: from Adiabatic to Zeno
• Advantages of Randomization in Coherent Quantum Dynamical Control
• Analysis of the quantum Zeno effect for quantum control and computation
• Quantum Zeno effect for open quantum systems
• Eternal Adiabaticity
• A polar decomposition for quantum channels (with applications to bounding error propagation in quantum circuits)
• Quantum Zeno effect generalized
• Randomized Dynamical Decoupling Techniques for Coherent Quantum Control
• Optimal convergence rate in the quantum Zeno effect for open quantum systems in infinite dimensions

Cited by in corpus (7)

• One bound to rule them all: from Adiabatic to Zeno
• Strong Error Bounds for Trotter & Strang-Splittings and Their Implications for Quantum Chemistry
• Purifying teleportation
• Lower Bounds for the Trotter Error
• Quantum control for the Zeno effect with noise
• Bath Dynamical Decoupling with a Quantum Channel
• Higher-order Zeno sequences