Fast simulation of continuous-variable circuits for photonic quantum computing

A quantum computer could revolutionize the way we do science by providing a platform in which to simulate quantum physics, and perform certain tasks that are computationally hard on a classical computer. Optical systems operate at room temperature, and suffer much less from decoherence than solid-state-based systems, making them a promising platform for universal, fault-tolerant quantum computing. However, generating non-Gaussian continuous-variable (CV) quantum states of light, which are crucial components for enabling universality and fault-tolerance, is difficult in optics, because of a lack of naturally available non-Gaussian operations.

When designing and building CV optical circuits for the purpose of generating non-Gaussian states, it is important to consider the effect of component inefficiencies and noise, which harms the quality of the output states. Here, simulations play an important role in testing and optimizing the designs to mitigate these effects. However, the computational complexity of the simulations scales exponentially with the number of modes, which is exacerbated when representing mixed states, making the simulation of these protocols a non-trivial task.

In this thesis, I develop a numerical framework to simulate CV optical circuits by approximating non-Gaussian states as linear combinations of Gaussians (LCoG), which forms a bridge between the photon-number basis and the Gaussian formalism, leveraging its speed and efficiency.

Within the LCoG framework, I investigate the optimization of realistic optical GKP state preparation circuits for which I develop fast cost function evaluation algorithms. In addition, I show how to obtain the gradients of parametrized Gaussian circuits. As a second application of the methodology, I investigate the experimental feasibility of the cat breeding protocol for fault-tolerant GKP state preparation by simulating the breeding circuit with non-ideal input states and non-ideal measurement results, which is made possible in the LCoG framework. My findings show that the threshold of tolerable losses is very low, highlighting the need for the development of optical components with ultra-low loss.

In summary, the numerical framework, aims to expand the growing toolbox of simulation methods for CV quantum circuits. The framework makes possible the simulation of multi-mode mixed bosonic systems in which the complexity grows solely due to the application of non-Gaussian operations.