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arXiv:1403.0226 · International Symposium on Communications, Control and Signal Processing

Characterization and control of quantum spin chains and rings

S. G. Schirmer, Frank C. Langbein

Published May 1, 2014• 3 citations
arXivHTMLPDF

Abstract

Information flow in quantum spin networks is considered. Two types of control - temporal bang-bang switching control and control by varying spatial degrees of freedom - are explored and shown to be effective in speeding up information transfer and increasing transfer fidelities. The control is modelbased and therefore relies on accurate knowledge of the system parameters. An efficient protocol for simultaneous identification of the coupling strength and the exact number of spins in a chain is presented.

DOI
10.1109/isccsp.2014.6877950

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Information flow in quantum spin networks is considered. Two types of control - temporal bang-bang switching control and control by varying spatial degrees of freedom - are explored and shown to be effective in speeding up information transfer and increasing transfer fidelities. The control is modelbased and therefore relies on accurate knowledge of the system parameters. An efficient protocol for simultaneous identification of the coupling strength and the exact number of spins in a chain is presented.
Spin chains have been proposed as quantum wires for information transfer in solid-state quantum architectures. We show that huge gains in both transfer speed and fidelity are possible using a minimalist control approach that relies only on a single local on-off switch actuator. Effective switching time sequences can be determined using optimization techniques for both ideal and disordered chains. Simulations suggest that effective optimization is possible even in the absence of knowledge of the Hamiltonian or accurate models.
Propagation of information encoded in spin degrees of freedom through networks of coupled spins enables important applications in spintronics and quantum information processing. We study control of information propagation in networks of spin-1/2 particles with uniform nearest neighbor couplings forming a ring with a single excitation in the network as simple prototype of a router for spin-based information. Specifically optimizing spatially distributed potentials, which remain constant during information transfer, simplifies the implementation of the routing scheme. However, the limited degrees of freedom makes finding a control that maximizes the transfer probability in a short time difficult. We show that the structure of the eigenvalues and eigenvectors must fulfill a specific condition to be able to maximize the transfer fidelity, and demonstrate that a specific choice among the many potential structures that fulfill this condition significantly improves the solutions found by optimal control.
The transmission of quantum states through spin chains is an important element in the implementation of quantum information technologies. Speed and fidelity of transfer are the main objectives which have to be achieved by the devices even in the presence of imperfections which are unavoidable in any manufacturing process. To reach these goals, several kinds of spin chains have been suggested, which differ in the degree of fine-tuning, or engineering, of the system parameters. In this work we present a systematic study of two important classes of such chains. In one class only the spin couplings at the ends of the chain have to be adjusted to a value different from the bulk coupling constant, while in the other class every coupling has to have a specific value. We demonstrate that configurations from the two different classes may perform similarly when subjected to the same kind of disorder in spite of the large difference in the engineering effort necessary to prepare the system. We identify the system features responsible for these similarities and we perform a detailed study of the transfer fidelity as a function of chain length and disorder strength, yielding empirical scaling laws for the fidelity which are similar for all kinds of chain and all disorder models. These results are helpful in identifying the optimal spin chain for a given quantum information transfer task. In particular, they help in judging whether it is worthwhile to engineer all couplings in the chain as compared to adjusting only the boundary couplings.
Quantum information and quantum computation are linked by a common mathematical and physical framework of quantum mechanics. The manipulation of the predicted dynamics and its optimization is known as quantum control. Many techniques, originating in the study of nuclear magnetic resonance, have found common usage in methods for processing quantum information and steering physical systems into desired states. This thesis expands on these techniques, with careful attention to the regime where competing effects in the dynamics are present, and no semi-classical picture exists where one effect dominates over the others. That is, the transition between the diabatic and adiabatic error regimes is examined, with the use of such techniques as time-dependent diagonalization, interaction frames, average-Hamiltonian expansion, and numerical optimization with multiple time-dependences. The results are applied specifically to superconducting systems, but are general and improve on existing methods with regard to selectivity and crosstalk problems, filtering of modulation of resonance between qubits, leakage to non-compuational states, multi-photon virtual transitions, and the strong driving limit.
The flip of quantum spin used as qubit has a significant effect on quantum computing and quantum information. Therefore, we study the dynamics of quantum spin in two-level spin-1/2 system by using Bang-Bang control protocol in this work. Here, system is driven by constant filed B0 along z-axis and controlled field B(t) along x or y-axis. when |B(t)| ≥ BC is satisfied, the optimal control time and switching time of spin, from state |1〉 to |0〉, of the system with and without amplitude damping or phase damping are given. Our results demonstrate that the fidelity of state of system with amplitude damping is still up to 0.9985 by Bang-Bang control protocol, even if the coupling strength, γ, of system with environment is equal to 0.3 and Bang-Bang control protocol is easier than oscillating filed to operate and analyze.
Experiments in coherent spectroscopy correspond to control of quantum mechanical ensembles guiding them from initial to final target states by unitary transformations. The control inputs (pulse sequences) that accomplish these unitary transformations should take as little time as possible so as to minimize the effects of relaxation and to optimize the sensitivity of the experiments. Here, we present a radically different and generally applicable approach to efficient control of dynamics in spin chains of arbitrary length. The approach relies on the creation of localized spin waves, ``spin solitons'', and efficient propagation of these soliton states through the spin chain. The methods presented are expected to find immediate applications in control of spin dynamics in coherent spectroscopy and quantum information processing.