Arbitrary multimode Gaussian operations on mechanical cluster states

Abstract

We consider opto- and electro-mechanical quantum systems composed of a driven cavity mode interacting with a set of mechanical resonators. It has been proposed that the latter can be initialized in arbitrary cluster states, including universal resource states for Measurement Based Quantum Computation (MBQC). We show that, despite the unavailability in this set-up of direct measurements over the mechanical resonators, computation can still be performed to a high degree of accuracy. In particular, it is possible to indirectly implement the measurements necessary for arbitrary Gaussian MBQC by properly coupling the mechanical resonators to the cavity field and continuously monitoring the leakage of the latter. We provide a thorough theoretical analysis of the performances obtained via indirect measurements, comparing them with what is achievable when direct measurements are instead available. We show that high levels of fidelity are attainable in parameter regimes within reach of present experimental capabilities.

12 pages, 8 figures

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Cited by in corpus (5)

• Linear-and-quadratic reservoir engineering of non-Gaussian states
• Solving quantum trajectories for systems with linear Heisenberg-picture dynamics and Gaussian measurement noise
• Estimation of squeezing in a nonlinear quadrature of a mechanical oscillator
• Continuous variable multipartite vibrational entanglement
• Generation of stable Gaussian cluster states in optomechanical systems with multifrequency drives