Elsevier

Physica B: Condensed Matter

Volume 407, Issue 17, 1 September 2012, Pages 3596-3599
Physica B: Condensed Matter

Multi-qubit controlled-NOT gates and Greenberger–Horne–Zeilinger state generation using one qubit simultaneously controlling n qubits

https://doi.org/10.1016/j.physb.2012.05.033Get rights and content

Abstract

Based on superconducting flux qubits coupled to a superconducting resonator. We propose a scheme for implementing multi-qubit controlled-NOT (C-NOT) gates and Greenberger–Horne–Zeilinger (GHZ) state with one flux qubit simultaneously controlling on n qubits. It is shown that the resonator mode is initially in the vacuum state, a high fidelity for operation procedure can be obtained. In addition, the gate operation time is independent of the number of the qubits, and can be controlled by adjusting detuning and coupling strengths. We also analyze the experimental feasibility that the conditions of the large detuning can be achieved by adjusting frequencies of the resonator and pulses.

Introduction

Since quantum systems have an information processing capability much greater than that of corresponding classical systems, much attention has been paid to quantum computers (QCs), which can solve some problems such as factorizing a large integer via Shor's algorithm [1] and searching for an item from a disordered system via Grover's algorithm [2]. It has been shown that any quantum operation can be decomposed into controlled-NOT (C-NOT) gates between two qubits and rotation on a single qubit [3]. Therefore, the realization of the two-qubit quantum gate plays a key role in the QC. Such gates have been demonstrated experimentally in cavity QED system [4], [5], trapped ions [6], quantum dots system [7], NMR [8], and superconducting qubits [9], [10]. It is well known that an useful QC must allow control of large qubits [11]. However, there are physical limitations on the number of qubits in an QC, and a large-scale quantum computation has not been experimentally achieved yet. Theoretically, some schemes for operating the multi-qubit controlled phase gates have been proposed based on n-controlled qubits acting on one target qubit in cavity QED or ion traps [12], [13], [14], [15]. Based on one qubit simultaneously controlling n target qubits, a novel scheme for achieving multiqubit controlled-phase gates was presented by Yang et al. [16]. Following their idea, we have presented a scheme for implementing n SWAP gates [17]. In this paper, we focus on how to realize n C-NOT gates and GHZ state by using one superconducting flux qubit simultaneously controlling n qubits in circuit cavity QED. For circuit cavity QED, some approach for performing quantum computation and quantum information processing have been proposed (see, e.g., Refs. [18], [19], [20], [21]).

This paper is organized as follows. In the following section, we introduce the model of the flux qubit coupled to a resonator and respective classical microwave pulses, and give the evolution operator of the system. In Section 3, we discuss how to realize n C-NOT gates and GHZ state. A brief discussion is given in Section 4.

Section snippets

Model and unitary evolution

Let us consider a rf-superconducting quantum interference device (rf-SQUID), the rf-SQUID has a Λ-type configuration formed by two lowest levels (|0 and |1) and an excited level (|e), as shown in Fig. 1. The Hamiltonian for a rf-SQUID, with junction capacitance C and loop inductance L, can be written in the usual form [22], [23]Hs=Q22C+(ΦΦx)22LEJcos2πΦΦ0,where Φ is the magnetic flux threading the ring, Q is the total charge on the capacitor, Φ and Q are the conjugate variables of the

Implementation of n C-NOT gates and GHZ state

The goal of this section is to demonstrate how the C-NOT gates and GHZ state can be implemented based on the unitary evolution operator (10).

Discussion

Finally, we give a brief discussion on the experimental issues:

  • (i)

    The conditions of the large detuning: for SQUIDs interacting with a resonator, the coupling strength is g0.18GHz [28]. If we choose Ω=1.05g, Δ1=20g and Δ2=21g, a simple calculation shows that δ=g, Ω2/Δ2=0.0525g, g2/Δ1=0.05g, and λ=0.05125g, which satisfy the conditions Δ1g, Δ2Ω, and δ{|g|2/Δ1,|Ω|2/Δ2,|λ|}.

  • (ii)

    The required operation time for n C-NOT gates or GHZ state generation: in terms of the values of the λ and δ, the total

Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant no. 11174100, and Key Project of Hunan Provincial Natural Science Foundation under Grant No. 11JJ2003.

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