A novel approach to reduce derivative costs in variational quantum algorithms

We present a detailed numerical study of an alternative approach, named Quantum Non-Demolition Measurement (QNDM), to efficiently estimate the gradients or the Hessians of a quantum observable. This is a key step and a resource-demanding task when we want to minimize the cost function associated with a quantum observable. In our detailed analysis, we account for all the resources needed to implement the QNDM approach with a fixed accuracy and compare them to the current state-of-the-art method. We find that the QNDM approach is more efficient, i.e. it needs fewer resources, in evaluating the derivatives of a cost function. These advantages are already clear in small dimensional systems and are likely to increase for practical implementations and more realistic situations. A significant outcome of our study is the implementation of the QNDM method in Python, provided in the supplementary material. Given that most Variational Quantum Algorithms can be formulated within this framework, our results can have significant implications in quantum optimization algorithms and make the QNDM approach a valuable alternative to implement Variational Quantum Algorithms on near-term quantum computers.

We present a detailed numerical study of an alternative approach, named quantum non-demolition measurement (QNDM) (Solinas et al 2023 Eur. Phys. J. D 77 76), to efficiently estimate the gradients or the Hessians of a quantum observable. This is a key step and a resource-demanding task when we want to minimize the cost function associated with a quantum observable. In our detailed analysis, we account for all the resources needed to implement the QNDM approach with a fixed accuracy and compare them to the current state-of-the-art method (Mari et al 2021 Phys. Rev. A 103 012405; Schuld et al 2019 Phys. Rev. A 99 032331; Cerezo et al 2021 Nat. Rev. Phys. 3 625). We find that the QNDM approach is more efficient, i.e. it needs fewer resources, in evaluating the derivatives of a cost function. These advantages are already clear in small dimensional systems and are likely to increase for practical implementations and more realistic situations. A significant outcome of our study is the implementation of the QNDM method in Python, provided in the supplementary material (Caletti and Minuto 2024 https://github.com/ simonecaletti/qndm-gradient). Given that most variational quantum algorithms (VQA) can be formulated within this framework, our results can have significant implications in quantum optimization algorithms and make the QNDM approach a valuable alternative to implement VQA on near-term quantum computers.