Alternating Projections Methods for Discrete-time Stabilization of Quantum States
arXiv:1612.05554 · doi:10.1109/TAC.2017.2731903
Abstract
We study sequences (both cyclic and randomized) of idempotent completely-positive trace-preserving quantum maps, and show how they asymptotically converge to the intersection of their fixed point sets via alternating projection methods. We characterize the robustness features of the protocol against randomization and provide basic bounds on its convergence speed. The general results are then specialized to stabilizing en- tangled states in finite-dimensional multipartite quantum systems subject to a resource constraint, a problem of key interest for quantum information applications. We conclude by suggesting further developments, including techniques to enlarge the set of stabilizable states and ensure efficient, finite-time preparation.
12 pages, no figures
References in corpus (10)
- An Open-System Quantum Simulator with Trapped Ions
- Feedback control of quantum state reduction
- Modeling and Control of Quantum Systems: An Introduction
- Quantum Feedback Networks: Hamiltonian Formulation
- The structure of preserved information in quantum processes
- Arbitrary quantum-state preparation of a harmonic oscillator via optimal control
- Towards the theory of control in observable quantum systems
- Decompositions of Hilbert Spaces, Stability Analysis and Convergence Probabilities for Discrete-Time Quantum Dynamical Semigroups
- Exact stabilization of entangled states in finite time by dissipative quantum circuits
- Switching Quantum Dynamics for Fast Stabilization