Global control methods for Greenberger-Horne-Zeilinger-state generation on a one-dimensional Ising chain

Journal Article · Thu Jul 15 00:00:00 EDT 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.82.012330· OSTI ID:21442893

Xiaoting, Wang; Schirmer, Sophie G ^[1]; Bayat, Abolfazl; Bose, Sougato ^[2]

---

1. Department of Applied Maths and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)
2. Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT (United Kingdom)

We discuss how to prepare an Ising chain in a GHZ state using a single global control field only. This model does not require the spins to be individually addressable and is applicable to quantum systems such as cold atoms in optical lattices, some liquid- or solid-state NMR experiments, and many nanoscale quantum structures. We show that GHZ states can always be reached asymptotically from certain easy-to-prepare initial states using adiabatic passage, and under certain conditions finite-time reachability can be ensured. To provide a reference useful for future experimental implementations, three different control strategies to achieve the objective--adiabatic passage, Lyapunov control, and optimal control--are compared, and their advantages and disadvantages discussed, in particular in the presence of realistic imperfections such as imperfect initial state preparation, system inhomogeneity, and dephasing.

• OSTI ID: 21442893
• Journal Information: Physical Review. A, Vol. 82, Issue 1; Other Information: DOI: 10.1103/PhysRevA.82.012330; (c) 2010 The American Physical Society; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
ATOMS
ISING MODEL
LYAPUNOV METHOD
NANOSTRUCTURES
NUCLEAR MAGNETIC RESONANCE
ONE-DIMENSIONAL CALCULATIONS
OPTIMAL CONTROL
QUANTUM STATES
SOLIDS
SPIN
ANGULAR MOMENTUM
CALCULATION METHODS
CONTROL
CRYSTAL MODELS
MAGNETIC RESONANCE
MATHEMATICAL MODELS
PARTICLE PROPERTIES
RESONANCE