Adaptive Online Learning of Quantum States
This work addresses the challenge of tracking dynamic quantum states for quantum computing applications, representing an incremental advance in online learning methods for quantum systems.
The paper tackled the problem of learning evolving quantum states, known as shadow tomography, by applying adaptive online learning techniques to achieve polynomial regret bounds in the number of qubits and sublinear bounds in the number of measurements.
The problem of efficient quantum state learning, also called shadow tomography, aims to comprehend an unknown $d$-dimensional quantum state through POVMs. Yet, these states are rarely static; they evolve due to factors such as measurements, environmental noise, or inherent Hamiltonian state transitions. This paper leverages techniques from adaptive online learning to keep pace with such state changes. The key metrics considered for learning in these mutable environments are enhanced notions of regret, specifically adaptive and dynamic regret. We present adaptive and dynamic regret bounds for online shadow tomography, which are polynomial in the number of qubits and sublinear in the number of measurements. To support our theoretical findings, we include numerical experiments that validate our proposed models.