Implementing quantum algorithms on temporal photonic cluster states

TL;DR

This paper explores implementing three quantum algorithms on temporal photonic cluster states, focusing on measurement-based operations, non-Gaussian state preparation, and error correction, advancing scalable quantum computation with continuous variables.

Contribution

It introduces methods for implementing Gaussian and non-Gaussian gates, including the cubic phase gate and inversion operator, within a temporal cluster state framework, enabling scalable quantum algorithms.

Findings

Gaussian Boson Sampling can be scaled with moderate online squeezing.

Methods for implementing non-Gaussian gates are integrated into the architecture.

Simulation of resource states demonstrates feasibility of the proposed algorithms.

Abstract

Implementing quantum algorithms is essential for quantum computation. We study the implementation of three quantum algorithms by performing homodyne measurements on a two-dimensional temporal continuous-variable cluster state. We first review the generation of temporal cluster states and the implementation of gates using the measurement-based model. Alongside this we discuss methods to introduce non-Gaussianity into the cluster states. The first algorithm we consider is Gaussian Boson Sampling in which only Gaussian unitaries need to be implemented. Taking into account the fact that input states are also Gaussian, the errors due to the effect of finite squeezing can be corrected, provided a moderate amount of online squeezing is available. This helps to construct a large Gaussian Boson Sampling machine. The second algorithm is the continuous-variable Instantaneous Quantum Polynomial circuit in which one needs to implement non-Gaussian gates, such as the cubic phase gate. We discuss several methods of implementing the cubic phase gate and fit them into the temporal cluster state architecture. The third algorithm is the continuous-variable version of Grover's search algorithm, the main challenge of which is the implementation of the inversion operator. We propose a method to implement the inversion operator by injecting a resource state into a teleportation circuit. The resource state is simulated using the Strawberry Fields quantum software package.