Physics-inspired neural networks as quasi inverse of quantum channels

TL;DR

This paper demonstrates how neural networks can learn to approximate the quasi-inverse of quantum channels for qubits, ensuring the resulting operations are physically realizable as CPTP maps using a physics-inspired loss function.

Contribution

It introduces a neural network approach with a specialized loss function to find physically valid quasi-inverses of quantum channels across all parameters.

Findings

Neural networks successfully approximate quasi-inverses for various quantum channels.

The method ensures the quasi-inverse remains a CPTP quantum operation.

Quantum process tomography confirms the physical validity of the learned channels.

Abstract

Quantum channels are not invertible in general. A quasi-inverse allows for a partial recovery of the input state, but its analytical results are found only in a restricted space of its parameters. This work explores the potential of neural networks to find the quasi-inverse of qubit channels for any values of the channel parameters while keeping the quasi-inverse as a physically realizable quantum operation. We introduce a physics-inspired loss function based on the mean of the square of the modified trace distance (MSMTD). The scaled trace distance is used so that the neural network does not increase the length of the Bloch vector of the quantum states, which ensures that the network behaves as a completely positive and trace-preserving (CPTP) quantum channel. The Kraus operators of the quasi-inverse channel were obtained by performing quantum process tomography on the trained neural network.