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Journal of the Physical Society of Japan

Generation of Macroscopic Entangled States in Coupled Superconducting Phase Qubits

Shigemasa Matsuo, Sahel Ashhab, Toshiyuki Fujii, Franco Nori, Katsuhiko Nagai, Noriyuki Hatakenaka

Published May 11, 2007• 25 citations
Publisher

Abstract

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.

DOI
10.1143/jpsj.76.054802

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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.
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.
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.
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 introduce a suit of simple entangling protocols for generating tripartite Greenberger-Horne-Zeilinger and W states in systems with anisotropic exchange interaction $g(XX+YY)+\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{g}ZZ$. An interesting example is provided by macroscopic entanglement in Josephson phase qubits with capacitive $(\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{g}=0)$ and inductive $(0<\ensuremath{\mid}\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{g}∕g\ensuremath{\mid}<0.1)$ couplings.
Entangled multiqubit states may be generated through a dispersive collective quantum nondemolition measurement of superconducting qubits coupled to a microwave transmission line resonator. Using the quantum trajectory approach, we analyze the stochastic measurement traces that would be observed in experiments. We illustrate the synthesis of three-qubit WWW and Greenberger-Horne-Zeilinger states, and we analyze how the fidelity and the entanglement evolve in time during the measurement. We discuss the influence of decoherence and relaxation, as well as of imperfect control over experimental parameters. We show that the desired states can be generated on time scales much faster than the qubit decoherence rates.
Nonpairwise multibody interactions have recently attracted much attention due to their promising applications in the realm of quantum information science and technology. In this work, we propose a method to synthesize a nonpairwise three-body interaction of superconducting qubits using a coupler qubit dispersively coupled to two spatially separated qubits and a microwave pulse. This interaction describes physical processes of an excitation from the coupler qubit to two spatially separated qubits and the reverse process. We show that the interaction can be utilized to deterministically generate three-body Greenberger-Horne-Zeilinger (GHZ) entangled states, transfer the state of the coupler qubit into a two-qubit entangled state, and construct three-qubit controlled-controlled-phase and Toffoli gates. Our proposal only requires a coupler qubit and a single-step operation; thus, the system architecture and method are quite simple. As examples, we numerically simulate the dynamics of the system, and the numerical results demonstrate that high-fidelity preparation of the proposed three-body GHZ entangled state and quantum gates is feasible with current superconducting circuit technology. This approach is general and applicable to a wide range of quantum systems.