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arXiv:cond-mat/0606034 · Physical Review B

Entanglement and Bell states in superconducting flux qubits

Mun Dae Kim, Sam Young Cho

Published Apr 18, 2007• 11 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.75.134514

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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 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.
In this paper we discuss solid-state nanoelectronic realizations of Josephson flux qubits with large tunneling \namplitude between the two macroscopic states. The latter can be controlled via the height and form of \nthe potential barrier, which is determined by quantum-state engineering of the flux qubit circuit. The simplest \ncircuit of the flux qubit is a superconducting loop interrupted by a Josephson nanoscale tunnel junction. \nThe tunneling amplitude between two macroscopically different states can be essentially increased, by \nengineering of the qubit circuit, if tunnel junction is replaced by a ScS contact. However, only Josephson \ntunnel junctions are particularly suitable for large-scale integration circuits and quantum detectors with preset- \nday technology. To overcome this difficulty we consider here the flux qubit with high-level energy separation \nbetween «ground» and «excited» states, which consists of a superconducting loop with two lowcapacitance \nJosephson tunnel junctions in series. We demonstrate that for real parameters of resonant superposition \nbetween the two macroscopic states the tunneling amplitude can reach values greater than 1 K. Analytical \nresults for the tunneling amplitude obtained within semiclassical approximation by instanton technique \nshow good correlation with a numerical solution.
In this paper we discuss solid-state nanoelectronic realizations of Josephson flux qubits with large tunneling amplitude between the two macroscopic states. The latter can be controlled via the height and form of the potential barrier, which is determined by quantum-state engineering of the flux qubit circuit. The simplest circuit of the flux qubit is a superconducting loop interrupted by a Josephson nanoscale tunnel junction. The tunneling amplitude between two macroscopically different states can be increased substantially by engineering of the qubit circuit if the tunnel junction is replaced by a ScS contact. However, only Josephson tunnel junctions are particularly suitable for large-scale integration circuits and quantum detectors with present-day technology. To overcome this difficulty we consider here a flux qubit with high energy-level separation between the “ground” and “excited” states, consisting of a superconducting loop with two low-capacitance Josephson tunnel junctions in series. We demonstrate that for real parameters of resonant superposition between the two macroscopic states the tunneling amplitude can reach values greater than 1K. Analytical results for the tunneling amplitude obtained within the semiclassical approximation by the instanton technique show good correlation with a numerical solution.
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.
Following the scheme proposed by X. L. He et al. [Phys. Rev. B76 (2007) 024517], we investigate the generation of a maximally entangled state between the charge and flux qubits. It is shown that macroscopic Einstein–Podolsky–Rosen (EPR) pairs can be created and the entanglement can be long-lived. Since the large Josephson junction is only virtually excited, no quantum information will be transferred from the charge and flux qubits to the large Josephson junction. Based on the strong inductive coupling, a fast entanglement operation can be achieved.
The consequences of the transition to a quantum description of magnetic flux motion in the superconducting ring closed by an ScS type Josephson junction are considered. Here we review the principal results regarding macroscopic quantum tunneling (MQT) of Bose condensate consisting of a macroscopically large number of Cooper electron pairs. These phenomena are illustrated by the original data obtained from the study of MQT and coherent states in a modified flux qubit with energy level depletion ΔE01 ≈ 2·10–23 J (ΔE01/h ≈ 30 GHz). State superposition properties in a two-well potential and the issues associated with quantum measurements of local curvature of qubits’ superposition energy levels are analyzed.