Improving photon detector efficiency using a high-fidelity optical controlled-not gate

A significant problem for optical quantum computing is inefficient or inaccurate photodetectors. It is possible to use controlled-not (cnot) gates to improve a detector by making a large cat state, then measuring every qubit in that state. In this paper we develop a code that compares five different schemes for making multiple measurements, some of which are capable of detecting loss and some of which are not. We explore how each of these schemes performs in the presence of different errors, and derive a formula to find at what probability of qubit loss it is worth detecting loss, and at what probability does this just lead to further errors than the loss introduces.

Figure 1

Five possible schemes for detecting the state of a qubit in the $|0\rangle$, $|1\rangle$ basis. Circuits (a) and (d) have no loss detection, while circuits (b), (c), and (e) can detect loss.

Figure 2

How the five detection schemes discussed in Sec. 4 perform with respect to the number of detectors in the circuit. The qubit we are detecting is initially in the state $|1\rangle$ and always present, the detector error is $0.1$, while the Pauli error on the cnot and $X$ gates is 0.001. The qubits used for detection are present with a $0.999$ probability, while the photon we are trying to detect is always present.

Figure 3

Here we see how the five techniques perform in the presence of different values of loss. Here we have a detector error of $0.1$ and the probability of a Pauli error or loss error in the $X$ and cnot gate is $0.001$.