Optimization of networks for measurement-based quantum computation

In this work we provide a recipe for mitigating the effects of finite squeezing, which affect the production of cluster states and the result of a measurement-based quantum computation in the continuous variable regime. To this aim, we derive a compact expression for the unitary matrix which describes the linear optics network that generates a certain cluster state from independently squeezed inputs. We show that this possesses tunable degrees of freedom, which can be exploited to minimize the noise effects. These strategies are readily implementable by several experimental groups.

Figure 1

Top: linear cluster state nullifier variances $\left\{{\Delta }^2{\widehat{\delta }}_i\right\}$ for a nonoptimized network (brown/gray), for the optimized network (yellow/light gray), as compared to the shot noise levels (black). Bottom: normalized nullifiers variances $\{{\Delta }^2{\widehat{\delta }}_i/{\Delta }^2{\widehat{\delta }}_i^0\}$ as a function of the iteration (“generation” in the language of evolutionary strategies) of the algorithm. Upper lines: The red (dark) line is ${\Delta }^2{\widehat{\delta }}_1/{\Delta }^2{\widehat{\delta }}_1^0$, the green (light) ${\Delta }^2{\widehat{\delta }}_3/{\Delta }^2{\widehat{\delta }}_3^0$. Lower lines: The blue (dark) is ${\Delta }^2{\widehat{\delta }}_2/{\Delta }^2{\widehat{\delta }}_2^0$, the cyan (light) line is ${\Delta }^2{\widehat{\delta }}_4/{\Delta }^2{\widehat{\delta }}_4^0$.

Figure 2

A MBQC scheme where a Fourier transform is implemented on an input state by attaching it to a linear cluster state and by performing measurements on the cluster modes.