Quantum State Tomography with a Multi-Mode Reservoir

Quantum state tomography is a critical task in quantum information processing, but it remains experimentally demanding due to its reliance on repeated quantum state preparation and ensemble averaging. In this work focusing on the tomography of a single qubit, we present a reservoir computing framework that reduces the number of required qubit preparations compared with traditional tomography by leveraging the multi-mode structure of a reservoir. Our reservoir is a set of bosonic modes coupled by a three-wave-mixing interaction. A set of dynamical observables is extracted from the reservoir as one of its modes interacts with a qubit to reconstruct the qubit’s density matrix. Our simulations show that the information carried in the multi-mode correlations allows high-fidelity reconstruction of the qubit’s quantum state without qubit rotations. We also present simulations of sequential measurements on the reservoir during its evolution, exploiting temporal diversity to further reduce the number of state preparations. Our implementation offers a scalable and efficient pathway toward quantum state estimation.