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Journal of Physics Conference Series

Macroscopic entangled states in superconducting flux qubits

Mun Dae Kim, Sam Young Cho

Published Feb 1, 2009• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1742-6596/150/2/022038

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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.
We investigate two types of genuine three-qubit entanglement, known as the Greenberger-Horne-Zeilinger (GHZ) and WWW states, in a macroscopic quantum system. Superconducting flux qubits are theoretically considered in order to generate such states. A phase coupling is proposed to offer enough strength of interactions between qubits. While an excited state can be the WWW state, the GHZ state is formed at the ground state of the three flux qubits. The GHZ and WWW states are shown to be robust against external flux fluctuations for feasible experimental realizations.
Going beyond the entanglement of microscopic objects (such as photons, spins, and ions), here we propose an efficient approach to produce and control the quantum entanglement of three macroscopic coupled superconducting qubits. By conditionally rotating, one by one, selected Josephson-charge qubits, we show that their Greenberger-Horne-Zeilinger (GHZ) entangled states can be deterministically generated. The existence of GHZ correlations between these qubits could be experimentally demonstrated by effective single-qubit operations followed by high-fidelity single-shot readouts. The possibility of using the prepared GHZ correlations to test the macroscopic conflict between the noncommutativity of quantum mechanics and the commutativity of classical physics is also discussed.
A theoretical scheme for the generation of maximally entangled states of two superconducting flux qubits via their sequential interaction with a monochromatic quantum field is presented. The coupling of the qubits with the quantized field can be tuned on and off resonance by modulating the effective Josephson energy of each qubit via an externally applied magnetic flux. The system operates in such a way as to transfer the entanglement from a bipartite field-qubit subsystem to the two qubits. This scheme is attractive in view of the implementation of practical quantum processing systems.
We consider the possibility of generating macroscopic entangled states in capacitively coupled phase qubits. First we discuss the operation of phase qubits and the implementation of the basic gate operations in them. We then analyze two possible procedures that can be used to generate n-qubit entangled states, such as the Greenberger-Horne-Zeilinger state for the case n = 3. The procedures we propose are constructed under the experimentally motivated constraint of trying to minimize the number of control lines used to manipulate the qubits.
There exists a large number of experimental and theoretical results supporting the picture of macroscopic qubits implemented by nanoscopic Josephson junctions of three different types -- charge qubit, flux qubit and phase qubit. The standard unified description of such systems is based on the formal quantization of the phenomenological Kirchhoff equations for the corresponding circuits. In this paper a simplified version of the BCS theory for superconductors is used to derive microscopic models for all types of small Josephson junctions. For these models the state-dependent individual tunneling of Cooper pairs couples ground pair states with excited pair states what leads to a more complicated structure of the lowest lying energy levels. In particular, the highly degenerate levels emerge, which act as probability sinks for the qubit. These models allow also for the coupling to phonons as an efficient mechanism of relaxation for all types of junctions. The alternative formulas concerning basic spectral parameters of superconducting qubits are presented and compared with the experimental data. Finally, the question whether small Josephson junctions can be treated as macroscopic quantum systems is briefly discussed.