Structure identification and state initialization of spin networks with limited access

For reliable and consistent quantum information processing carried out on a quantum network, the network structure must be fully known and a desired initial state must be accurately prepared on it. In this paper, for a class of spin networks with only its single node accessible, we provide two continuous-measurement-based methods to achieve the above requirements; the first identifies the unknown network structure with a high probability, based on a continuous-time Bayesian update of the graph structure and the second is, with the use of an adaptive measurement technique, able to deterministically drive any mixed state to a spin coherent state for network initialization.

[1]  Lloyd,et al.  Almost any quantum logic gate is universal. , 1995, Physical review letters.

[2]  N. Bloembergen,et al.  On the interaction of nuclear spins in a crystalline lattice , 1949 .

[3]  Naoki Yamamoto,et al.  Feedback control of quantum entanglement in a two-spin system , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[4]  Matthew R. James,et al.  An Introduction to Quantum Filtering , 2006, SIAM Journal of Control and Optimization.

[5]  D. DiVincenzo,et al.  The Physical Implementation of Quantum Computation , 2000, quant-ph/0002077.

[6]  Michael D. Siciliano,et al.  Estimating network structure via random sampling: Cognitive social structures and the adaptive threshold method , 2012, Soc. Networks.

[7]  Makoto Negoro,et al.  Scalable spin amplification with a gain over a hundred. , 2011, Physical review letters.

[8]  Mazyar Mirrahimi,et al.  Stabilizing Feedback Controls for Quantum Systems , 2005, SIAM J. Control. Optim..

[9]  R. Khasminskii.  Stochastic Stability of Differential Equations , 1980 .

[10]  Xiaoting Wang,et al.  Symmetry and Subspace Controllability for Spin Networks With a Single-Node Control , 2010, IEEE Transactions on Automatic Control.

[11]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[12]  Franco Nori,et al.  Scalable quantum computation via local control of only two qubits , 2009, 0905.3373.

[13]  Jason F. Ralph,et al.  Frequency tracking and parameter estimation for robust quantum state estimation , 2009, 0907.5034.

[14]  L. Ioffe,et al.  Physical implementation of protected qubits , 2012, Reports on progress in physics. Physical Society.

[15]  Vittorio Giovannetti,et al.  Local controllability of quantum networks , 2009 .

[16]  R. Handel,et al.  Deterministic Dicke-state preparation with continuous measurement and control , 2004, quant-ph/0402137.

[17]  Kurt Jacobs,et al.  Feedback control using only quantum back-action , 2009, 0904.3745.

[18]  Hiromichi Nakazato,et al.  Preparation and entanglement purification of qubits through Zeno-like measurements , 2004 .

[19]  I. Chuang,et al.  Quantum Computation and Quantum Information: Bibliography , 2010 .

[20]  Gustavo Stolovitzky,et al.  Reconstructing biological networks using conditional correlation analysis , 2005, Bioinform..

[21]  P. Zoller,et al.  Preparation of entangled states by quantum Markov processes , 2008, 0803.1463.

[22]  Vittorio Giovannetti,et al.  Full control by locally induced relaxation. , 2007, Physical review letters.

[23]  H. M. Wiseman,et al.  State and dynamical parameter estimation for open quantum systems , 2001 .

[24]  DiVincenzo.  Two-bit gates are universal for quantum computation. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[25]  S.G. Schirmer,et al.  Control paradigms for quantum engineering , 2008, 2008 3rd International Symposium on Communications, Control and Signal Processing.

[26]  Franco Nori,et al.  Coupling strength estimation for spin chains despite restricted access , 2008, 0810.2866.

[27]  D. Deutsch.  Quantum computational networks , 1989, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[28]  Hiromichi Nakazato,et al.  Purification through Zeno-like measurements. , 2003, Physical review letters.

[29]  V. P. Belavkin,et al.  Quantum stochastic calculus and quantum nonlinear filtering , 1992 .

[30]  Koji Maruyama,et al.  Indirect Hamiltonian identification through a small gateway , 2009, 0903.0612.

[31]  Matthias Christandl,et al.  Perfect state transfer in quantum spin networks. , 2004, Physical review letters.

[32]  M S Kim,et al.  Hamiltonian tomography in an access-limited setting without state initialization. , 2008, Physical review letters.

[33]  E. Lieb,et al.  Two Soluble Models of an Antiferromagnetic Chain , 1961 .

[34]  Sonia G. Schirmer,et al.  Global controllability with a single local actuator , 2008 .

[35]  Ramon van Handel,et al.  Feedback control of quantum state reduction , 2005, IEEE Transactions on Automatic Control.

[36]  Naoki Yamamoto.  Parametrization of the feedback Hamiltonian realizing a pure steady state , 2005 .

[37]  Mikio Nakahara,et al.  Estimation of coupling constants of a three-spin chain: a case study of Hamiltonian tomography with nuclear magnetic resonance , 2011, 1111.1381.

[38]  G. Milburn,et al.  Quantum Measurement and Control , 2009 .

[39]  K. Mølmer,et al.  Bayesian parameter inference from continuously monitored quantum systems , 2012, 1212.5700.

[40]  D. Burgarth,et al.  Quantum system identification. , 2011, Physical review letters.

[41]  Michael Schweinberger,et al.  MAXIMUM LIKELIHOOD ESTIMATION FOR SOCIAL NETWORK DYNAMICS. , 2010, The annals of applied statistics.

[42]  Franco Nori,et al.  Indirect quantum tomography of quadratic Hamiltonians , 2010, 1004.5018.

[43]  Barenco,et al.  Elementary gates for quantum computation. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[44]  Bradley A. Chase,et al.  Single-shot parameter estimation via continuous quantum measurement , 2008, 0811.0601.

[45]  Hideo Mabuchi.  Dynamical identification of open quantum systems , 1996 .