Evaluation of derivatives using approximate generalized parameter shift rule

TL;DR

This paper introduces an approximate generalized parameter shift rule (aGPSR) that efficiently estimates derivatives in quantum algorithms, especially on noisy hardware, reducing computational costs significantly while maintaining accuracy.

Contribution

The paper proposes aGPSR, a novel method that handles arbitrary device Hamiltonians and reduces the computational burden of derivative estimation in quantum algorithms.

Findings

aGPSR reduces expectation calls by up to 504 times in VQE tests.

aGPSR achieves exact target energies with fewer expectation calls.

The method is effective on systems with 3 to 6 qubits.

Abstract

Parameter shift rules are instrumental for derivatives estimation in a wide range of quantum algorithms, especially in the context of Quantum Machine Learning. Application of single-gap parameter shift rule is often not possible in algorithms running on noisy intermediate-scale quantum (NISQ) hardware due to noise effects and interaction between device qubits. In such cases, generalized parameter shift rules must be applied yet are computationally expensive for larger systems. In this paper we present the approximate generalized parameter rule (aGPSR) that can handle arbitrary device Hamiltonians and provides an accurate derivative estimation while significantly reducing the computational requirements. When applying aGPSR for a variational quantum eigensolver test case ranging from 3 to 6 qubits, the number of expectation calls is reduced by a factor ranging from 7 to 504 while reaching the exact same target energy, demonstrating its huge computational savings capabilities.