Non-linear Amplifiers for Quantum State Readout

Dispersive readout has been established as an efficient non-demolition qubit measurement scheme in circuit QED. However, high-fidelity readout requires optimized quantum hardware, including high-gain, large dynamic range quantum-limited amplifiers, with optimal operating conditions that become increasingly complicated as the number of states and qubits increases. 

Recurrent neural networks have been employed for dispersive readout, allowing improvements in state classification, although with a costly training overhead. We instead consider the application of reservoir computing to qubit readout tasks, which forgoes hardware optimization in favor of a trained linear output layer [1, 2], efficiently trained by solving a simple convex optimization problem. We apply this framework to dispersive qubit readout using a SNAIL-based parametric amplifier. Particularly, we analyze the operation of this amplifier as a reservoir across complex dynamical regimes that are not conventionally considered for qubit readout. We find that the reservoir can be successfully applied to multi-state classification of qubits across these regimes, and outperforms standard linear filters while requiring only a fraction of the training data to achieve the same fidelity.