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International Journal of Quantum Information

IMPLEMENTATION OF QUANTUM COMMUNICATION PROTOCOLS IN JOSEPHSON JUNCTION ARRAYS

Alessandro Romito, Gabriele De Chiara, Davide Rossini, Simone Montangero

Published Jun 1, 2006• 1 citation
Publisher

Abstract

We discuss simple protocols to realize state transfer with high fidelity in Josephson junction arrays. We consider both the cases of constant and properly modulated couplings between the site of the chain. We investigate the influence of static disorder both in the Josephson energies and in the coupling to the background gate charges and we show that they can lead to a fractal fidelity. We also analyze the readout process, and its backaction on the state transfer.

DOI
10.1142/s0219749906001967

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We discuss simple protocols to realize state transfer with high fidelity in Josephson junction arrays. We consider both the cases of constant and properly modulated couplings between the site of the chain. We investigate the influence of static disorder both in the Josephson energies and in the coupling to the background gate charges and we show that they can lead to a fractal fidelity. We also analyze the readout process, and its backaction on the state transfer.
Josephson junction arrays can be used as quantum channels to transfer quantum information between distant sites. In this paper we discuss simple protocols to realize state transfer with high fidelity. The channels do not require complicated gating but use the natural dynamics of a properly designed array. We investigate the influence of static disorder both in the Josephson energies and in the coupling to the background gate charges, as well as the effect of dynamical noise. We also analyze the readout process, and its back action on the state transfer.
Perfect state transfer is possible in modulated spin chains [Phys. Rev. Lett. 92, 187902 (2004)], imperfections, however, are likely to corrupt the state transfer. We study the robustness of this quantum communication protocol in the presence of disorder both in the exchange couplings between the spins and in the local magnetic field. The degradation of the fidelity can be suitably expressed, as a function of the level of imperfection and the length of the chain, in a scaling form. In addition the time signal of fidelity becomes fractal. We further characterize the state transfer by analyzing the spectral properties of the Hamiltonian of the spin chain.
In this paper, we describe a possible experimental realization of Bose's idea to use spin chains for short-distance quantum communication (Bose 2003 Phys. Rev. Lett. 91 207901). Josephson arrays have been proposed and analysed as transmission channels for systems of superconducting charge qubits. Here, we consider a chain of persistent-current qubits, that is appropriate for state transfer with high fidelity in systems containing flux qubits. We calculate the fidelity of state transfer for this system. In general, the Hamiltonian of this system is not of XXZ-type, and we analyse the magnitude and the effect of the terms that do not conserve the z-component of the total spin.
We study coherent quantum phase slips in a Josephson junction chain, including two types of quenched disorder: random spatial modulation of the junction areas and random induced background charges. Usually, the quantum phase-slip amplitude is sensitive to the normal-mode structure of superconducting phase oscillations in the ring (Mooij-Sch\"on modes, which are all localized by the area disorder). However, we show that the modes' contribution to the disorder-induced phase-slip action fluctuations is small, and the fluctuations of the action on different junctions are mainly determined by the local junction parameters. We study the statistics of the total quantum phase-slip amplitude on the chain and show that it can be non-Gaussian for not sufficiently long chains.
Quantum state transfer in the presence of static disorder and noise is one of the main challenges in building quantum computers. We compare the quantum state transfer properties for two classes of qubit chains under the influence of static disorder. In fully engineered chains all nearest-neighbor couplings are tuned in such a way that a single-qubit state can be transferred perfectly between the ends of the chain, while in chains with modified boundaries only the two couplings between the transmitting and receiving qubits and the remainder of the chain can be optimized. We study how the disorder in the couplings affects the state transfer fidelity depending on the disorder model and strength as well as the chain type and length. We show that the desired level of fidelity and transfer time are important factors in designing a chain. In particular we demonstrate that transfer efficiency comparable or better than that of the most robust engineered systems can also be reached in chains with modified boundaries without the demanding engineering of a large number of couplings.
We study transfer of a quantum state through XXXXXX spin chains with static imperfections. We combine the two standard approaches for state transfer based on (i) modulated couplings between neighboring spins throughout the spin chain and (ii) weak coupling of the outermost spins to an unmodulated spin chain. The combined approach allows us to design spin chains with modulated couplings and localized boundary states, permitting high-fidelity state transfer in the presence of random static imperfections of the couplings. The modulated couplings are explicitly obtained from an exact algorithm using the close relation between tridiagonal matrices and orthogonal polynomials [Linear Algebr. Appl. 21, 245 (1978)]. The implemented algorithm and a graphical user interface for constructing spin chains with boundary states (spinGUIn) are provided as Supplemental Material.