Correcting and extending Trotterized quantum dynamics with a quantum-classical hybrid ansatz

A complex but important challenge in understanding quantum mechanical phenomena is the simulation of quantum many-body dynamics. Although quantum computers offer significant potential to accelerate these simulations, their practical application is currently limited by noise and restricted scalability. In this work, we address these problems by proposing a hybrid ansatz combining the strengths of quantum and classical computational methods. Using Trotterization, we evolve an initial state on the quantum computer according to a simplified Hamiltonian, focusing on terms that are difficult to simulate classically. A classical model then corrects the simulation by including the terms omitted in the quantum circuit.

We demonstrate three applications of this hybrid method. First, the method can avoid SWAP gates in the quantum circuit by restricting the quantum part of the ansatz to hardware-efficient terms of the Hamiltonian. Second, with an expressive classical ansatz, we can mitigate errors arising from the Trotterization of the Hamiltonian. Finally, we can extend the system size while keeping the number of qubits constant by including additional degrees of freedom in the classical ansatz.