I discuss how numerical estimation schemes (such as the finite-difference and scaled parameter-shift strategies) can be beneficial to variational quantum algorithms (VQAs) when used correctly, and debunk a common consensus that these schemes are "bad" in comparison with analytical ones because of the presence of approximation errors. Quite the contrary, the additional parameter in numerical estimator should be optimized over to minimize the TOTAL statistical estimation error and what comes out is an optimal estimator that is compatible with circuit barren plateaus, which exist in typical circuits ansatze.
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Optimized numerical gradient and Hessian estimation for variational quantum algorithms
Phys. Rev. A 107, 042421 (2023): journals.aps.o...
It turns out that heuristic optimization of the numerical estimators can also be carried out for noisy circuits if the error rate $\eta$ is known. In this case, the scaled parameter-shift strategy is the method of choice.
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Robustness of optimized numerical estimation schemes for noisy variational quantum algorithms
Phys. Rev. A 109, 012620 (2024):
journals.aps.o...
Негізгі бет COMCAS2024: Optimized Numerical Estimation for Variational Quantum Algorithms
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