Quantum error cancellation in photonic systems -- undoing photon losses

TL;DR

This paper introduces a quantum error mitigation protocol for photonic systems that can undo photon losses in expectation value estimation, using a probabilistic approach inspired by error cancellation techniques, validated through simulations.

Contribution

It develops a novel error mitigation protocol for continuous variable photonic systems that counteracts photon losses without full fault tolerance.

Findings

The protocol can effectively undo photon losses in expectation value estimation.

It requires a noiseless amplification and photon-subtractions, which can be probabilistically implemented.

Simulations on various quantum states validate the protocol's effectiveness.

Abstract

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.