# SPSA Hyperparameter Tuning for Variational Quantum Natural Language Inference

arXiv: https://arxiv.org/abs/2608.16939 · HTML: https://mlsanity.com/paper/2608.16939/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 27 references that are in the map.
- First posted on arXiv 11 Aug 2026.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Effect of barren plateaus on gradient-free optimization](https://mlsanity.com/paper/2011.12245/) (2020)
- [Foundations for Near-Term Quantum Natural Language Processing](https://mlsanity.com/paper/2012.03755/) (2020)
- [Quantum Natural Language Processing on Near-Term Quantum Computers](https://mlsanity.com/paper/2005.04147/) (2020)
- [Low-depth gradient measurements can improve convergence in variational hybrid quantum-classical algorithms](https://mlsanity.com/paper/1901.05374/) (2019)

## Abstract (arXiv)

Training variational quantum models requires choosing between parameter-shift gradients, which are exact but cost O(P) forward evaluations, and simultaneous perturbation stochastic approximation (SPSA), which uses only two samples but produces high-variance estimates that can degrade optimisation on small supervised tasks. Whether the cheap gradient is usable depends on the variance that results from different choices of the SPSA perturbation scale, learning rate, and gain-decay schedule. We varied those quantities across a broad grid on a 6-qubit, 60-parameter QNLI classifier and compared the best configurations to parameter-shift AdamW and BuresQNG. AdamW-style SPSA with c0=0.01, η=0.10, γ=0.10 reached 55% ± 11% test accuracy, improving over the default configuration (49% ± 6%) but remaining 16-19 percentage points below the parameter-shift baselines because the two-sample SPSA gradient estimate has too much variance for reliable optimisation of 60 parameters in 40 epochs. Classical-gain SPSA and Bures-preconditioned SPSA performed worse, at 51% and 46% respectively. Bures-preconditioning a noisy two-sample SPSA gradient amplifies perturbation noise.