Figure 4: Server implementing Z and X gates.

(a) Experimental setup. Ensembles of encrypted input states were generated by two EOMs driven by two Gaussian white noise sources. The encrypted quantum states were then sent to the server through a channel with transmittivity t simulated by a half-wave plate and a polarizing beam splitter. The server performed ensembles of displacements by using a second pair of modulators driven by independent Gaussian white noise generators. After sending the quantum state back to the client, the output of the quantum computer was decrypted by applying phase shifted modulations using the encryption noise only known to the client. (b) The signal-to-noise ratios of the phase quadrature measured by homodyne detection behind each stage of the protocol. An ensemble of coherent input states and gate displacements were used and the transmissivity of the channels was set to 1. The output of the homodyne detector was recorded by a spectrum analyser measuring zero span around 10.5 MHz with a resolution bandwidth of 300 kHz and a video bandwidth of 30 Hz. A small input state was prepared (red) and subsequently encrypted (green). Then a small displacement was performed by the server (yellow), acting as the gate. Afterwards the state was returned to the client for decryption (blue), which yields the output of the quantum computation. For comparison, we have recorded the outcome without encrypting the input (upper trace). The difference between these is indicative of the loss for signal-to-noise ratio from imperfect decryption. (c) Fidelities between the output state ensembles using quantum computation on encrypted states and using quantum computation on plain-text states versus the channel transmission t. Statistical error bars are smaller than the point size. The variation in the fidelities comes mainly from systematic errors in the fine tuning of the phase and gain settings of the decryption noise for optimal decryption.