Explicitly Quantum-parallel Computation by Displacements

We introduce an encoding of information in the relative displacement or photon number of different optical modes. Since the loss rate to interference is insensitive to squeezing and many non-Gaussian fluctuations, such a space is relatively protected from imperfections. We show that photon subtraction protocols can be used to create high-quality quantum superpositions of squeezed states with much higher fidelity than when the protocol is restricted to producing only cat states (superpositions of coherent states). We also show that the amount of squeezing and anti-squeezing introduced is moderate, and unlikely to dominate the photon number. This parallel processing allows for explicit use of non-Gaussian interference as opposed to the more incidental role played by non-Gaussianity in all-optical coherent Ising machines. A key observation we make is that displacements of optical states provide a convenient degree of freedom to encode information for quantum parallel processing. Furthermore, we discuss important considerations for realizing an optical quantum annealer based on differential photon number encoding. In particular, we discuss the need to perform quantum erasure on loss channels from interference, as well as the ability to correct degrees of freedom not used for the encoding without disrupting the processed quantum information.