Increasing efficiency of a linear-optical quantum gate using electronic feed-forward

We have successfully used fast electronic feed-forward to increase the probability of success of a linear optical implementation of a programmable phase gate from 25$\%$ to its theoretical limit of 50$\%$. The feed-forward applies a conditional unitary operation, which changes the incorrect output states of the data qubit to the correct ones. The gate itself rotates an arbitrary quantum state of the data qubit around the $z$ axis of the Bloch sphere with the angle of rotation being fully determined by the state of the program qubit. The gate implementation is based on fiber optics components. Qubits are encoded into spatial modes of single photons. The signal from the feed-forward detector is led directly to a phase modulator using only a passive voltage divider. We have verified the increase of the probability of success and characterized the gate operation by means of quantum process tomography. We have demonstrated that the use of feed-forward affects neither the process fidelity nor the output-state fidelities.

Figure 1

Scheme of the experiment. FC, fiber couplers; VRC, variable ratio couplers; PM, phase modulators; AG, air gaps; and D, detectors.

Figure 2

Choi matrix for the gate with the feed-forward when $\phi =\pi /2$ is encoded into the program qubit. The left top panel shows the real part of the reconstructed process matrix, and the left bottom one displays its imaginary part. The two right panels show the real and imaginary parts of the ideal matrix.

Figure 3

Choi matrix for the gate with the feed-forward when $\phi =\pi$ is encoded into the program qubit. The left top panel shows the real part of the reconstructed process matrix, and the left bottom one displays its imaginary part. The two right panels show the real and imaginary parts of the ideal matrix.