Quantifying resources for quantum computation with continuous-variables

Abstract

For quantum computers that employ continuous variables to have exponential computational advantage over classical computers, as well as good error-correcting components, quantum states with the property of being non-Gaussian need to be implemented. These, however, are often hard to create. One solution is to approximate them with states of lower stellar rank, with the accuracy of approximation calculated via stellar fidelity.

In this thesis, stellar fidelities of three different non-Gaussian states have been numerically computed using optimization programs in Python. It was found that: 1. For Fock states, it is more beneficial to use core states rather than single-component Fock states to approximate them. Further, as the n for Fock target states increases, the stellar fidelity of core states with stellar rank n − 1 follows an interesting pattern. 2. For binomial plus states, some of them, despite their stellar rank being high, resemble Gaussian states, which gives stellar fidelity measurements support as a complement to stellar rank. 3. Even cat states are dependent on the parameter α, which should be high for optimal error correction, but the stellar fidelity computations in this thesis show that stellar fidelity is lower when α increases. An interesting phase transition in the stellar profiles of cat states was also found.