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arXiv:0706.2402 · Physical Review B

Realizable spin models and entanglement dynamics in superconducting flux qubit systems

Qian‐Qian Shi, Sam Young Cho, Bo Li, Mun Dae Kim

Published Mar 12, 2008• 0 citations
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Abstract

Realizable spin models are investigated in a superconducting flux qubit system. By adjusting system parameters, it is shown that various artificial spin systems can be realized such as the quantum Ising model and the class of $XXZ$ spin model in the same flux qubit system. The entanglement dynamics of the realizable systems, especially for the two-qubit system, is discussed by means of their concurrence and fidelity. It is found that an unentangled input state can evolve to be a maximally entangled output state periodically due to the exchange interactions induced by two-qubit flipping tunneling processes.

DOI
10.1103/physrevb.77.104511

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Publisher's Note: Realizable spin models and entanglement dynamics in superconducting flux qubit systems [Phys. Rev. B77, 104511 (2008)]

Qian‐Qian Shi, Sam Young Cho, Bo Li +1 more

Physical Review B•Mar 27, 2008•0 citations
Realizable spin models are investigated in a superconducting flux qubit system. By adjusting system parameters, it is shown that various artificial spin systems can be realized such as the quantum Ising model and the class of XXZXXZXXZ spin model in the same flux qubit system. The entanglement dynamics of the realizable systems, especially for the two-qubit system, is discussed by means of their concurrence and fidelity. It is found that an unentangled input state can evolve to be a maximally entangled output state periodically due to the exchange interactions induced by two-qubit flipping tunneling processes.
We theoretically study the macroscopic quantum entanglement in superconducting flux qubits. A phase-coupling scheme is proposed to offer enough strength of interactions between qubits. It is shown that due to the two-qubit tunneling processes both the ground state and excited states of coupled two flux qubits can be Bell type states, maximally entangled, in experimentally accessible regimes. The parameter regimes for the Bell states are discussed in terms of external magnetic flux and Josephson coupling energies. We also investigate two types of genuine three-qubit entanglement, known as the Greenberger-Horne- Zeilinger(GHZ) and W states. While an excited state can be the W state, the GHZ state is formed at the ground state of the coupled three flux qubits. The GHZ and W states are shown to be robust against external flux fluctuations for feasible experimental realizations.
We theoretically study macroscopic quantum entanglement in two superconducting flux qubits. To manipulate the state of two flux qubits, a Josephson junction is introduced in the connecting loop coupling the qubits. Increasing the coupling energy of the Josephson junction makes it possible to achieve relatively strong coupling between the qubits, causing two-qubit tunneling processes to be even dominant over the single-qubit tunneling processes in the states of two qubits. It is shown that due to the two-qubit tunneling processes, both the ground state and excited states of the coupled flux qubits can be a Bell type of maximally entangled state, in experimentally accessible regimes. The parameter regimes for the Bell states are discussed in terms of magnetic flux and Josephson coupling energies.
Superconducting flux qubits are considered to investigate macroscopic many-qubit interactions. Many-qubit states based on current states can be manipulated through the current-phase relation in each superconducting loop. For flux qubit systems comprised of NNN-qubit loops, a general expression of low-energy Hamiltonian is presented in terms of low-energy levels of qubits and macroscopic quantum tunnelings between the many-qubit states. Many-qubit interactions classified by Ising-type or tunnel exchange interactions can be observable experimentally. Flux qubit systems can provide various artificial-spin systems to study many-body systems that cannot be found naturally.
Abstract This study aims to quantify entanglement in low-temperature superconducting flux qubits using mutual information and concurrence. It presents a theoretical framework, experimental setup for two-qubit systems, and simulations. Results show that the entanglement strength varies periodically with external magnetic flux and saturates with increasing inter-qubit coupling. These results offer guidance for optimizing superconducting quantum circuits in various quantum information processing applications.
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.