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arXiv:cond-mat/0509478 · New Journal of Physics

Quantum state transfer in arrays of flux qubits

Andriy O. Lyakhov, Christoph Bruder

Published Aug 26, 2005• 59 citations
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Abstract

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.

DOI
10.1088/1367-2630/7/1/181

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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.
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A type of Josephson charge qubit circuit is constructed in this paper, and properties of four-qubit quantum state transfer through this system is also investigated. By modulating the external magnetic flux, we show that ideal transfer of an excited state 1〉 from the first qubit to the fourth qubit can be realized for both homogeneous and inhomogeneous transmission channels. Moreover, the average fidelity of state transfer across this system is also analyzed, the result revealed that it cannot be used to transfer an arbitrary quantum state.
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.
This thesis presents results of theoretical and experimental work on superconducting persistent-current flux quantum bits. These qubits are promising candidates for the implementation of scalable quantum information processing. This work focuses on the study of one dimensional chains of inductively coupled flux qubits and on qubits with a tunable energy gap. Chains of flux qubits can be used as models of quantum spin chains, one of the most basic systems in many-body physics that has been extensively studied theoretically. The ability to design and tune the qubit and coupling parameters enables exploration of different phase regimes during measurements, in parameter regimes that are not accessible with magnetic materials. The study of the dynamics of quantum waves in an artificial spin chain can also be used to explore novel quantum phenomena with possible applications in quantum computing. Tunability of the minimal energy splitting (the gap) enables one to rapidly bring the flux qubit in and out of resonance with other quantum systems, including a harmonic oscillator. With tunable qubits it also becomes possible to create inter-qubit couplings of different vector nature, using magnetic fluxes. This permits the design of various interaction Hamiltonians for multiple qubit systems. These operations can be performed at the degeneracy point of the qubit, where coherence properties are optimal. Therefore the tunable flux qubit provides an attractive component for the implementation of scalable quantum computation.
The XX model with uniform couplings represents the most natural choice for quantum state transfer through spin chains. Given that it has long been established that single-qubit states cannot be transferred with perfect fidelity in this model, the notion of pretty good state transfer has been recently introduced as a relaxation of the constraints on fidelity. In this paper, we study the transfer of multi-qubit entangled and unentangled states through unmodulated spin chains, and we prove that it is possible to have pretty good state transfer of any multi-particle state. This significantly generalizes the previous results on single-qubit state transfer and opens the way to using uniformly coupled spin chains as short-distance quantum channels for the transfer of arbitrary states of any dimension. Our results could be tested with current technology.
We investigate the fidelity of the quantum state transfer (QST) of two qubits by means of an arbitrary spin-12\frac{1}{2}21​ network, on a lattice of any dimensionality. Under the assumptions that the network Hamiltonian preserves the magnetization and that a fully polarized initial state is taken for the lattice, we obtain a general formula for the average fidelity of the two qubits QST, linking it to the one- and two-particle transfer amplitudes of the spin excitations among the sites of the lattice. We then apply this formalism to a 1D spin chain with XXXXXX-Heisenberg type nearest-neighbour interactions adopting a protocol that is a generalization of the single qubit one proposed in Paganelli et al. [Phys. Rev. A 87, 062309 (2013)]. We find that a high-quality two qubit QST can be achieved provided one can control the local fields at sites near the sender and receiver. Under such conditions, we obtain an almost perfect transfer in a time that scales either linearly or, depending on the spin number, quadratically with the length of the chain.