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arXiv:1303.5355 · New Journal of Physics

Compact Gaussian quantum computation by multi-pixel homodyne detection

Giulia Ferrini, Jean‐Pierre Gazeau, T. Coudreau, Claude Fabre, Nicolas Treps

Published Sep 10, 2013• 61 citations
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Abstract

We study the possibility of producing and detecting continuous variable cluster states in an extremely compact optical setup. This method is based on a multi-pixel homodyne detection system recently demonstrated experimentally, which includes classical data post-processing. It allows the incorporation of the linear optics network, usually employed in standard experiments for the production of cluster states, in the stage of the measurement. After giving an example of cluster state generation by this method, we further study how this procedure can be generalized to perform Gaussian quantum computation.

DOI
10.1088/1367-2630/15/9/093015

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Continuous-variable cluster states offer a potentially promising method of implementing a quantum computer. This paper extends and further refines theoretical foundations and protocols for experimental implementation. We give a cluster-state implementation of the cubic phase gate through photon detection, which, together with homodyne detection, facilitates universal quantum computation. In addition, we characterize the offline squeezed resources required to generate an arbitrary graph state through passive linear optics. Most significantly, we prove that there are universal states for which the offline squeezing per mode does not increase with the size of the cluster. Simple representations of continuous-variable graph states are introduced to analyze graph state transformations under measurement and the existence of universal continuous-variable resource states.
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ABSTRACT Measurement‐based quantum computing relies on the preparation of large‐scale multipartite entanglement, typically realized through cluster states. Quantum frequency combs provide a naturally multimode platform for constructing such states, yet prior pulse‐shaping methods are inherently sequential, thereby hindering scalability and making the reconstructed state vulnerable to system drifts. Here, we address this limitation by developing a multipixel homodyne detection scheme that enables the parallel characterization of quantum noise across multiple frequency modes and the single‐step reconstruction of the full covariance matrix, ensuring high measurement stability independent of long‐term system drifts. In an eight‐mode quantum frequency comb system, we experimentally determine sixteen entangled bipartitions (out of 127 possible bipartitions) and extract three squeezed supermodes via eigenmode decomposition of the covariance matrix. Through constructing linear optical networks in classical post‐processing, these resources enable the deterministic construction of cluster states ranging from one‐dimensional chains based on supermodes to three‐dimensional topological graphs formed by bipartite entangled pairs. The synergy between the parallel measurement capability of multipixel homodyne detection and the scalability of quantum frequency combs provides a compact and versatile platform for large‐scale, reconfigurable quantum information processing.