Abstract
We propose a scalable approach to building cluster states of matter qubits using coherent states of light. Recent work on the subject relies on the use of single photonic qubits in the measurement process. These schemes can be made robust to detector loss, spontaneous emission and cavity mismatching but as a consequence the overhead costs grow rapidly, in particular when considering single photon loss. In contrast, our approach uses continuous variables and highly efficient homodyne measurements. We present a two-qubit scheme, with a simple bucket measurement system yielding an entangling operation with success probability 1/2. Then we extend this to a three-qubit interaction, increasing this probability to 3/4. We discuss the important issues of the overhead cost and the time scaling. This leads to a ‘no-measurement’ approach to building cluster states, making use of geometric phases in phase space.
Highlights
The intriguing idea of one-way or cluster state quantum computing was initially developed by Briegel and Raussendorf [1]
In this paper we have considered the usefulness of weak non-linearities in the building of matter qubit cluster states enabling us to work in the success probability regime of p ≥ 1/2
We first developed a 2-qubit parity check, based on a single non-linearity per qubit and a simple measurement of the probe bus. At this point we already noticed the advantage of using continuous variables to mediate an interaction between the qubits and to provide us with an efficient measurement system
Summary
The intriguing idea of one-way or cluster state quantum computing was initially developed by Briegel and Raussendorf [1]. The logical gates are prepared off-line and imprinted onto the qubits as they are transmitted through the cluster This approach was quickly applied [2,3,4,5,6] to linear optics quantum computing [7] and was experimentally demonstrated on the scale of several qubits (see the review [8] for a full set of references). A further issue is that in order for some solid state qubits to interact directly, they may need to be in such close proximity that application of individual control fields and measurements becomes infeasible To overcome these problems, the concept of distributed quantum computing has arisen, in which interactions between the qubits used in a computation is mediated by a third party. In this paper we will show how this and other factors make continuous variables a very powerful tool for growing cluster states
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