Novel Schemes for Measurement-Based Quantum Computation

We establish a framework which allows one to construct novel schemes for measurement-based quantum computation. The technique develops tools from many-body physics—based on finitely correlated or projected entangled pair states—to go beyond the cluster-state based one-way computer. We identify resource states radically different from the cluster state, in that they exhibit nonvanishing correlations, can be prepared using nonmaximally entangling gates, or have very different local entanglement properties. In the computational models, randomness is compensated in a different manner. It is shown that there exist resource states which are locally arbitrarily close to a pure state. We comment on the possibility of tailoring computational models to specific physical systems.

Figure 1

Two resources for universal measurement-based quantum computing. (a) depicts a weighted graph state, where solid lines correspond to a controlled $\pi$-phase gate, dashed lines to $\pi /2$. (b) represents a scheme deriving from an AKLT-type model. Dashed lines represent a state with nonvanishing correlation functions, solid lines correspond to $\pi$-phase gates in $\{|1⟩,|2⟩\}$.