Comparison of LOQC C-sign gates with ancilla inefficiency and an improvement to functionali.pdfVIP

a r X i v : q u a n t - p h / 0 3 0 8 0 7 1 v 1 1 2 A u g 2 0 0 3 vertical Comparison of LOQC C-sign gates with ancilla inefficiency and an improvement to functionality under these conditions A. P. Lund, T. B. Bell, and T. C. Ralph Centre for Quantum Computer Technology, Department of Physics University of Queensland, QLD 4072, Australia Fax: +61 7 3365 1242 Telephone: +61 7 3365 3412 email: lund@physics.uq.edu.au Abstract We compare three proposals for non-deterministic C-sign gates implemented using linear optics and conditional measurements with non-ideal ancilla mode production and detection. The simpli- fied KLM gate [Ralph et al, Phys.Rev.A 65, 012314 (2001)] appears to be the most resilient under these conditions. We also find that the operation of this gate can be improved by adjusting the beamsplitter ratios to compensate to some extent for the effects of the imperfect ancilla. 1 I. INTRODUCTION Linear optics Quantum Computation (LOQC) [1] offers an elegant way of implementing quantum gates on optical qubits using the inherent non-linearity of conditional measure- ments. This is achieved by introducing ancilla photons which interact with the linear circuit and are then detected. However, it has been shown that the accuracy of the gate operation is strongly dependent on the quality of the detectors used to detect the ancilla photons [2]. Three distinct architectures have now been suggested for implementing the fundamental two qubit gate, the control-sign (C-sign) [3, 4, 5]. It is natural to ask firstly whether all these architectures are equally sensitive to ancilla detector efficiency and secondly if it is possible to optimize gate operation to counter (to some extent) the effects of detector inefficiency. In this paper we address these questions and include in our analysis the converse issue of inefficiency in ancilla production. We begin in section II by presenting our analysis technique. In section III we introduce the three versions of the C-sign g