Accelerating NISQ variational methods using geometry

Touheed Anwar Atif; Uchenna Chukwu; Jesse Berwald; Raouf Dridi

doi:10.1117/12.2655793

8 March 2023 Accelerating NISQ variational methods using geometry

Touheed Anwar Atif, Uchenna Chukwu, Jesse Berwald, Raouf Dridi

Author Affiliations +

Proceedings Volume 12446, Quantum Computing, Communication, and Simulation III; 1244607 (2023) https://doi.org/10.1117/12.2655793
Event: SPIE Quantum West, 2023, San Francisco, California, United States

Abstract

We consider the Quantum Natural Gradient Descent (QNGD) scheme which was recently proposed to train variational quantum algorithms. QNGD is Steepest Gradient Descent (SGD) operating on the complex projective space equipped with the Fubini-Study metric. Here we present an adaptive implementation of QNGD based on Armijo’s rule, which is an efficient backtracking line search that enjoys a proven convergence. The proposed algorithm is tested using noisy simulators on three different models with various initializations. Our results show that Adaptive QNGD dynamically adapts the step size and consistently outperforms the original QNGD, which requires knowledge of optimal step size to perform competitively. In addition, we show that the additional complexity involved in performing the line search in Adaptive QNGD is minimal, ensuring the gains provided by the proposed adaptive strategy dominates any increase in complexity. Additionally, our benchmarking demonstrates that a simple SGD algorithm (implemented in the Euclidean space) equipped with the adaptive scheme above, can yield performances similar to the QNGD scheme with optimal step size. Our results are yet another confirmation of the importance of differential geometry in variational quantum computations. As a matter of fact, we foresee advanced mathematics to play a prominent role in the NISQ era in guiding the design of faster and more efficient algorithms.

Citation Download Citation

Touheed Anwar Atif, Uchenna Chukwu, Jesse Berwald, and Raouf Dridi "Accelerating NISQ variational methods using geometry", Proc. SPIE 12446, Quantum Computing, Communication, and Simulation III, 1244607 (8 March 2023); https://doi.org/10.1117/12.2655793

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KEYWORDS

Hydrogen

Machine learning

Quantum entanglement

Quantum space

Quantum states

Quantum machine learning

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