Improved Quantum Computation using Operator Backpropagation

TL;DR

This paper introduces a hybrid quantum-classical framework that reduces quantum circuit depth by partitioning circuits and using classical backpropagation, leading to more accurate observable estimates in quantum simulations.

Contribution

It presents a novel operator backpropagation method that combines classical and quantum computations to improve quantum simulation accuracy.

Findings

Reduced quantum circuit depth achieved

More accurate expectation value estimates

Effective on Hamiltonian simulation problems

Abstract

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 an observable's expectation value by reducing the quantum circuit depth. 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 Schr\"odinger evolution run on quantum processors. The overall effect is to reduce the depths of the circuits executed on quantum devices, trading this with classical overhead and an increased number of circuit executions. We demonstrate the effectiveness of this method on a Hamiltonian simulation problem, achieving more accurate expectation value estimates compared to using quantum hardware alone.