Measurement reduction for expectation values via fine-grained commutativity
Ben DalFavero, Rahul Sarkar, Jeremiah Rowland, Daan Camps, Nicolas P. D. Sawaya, Ryan LaRose · Physical Review A · 2025
We introduce a notion of commutativity between operators on a tensor product space, nominally Pauli strings on qubits, that interpolates between qubitwise commutativity and (full) commutativity. We apply this notion, which we call $k$-commutativity, to measuring expectation values of observables in quantum circuits and show a reduction in the number measurements at the cost of increased circuit depth. We discuss the asymptotic measurement complexity of $k$-commutativity for several families of $n$-qubit Hamiltonians, showing examples with $O(1)$, $O(\sqrt{n})$, and $O(n)$ scaling.