Universal measurement-based quantum computation with opto-mechanical systems

Quantum computation over continuous variables using the measurement-based approach has recently attracted much attention. This approach allows to process quantum information provided a suitable entangled state —dubbed... [ view full abstract ]

Quantum computation over continuous variables using the measurement-based approach has recently attracted much attention. This approach allows to process quantum information provided a suitable entangled state —dubbed cluster state— is used as a resource and additional measurements are locally performed over its constituents. Despite the limitations of finite squeezing, this model has been theoretically proven to be fault tolerant.

Much effort has been devoted towards the generation of cluster states constituted of light modes. However, recent advances have shown that various types of massive mechanical oscillators can operate in the quantum regime, promoting these systems to interesting candidates for quantum technologies. In this context, the aim of the present work is to introduce a scheme to generate, verify, and process information over mechanical oscillators.

We consider electro-mechanical quantum systems composed of a driven microwave cavity interacting with a set of mechanical resonators (see Figure). We show that this set-up is rich enough to allow for (i) the generation of universal continuous-variable cluster states, (ii) their tomographic reconstruction, and (iii) universal measurement-based quantum computation. In particular, we first introduce a scheme for generating continuous-variable cluster states of arbitrary size and shape. The main feature of this scheme is that the cluster states are hosted in the mechanical degrees of freedom, which are dissipatively driven to the desired target state via a multi-tone drive of the cavity mode. Second, we show that, designing a suitable interaction profile between the cavity mode and the mechanical resonators, the statistics of an arbitrary mechanical quadrature can be encoded in the cavity field, which can then be measured. This in turn allows for the full tomographic reconstruction of the resonators state. Then, exploiting again measurements of the cavity field only, we provide a method to realize the measurements over the mechanical cluster state needed to perform arbitrary Gaussian gates. Finally, we show how universal quantum computation can be attained by making use of cubic non-linearities to generate a universal non-Gaussian gate. The collection of these results promotes nano- and micro-resonators to valid candidates for quantum computation over continuous variables.