Title: Improved Quantum Computations using Operator Backpropagation

Decoherence of quantum hardware is currently limiting its practical applications. At the same time, classical algorithms for simulating quantum circuits have progressed substantially. Here, we demonstrate a hybrid framework that integrates classical simulations with quantum hardware to improve the computation of the expectation value of an observable. In this framework, a quantum circuit is partitioned into two subcircuits: one that describes the backpropagated Heisenberg evolution of an observable, executed on a classical computer, while the other is a Schroedinger evolution run on quantum processors. The overall effect is to reduce the depths of the circuits executed on the quantum device, trading this with increased number of circuits. We demonstrate the effectiveness of this method on a Hamiltonian simulation problem, achieving more accurate computation compared to using quantum hardware alone.