Hamiltonian tomography of dissipative systems under limited access: A biomimetic case study

The identification of parameters in the Hamiltonian that describes complex many-body quantum systems is generally a very hard task. Recent attention has focused on such problems of Hamiltonian tomography for networks constructed with two-level systems. For open quantum systems, the fact that injected signals are likely to decay before they accumulate sufficient information for parameter estimation poses additional challenges. In this paper, we consider use of the gateway approach to Hamiltonian tomography \cite{Burgarth2009,Burgarth2009a} to complex quantum systems with a limited set of state preparation and measurement probes. We classify graph properties of networks for which the Hamiltonian may be estimated under equivalent conditions on state preparation and measurement. We then examine the extent to which the gateway approach may be applied to estimation of Hamiltonian parameters for network graphs with non-trivial topologies mimicking biomolecular systems.Comment: 6 page

Dynamics of two-process astrocyte networks

http://deepblue.lib.umich.edu/bitstream/2027.42/112971/1/12868_2013_Article_3367.pd

Indirect Hamiltonian Identification through a small gateway

Identifying the nature of interactions in a quantum system is essential in understanding any physical phenomena. Acquiring information on the Hamiltonian can be a tough challenge in many-body systems because it generally requires access to all parts of the system. We show that if the coupling topology is known, the Hamiltonian identification is indeed possible indirectly even though only a small gateway to the system is used. Surprisingly, even a degenerate Hamiltonian can be estimated by applying an extra field to the gateway.Comment: 5 pages, 1 figure; see Video Abstract at http://www.quantiki.org/video_abstracts/0903061

Indirect quantum tomography of quadratic Hamiltonians

A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few resources. We find that almost all properties of the Hamiltonian are determined by its surface, and that these properties can be measured even if the system can only be initialised to a mixed state. Therefore our method can be applied to various physical models, with important examples including coupled nano-mechanical oscillators, hopping fermions in optical lattices, and transverse Ising chains

Characterizing Communication Networks Associated with Political Hashtags.

Among the diverse forms of communication and information networks found in the Web 2.0 environment, “social” and “informational” communication networks have been characterized in terms of their network metrics. Although Twitter is partly based on relationships between actors, activity has been shown to reflect characteristics of information networks. This study examines activity in Twitter within spaces defined by hashtags on political topics. We gathered our own data on a hashtag associated with the 2012 Hawaii senatorial race and compared our results to those from other political hashtag networks, and to typical social and information networks as well as random graphs. Results show that hashtag-centered reply and retweet networks in this domain do not fall clearly into the social or informational categories. There appears to be a third kind of network associated with political debate. More generally, it may be productive to conceive of communication networks in terms of multidimensional characteristics rather than categories

Estimation of coupling constants of a three-spin chain: a case study of Hamiltonian tomography with nuclear magnetic resonance

It has been shown that inter-spin interaction strengths in a spins-1/2 chain can be evaluated by accessing one of the edge spins only. We demonstrate this experimentally for the simplest case, a three-spin chain, with nuclear magnetic resonance (NMR) technique. The three spins in the chain interact through nearest-neighbor Ising interactions under site-dependent transverse fields. The employed molecule is an alanine containing three $^{13}$C nuclei, each of which has spin-1/2.Comment: 7 pages, 18 figure

Spin-chain-based full quantum computation by accessing only two spins

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/98702/1/APC000169.pd