Classical splitting of parametrized quantum circuits

Abstract

Abstract Barren plateaus appear to be a major obstacle for using variational quantum algorithms to simulate large-scale quantum systems or to replace traditional machine learning algorithms. They can be caused by multiple factors such as the expressivity of the ansatz, excessive entanglement, the locality of observables under consideration, or even hardware noise. We propose classical splitting of parametric ansatz circuits to avoid barren plateaus. Classical splitting is realized by subdividing an N qubit ansatz into multiple ansätze that consist of $$\mathcal {O}(\log N)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:mo>log</mml:mo> <mml:mi>N</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> qubits. We show that such an approach allows for avoiding barren plateaus and carry out numerical experiments, and perform binary classification on classical and quantum datasets. Moreover, we propose an extension of the ansatz that is compatible with variational quantum simulations. Finally, we discuss a speed-up for gradient-based optimization and hardware implementation, robustness against noise and parallelization, making classical splitting an ideal tool for noisy intermediate scale quantum (NISQ) applications.