Quantum computing of analytical functions by linear optics methods

Abstract

We propose a model for computing of a certain set of analytical functions based on estimating the output distribution of multiphoton outcomes in an optical scheme with an initial single-mode squeezed vacuum (SMSV) state and photonic states measuring the number of photons in one of the output modes of the beam splitter (BS) by photon number resolving (PNR) detector. The set of considered analytical functions is polynomial expressions including arbitrary derivatives of certain functions which can take on very large values even on small interval in their argument and small values of the parameter indicating the number of the subtracted photons. The large values that the analytic functions can take are offset by a very small term including the factorial of the number of subtracted photons, which guarantees an output normalized distribution of multiphoton measurement outcomes. The quantum computing algorithm makes it possible to find the values of the analytical functions for each number of extracted photons after a sufficiently large number of trials that would allow replacing the measurement repetition rate of multiphoton events by their probabilities. Changing the initial parameters (squeezing amplitude of the SMSV state and BS parameter) makes it possible to implement calculations of the functions over the entire (or, at least, significant) continuous interval of alteration in their argument. The potential of optical quantum computing based on nonclassical states of a certain parity can be expanded both by adding new optical elements such as BSs, and by using other continuous variable (CV) states of definite parity.