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arXiv:1911.11511

Finding the optimal cluster state configuration. Cluster states classification by type of computations

S. B. Korolev, Golubeva T. Yu., Golubev Yu. M

Published Nov 26, 2019• 0 citations
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Abstract

In this paper, we study the transformations that are obtained in one-way quantum computation on continuous-variable cluster states of various configurations. Of all possible cluster configurations, we choose those that are suitable for universal Gaussian operations.
DOI
10.48550/arxiv.1911.11511

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Abstract In this paper, we estimate the errors of Gaussian transformations implemented using one-way quantum computations on cluster states of various configurations. From all possible cluster state configurations, we choose those that give the smallest computation error. Furthermore, we evaluate errors in hybrid computational schemes, in which Gaussian operations are performed using one-way computations with additional linear transformations. As a result, we find the optimal strategy for the implementation of universal Gaussian computations with minimal errors.
Simple examples that illustrate the principles of one-way quantum computation using Gaussian continuous-variable cluster states are given. In these examples, only single-mode evolutions, realizable via linear clusters, are considered. In particular, one can focus on Gaussian single-mode transformations performed through the cluster state. These examples highlight the differences between cluster-based schemes and protocols in which special quantum states are prepared off-line and then used as a resource for the on-line computation.
Continuous-variable (CV) cluster states are a universal quantum computing platform that has experimentally outscaled qubit platforms by orders of magnitude.Room-temperature implementation of CV cluster states has been achieved with quantum optics by using multimode squeezed Gaussian states.It has also been proven that fault tolerance thresholds for CV quantum computing can be reached at realistic squeezing levels.In this paper, we show that standard approaches to design and characterize CV cluster states can miss entanglement present in the system.Such hidden entanglement may be used to increase the power of a quantum computer but it can also, if undetected, hinder the successful implementation of a quantum algorithm.By a detailed analysis of the structure of Gaussian states, we derive an algorithm that reveals hidden entanglement in an arbitrary Gaussian state and optimizes its use for one-way quantum computing.
We describe a generalization of the cluster-state model of quantum computation to continuous-variable systems, along with a proposal for an optical implementation using squeezed-light sources, linear optics, and homodyne detection. For universal quantum computation, a nonlinear element is required. This can be satisfied by adding to the toolbox any single-mode non-Gaussian measurement, while the initial cluster state itself remains Gaussian. Homodyne detection alone suffices to perform an arbitrary multimode Gaussian transformation via the cluster state. We also propose an experiment to demonstrate cluster-based error reduction when implementing Gaussian operations.