Quantum Divide and Conquer for Classical Shadows

Classical shadow tomography is a sample-efficient technique for characterizing a quantum system and predicting many of their properties. Circuit cutting is a technique for dividing large quantum circuits into smaller fragments that can be executed more robustly using fewer quantum resources. We introduce a divide-and-conquer circuit cutting method for estimating the expectation values of observables using classical shadows. We derive a general formula for making predictions using the classical shadows of circuit fragments from arbitrarily cut circuits. In addition, we provide the sample complexity required to estimate an observable to a desired additive error with high probability. Lastly, we numerically show that our divide-and-conquer method outperforms traditional uncut shadow tomography when estimating high-weight observables that act nontrivially on many qubits, and discuss the mechanisms for this advantage.