Measurement-based Quantum Computation

Measurement-based quantum computation (MBQC) is one of the leading paradigms for the implementation of a quantum computer. In MBQC, a quantum computation is driven by sequences of measurements performed on an entangled quantum many-body state, whereby the pre-existing quantum correlations in this initial resource state are exploited for logical processing [1]. The most prominent example of such a quantum-many body state is the cluster state [2] which is a universal resource for quantum computation.

Measurement-based quantum computation
Any quantum computation can be realized by measuring the qubits of an entangled cluster state.

The development of the theory of MBQC, with a view to both fundamental and practical issues, has been one focus of research in the group. For example, we have explored the connection of the entanglement properties of the resource states with their quantum computational power, connections between the computational universality of resource graph states and the decidability of formal languages on the underlying graphs, and the application of methods from MBQC to classical statistical mechanics models [3]. 

Recently we have started to investigate schemes for hybrid quantum computation. Hybrid quantum computation combines elements from MBQC with other approaches, in particular the quantum circuit model, which exploits and combines the specific advantages of the different approaches. MBQC offers advantages beyond quantum computing, and is also a leading paradigm in the contexts of quantum communication, and quantum networks. To begin with, applying the concepts and the ideas of MBQC for quantum communication, including entanglement purification and the quantum repeater, has proven to be expedient. Using MBQC techniques, we have achieved a significant increase in the robustness of the protocols against noise as measured by the thresholds for fault-tolerant processing. The development of such (special purpose) small-scale quantum machines turns out to be very promising for practical applications, in particular in the context of quantum communication [4]. Furthermore, MBQC has proven to be the ideal architecture for protocols for secure delegated quantum computation (DQC). DQC is a relatively novel functionality, which is central in the quantum cloud computing networks. Here, a computation is delegated by a client to an untrusted remote server, while maintaining perfect privacy, and guaranteed correctness of the resulting computation. Importantly, the client is required to only have very modest quantum powers. In recent works in the group we have used the MQBC formalism to provide protocols for DQC which have the weakest requirements on the client to date [5].