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arXiv:1410.5444 · Physical Review A

Simulating long-distance entanglement in quantum spin chains by superconducting flux qubits

Stefano Zippilli, M. Grajcar, Evgeni V. Il’ichev, Fabrizio Illuminati

Published Feb 17, 2015• 14 citations
arXivHTMLPDF

Abstract

We investigate the performance of superconducting flux qubits for the adiabatic quantum simulation of long-distance entanglement (LDE), namely, a finite ground-state entanglement between the end spins of a quantum spin chain with open boundary conditions. As such, LDE can be considered an elementary precursor of edge modes and topological order. We discuss two possible implementations which simulate open chains with uniform bulk and weak end bonds, either with Ising or with $XX$ nearest-neighbor interactions. In both cases, we discuss a suitable protocol for the adiabatic preparation of the ground state in the physical regimes featuring LDE. In the first case, the adiabatic manipulation and the Ising interactions are realized using dc currents, while in the second case microwaves fields are used to control the smoothness of the transformation and to realize the effective $XX$ interactions. We demonstrate the adiabatic preparation of the end-to-end entanglement in chains of four qubits with realistic parameters and on a relatively fast time scale.

DOI
10.1103/physreva.91.022315

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We investigate the performance of superconducting flux qubits for the adiabatic quantum simulation of long-distance entanglement (LDE), namely, a finite ground-state entanglement between the end spins of a quantum spin chain with open boundary conditions. As such, LDE can be considered an elementary precursor of edge modes and topological order. We discuss two possible implementations which simulate open chains with uniform bulk and weak end bonds, either with Ising or with XXXXXX nearest-neighbor interactions. In both cases, we discuss a suitable protocol for the adiabatic preparation of the ground state in the physical regimes featuring LDE. In the first case, the adiabatic manipulation and the Ising interactions are realized using dc currents, while in the second case microwaves fields are used to control the smoothness of the transformation and to realize the effective XXXXXX interactions. We demonstrate the adiabatic preparation of the end-to-end entanglement in chains of four qubits with realistic parameters and on a relatively fast time scale.
Recent numerical results showed that spin chains are able to produce long-distance entanglement (LDE). We develop a formalism that allows the computation of LDE for weakly interacting probes with gapped many-body systems. At zero temperature, a dc response function determines the ability of the physical system to generate genuine quantum correlations between the probes. We show that the biquadratic Heisenberg spin-1 chain is able to produce LDE in the thermodynamic limit and that the finite antiferromagnetic Heisenberg chain maximally entangles two spin-1/21/21/2 probes very far apart. These results support the current perspective of using quantum spin chains as entanglers or quantum channels in quantum information devices.
We investigate theoretically systems of ions in segmented linear Paul traps for the quantum simulation of quantum spin models with tunable interactions. The scheme is entirely general and can be applied to the realization of arbitrary spin-spin interactions. As a specific application we discuss in detail the quantum simulation of models that exhibit long-distance entanglement in the ground state. We show how tailoring of the axial trapping potential allows for generating spin-spin coupling patterns that are suitable to create long-distance entanglement. We discuss how suitable sequences of microwave pulses can implement Trotter expansions and realize various kinds of effective spin-spin interactions. The corresponding Hamiltonians can be varied on adjustable time scales, thereby allowing the controlled adiabatic preparation of their ground states.
We discuss the phenomenon of long-distance entanglement (LDE) in the ground state of quantum spin models, its use in high-fidelity and robust quantum communication, and its realization in many-body systems of ultracold atoms in optical lattices and in arrays of coupled optical cavities. We investigate XX quantum spin models on one-dimensional lattices with open ends and different patterns of site-dependent interaction couplings, singling out two general settings: patterns that allow for perfect LDE in the ground state of the system, namely such that the end-to-end entanglement remains finite in the thermodynamic limit, and patterns of quasi-long-distance entanglement (QLDE) in the ground state of the system, namely such that the end-to-end entanglement vanishes with a very slow power-law decay as the length of the spin chain is increased. We discuss physical realizations of these models in ensembles of ultracold bosonic atoms loaded in optical lattices. We show how, using either suitably engineered super-lattice structures or exploiting the presence of edge impurities in lattices with single periodicity, it is possible to realize models endowed with nonvanishing LDE or QLDE. We then study how to realize models that optimize the robustness of QLDE at finite temperature and in the presence of imperfections using suitably engineered arrays of coupled optical cavities. For both cases the numerical estimates of the end-to-end entanglement in the actual physical systems are thoroughly compared with the analytical results obtained for the spin model systems. We finally introduce LDE-based schemes of long-distance quantum teleportation in linear arrays of coupled cavities, and show that they allow for high-fidelity and high success rates even at moderately high temperatures.
We propose the generation of entangled qubits by utilizing the properties of edge states appearing at one end of a periodically driven (Floquet) superconducting qubit chain. Such qubits are naturally protected by the system's topology and their manipulation is possible through adiabatic control of the system parameters. By utilizing a Y-junction geometry, we then develop a protocol to perform high-fidelity transfer of entangled qubits from one end to another end of a qubit chain. Our quantum state transfer protocol is found to be robust against disorder and imperfection in the system parameters. More importantly, our proposed protocol also performs remarkably well at larger system sizes due to nonvanishing gaps between the involved edge states and the bulk states, thus allowing us in principle to transfer entangled states over an arbitrarily large distance. This work hence indicates that Floquet topological edge states are not only resourceful for implementing quantum gate operations, but also useful for high-fidelity and long-distance transfer of entangled states along solid-state qubit chains.
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We propose a quantum simulator based on driven superconducting qubits where the interactions are generated parametrically by a bichromatic magnetic flux modulation of a tunable bus element. Using a time-dependent Schrieffer-Wolff transformation, we analytically derive a multiqubit Hamiltonian which features independently tunable XXXXXX- and YYYYYY-type interactions as well as local bias fields over a large parameter range. We demonstrate the adiabatic simulation of the ground state of a hydrogen molecule using two superconducting qubits and one tunable bus element. The time required to reach chemical accuracy lies in the few microsecond range. Therefore, the proposed adiabatic protocol could be implemented using currently available superconducting circuits. Further applications of this technique may also be found in the simulation of interacting spin systems.