  Real photonic devices are subject to photon losses that can decohere quantum
information encoded in the system. In the absence of full fault tolerance,
quantum error mitigation techniques have been introduced to help manage errors
in noisy quantum devices. In this work, we introduce an error mitigation
protocol inspired by probabilistic error cancellation (a popular error
mitigation technique in discrete variable systems) for continuous variable
systems. We show that our quantum error cancellation protocol can undo photon
losses in expectation value estimation tasks. To do this, we analytically
derive the (non-physical) inverse photon loss channel and decompose it into a
sum over physically realisable channels with potentially negative coefficients.
The bias of our ideal expectation value estimator can be made arbitrarily small
at the cost of increasing the sampling overhead. The protocol requires a
noiseless amplification followed by a series of photon-subtractions. While
these operations can be implemented probabilistically, for certain classes of
initial state one can avoid the burden of carrying out the amplification and
photon-subtractions by leveraging Monte-Carlo methods to give an unbiased
estimate of the ideal expectation value. We validate our proposed mitigation
protocol by simulating the scheme on squeezed vacuum states, cat states and
entangled coherent states.
