Regensburg 2022 – scientific programme

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QI: Fachverband Quanteninformation

QI 12: Quantum Computing and Algorithms

QI 12.3: Talk

Thursday, September 8, 2022, 15:30–15:45, H8

Optimal gradient estimation for variational quantum algorithms — •Lennart Bittel, Jens Watty, and Martin Kliesch — Heinrich Heine Universität, Düsseldorf

Variational quantum algorithms (VQAs) are a leading approach for achieving a practically relevant near-term quantum advantage. A bottleneck of this approach is the estimation of derivatives of a given energy functional w.r.t. the parameters of the underlying variational quantum circuit. The parameter shift rule and its extensions allow for such and estimation without systematic errors. However, due to the measurement shot noise, they can have a large statistical error. As a consequence, many measurement rounds are required, which result in non-optimal VQA run-times.

In this work, we reduce this measurement overhead by using a Bayesian estimation framework. For this, we use prior knowledge about the circuit to then determine optimal measurement settings that minimize the expected statistical and systematic errors simultaneously. With accurate priors, this approach can significantly outperform traditional methods. We test our estimation algorithm numerically for a common quantum approximate optimization algorithm (QAOA). For a desired estimation accuracy we can reduce the number of measurements by an order of magnitude compared to traditional estimation methods. This also leads to significantly improved convergence times for the gradient descent algorithm.