Hybrid Quantum-Classical Approach to Reservoir Computing for Efficient Quantum State Classification and Tomography

Quantum reservoir computing is a modern paradigm in quantum information processing inspired by artificial neural networks [1]. The Quantum Reservoir Neural Network (QRNN) can solve tasks such as regression or classification in both classical and quantum domains. An integral part of the QRNN is a reservoir created by randomly coupled quantum nodes that process quantum input data and reveal hidden correlations in a way that classical algorithms can interpret. Nevertheless, due to the exponential scaling of computational complexity, simulating large-scale bosonic reservoirs by solving the Lindblad Master Equation is inefficient. In this study, we employ the Positive-P method [2] to simulate the dynamics of large (here with more than 15 bosonic nodes), high-density reservoirs. This study demonstrates that using a quantum reservoir coupled to a classical artificial neural network we can perform quantum tomography by predicting the Wigner quasi-probability distribution function of quantum states including coherent states, squeezed vacuum states, and Schrödinger’s cat states, across a broad range of parameters. Furthermore, we have shown that by utilizing the quantum-classical approach to reservoir computing an accuracy of over 96% in distinguishing between thermal, squeezed vacuum, and Schrödinger’s cat states can be achieved despite the comparable density of these states.

[1] S. Ghosh, A. Opala, et al., npj Quantum Inf 5 , 35 (2019).

[2] P. Deuar, A. Ferrier, et al., Phys. Rev. X Quantum 2, 010319 (2021).