# Stochastic Gradient Line Bayesian Optimization for Efficient Noise-Robust Optimization of Parameterized Quantum Circuits

arXiv: https://arxiv.org/abs/2111.07952 · HTML: https://mlsanity.com/paper/2111.07952/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 97 references that are in the map.
- First posted on arXiv 15 Nov 2021.

## Builds on (most cited first, 27 of 27)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Scalable Bayesian Optimization Using Deep Neural Networks](https://mlsanity.com/paper/1502.05700/) (2015)
- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [High Dimensional Bayesian Optimisation and Bandits via Additive Models](https://mlsanity.com/paper/1503.01673/) (2015)
- [Quantum Natural Gradient](https://mlsanity.com/paper/1909.02108/) (2019)
- [Entanglement Induced Barren Plateaus](https://mlsanity.com/paper/2010.15968/) (2020)
- [Tight Analyses for Non-Smooth Stochastic Gradient Descent](https://mlsanity.com/paper/1812.05217/) (2018)
- [Adaptive and Safe Bayesian Optimization in High Dimensions via One-Dimensional Subspaces](https://mlsanity.com/paper/1902.03229/) (2019)
- [Quantum Recommendation Systems](https://mlsanity.com/paper/1603.08675/) (2016)
- [High-Dimensional Bayesian Optimization via Additive Models with Overlapping Groups](https://mlsanity.com/paper/1802.07028/) (2018)
- [Stochastic gradient descent for hybrid quantum-classical optimization](https://mlsanity.com/paper/1910.01155/) (2019)
- [An Analysis of Constant Step Size SGD in the Non-convex Regime: Asymptotic Normality and Bias](https://mlsanity.com/paper/2006.07904/) (2020)
- [A Progressive Batching L-BFGS Method for Machine Learning](https://mlsanity.com/paper/1802.05374/) (2018)
- [Low-depth gradient measurements can improve convergence in variational hybrid quantum-classical algorithms](https://mlsanity.com/paper/1901.05374/) (2019)
- [Coupling Adaptive Batch Sizes with Learning Rates](https://mlsanity.com/paper/1612.05086/) (2016)
- [Adaptive Sampling Strategies for Stochastic Optimization](https://mlsanity.com/paper/1710.11258/) (2017)
- [Probabilistic Line Searches for Stochastic Optimization](https://mlsanity.com/paper/1502.02846/) (2015)
- [Efficient estimation of Pauli observables by derandomization](https://mlsanity.com/paper/2103.07510/) (2021)
- [Optimizing quantum heuristics with meta-learning](https://mlsanity.com/paper/1908.03185/) (2019)
- [Optimal training of variational quantum algorithms without barren plateaus](https://mlsanity.com/paper/2104.14543/) (2021)
- [Adaptive shot allocation for fast convergence in variational quantum algorithms](https://mlsanity.com/paper/2108.10434/) (2021)
- [Learning with Optimized Random Features: Exponential Speedup by Quantum Machine Learning without Sparsity and Low-Rank Assumptions](https://mlsanity.com/paper/2004.10756/) (2020)
- [Exponential Error Convergence in Data Classification with Optimized Random Features: Acceleration by Quantum Machine Learning](https://mlsanity.com/paper/2106.09028/) (2021)

## Built on by (most cited first, 7 of 7)

- [QuACK: Accelerating Gradient-Based Quantum Optimization with Koopman Operator Learning](https://mlsanity.com/paper/2211.01365/) (2022)
- [BayeSQP: Bayesian Optimization through Sequential Quadratic Programming](https://mlsanity.com/paper/2602.03232/) (2026)
- [Quantum approximate optimization via learning-based adaptive optimization](https://mlsanity.com/paper/2303.14877/) (2023)
- [Lean classical-quantum hybrid neural network model for image classification](https://mlsanity.com/paper/2412.02059/) (2024)
- [CONGO: Compressive Online Gradient Optimization](https://mlsanity.com/paper/2407.06325/) (2024)
- [Bayesian Parameter Shift Rule in Variational Quantum Eigensolvers](https://mlsanity.com/paper/2502.02625/) (2025)
- [Gradient-based Sample Selection for Faster Bayesian Optimization](https://mlsanity.com/paper/2504.07742/) (2025)

## Abstract (arXiv)

Optimizing parameterized quantum circuits is a key routine in using near-term quantum devices. However, the existing algorithms for such optimization require an excessive number of quantum-measurement shots for estimating expectation values of observables and repeating many iterations, whose cost has been a critical obstacle for practical use. We develop an efficient alternative optimization algorithm, stochastic gradient line Bayesian optimization (SGLBO), to address this problem. SGLBO reduces the measurement-shot cost by estimating an appropriate direction of updating circuit parameters based on stochastic gradient descent (SGD) and further utilizing Bayesian optimization (BO) to estimate the optimal step size for each iteration in SGD. In addition, we formulate an adaptive measurement-shot strategy and introduce a technique of suffix averaging to reduce the effect of statistical and hardware noise. Our numerical simulation demonstrates that the SGLBO augmented with these techniques can drastically reduce the measurement-shot cost, improve the accuracy, and make the optimization noise-robust.