Hui Zhang

We map the perfect matching problem in graph theory to a reconfigurable GBS model with the connection of the Hafnian of a matrix. We configure the linear optical circuit and squeeze parameter of the GBS model according to the decomposed unitary matrix and diagonal matrix of the graph’s adjacency matrix. The perfect matching numbers can be directly acquired from the 4-photon coincidence counts with a distribution similarity of 0.9304.

We design and fabricate a quantum photonic circuit to generate a 4-qubit state to load single qubit information and implement a quantum error correction code to demonstrate its capability of detecting and correcting a single-bit error. The encoded quantum information can be reconstructed from different types of errors and achieve an average state fidelity of 86%. We further extend the scheme to demonstrate fault-tolerant measurement-based quantum computing that allows us to redo the qubit operation against the failure of the teleportation process.

Currently most quantum teleportation experiments are based on qubits. Here, we demonstrate a quantum autoencoder assisted teleportation for high-dimensional quantum states. Our method of training the autoencoder allows us to take a finite sample of those states, learn how to compress them to qubits with nearly unit fidelity. After training, we can teleport any further states from the sender and reconstruct them with high fidelity on the receiver part. We verify the proposed scheme by teleporting a qutrit via a silicon-photonic chip. High fidelity is achieved between the input qutrit and the qutrit recovered from the teleported qubit.