Guided-SPSA: Simultaneous Perturbation Stochastic Approximation assisted by the Parameter Shift Rule
CoRR(2024)
摘要
The study of variational quantum algorithms (VQCs) has received significant
attention from the quantum computing community in recent years. These hybrid
algorithms, utilizing both classical and quantum components, are well-suited
for noisy intermediate-scale quantum devices. Though estimating exact gradients
using the parameter-shift rule to optimize the VQCs is realizable in NISQ
devices, they do not scale well for larger problem sizes. The computational
complexity, in terms of the number of circuit evaluations required for gradient
estimation by the parameter-shift rule, scales linearly with the number of
parameters in VQCs. On the other hand, techniques that approximate the
gradients of the VQCs, such as the simultaneous perturbation stochastic
approximation (SPSA), do not scale with the number of parameters but struggle
with instability and often attain suboptimal solutions. In this work, we
introduce a novel gradient estimation approach called Guided-SPSA, which
meaningfully combines the parameter-shift rule and SPSA-based gradient
approximation. The Guided-SPSA results in a 15
of circuit evaluations required during training for a similar or better
optimality of the solution found compared to the parameter-shift rule. The
Guided-SPSA outperforms standard SPSA in all scenarios and outperforms the
parameter-shift rule in scenarios such as suboptimal initialization of the
parameters. We demonstrate numerically the performance of Guided-SPSA on
different paradigms of quantum machine learning, such as regression,
classification, and reinforcement learning.
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