# Variational Quantum Optimization with Continuous Bandits

arXiv: https://arxiv.org/abs/2502.04021 · HTML: https://mlsanity.com/paper/2502.04021/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 46 references that are in the map.
- First posted on arXiv 6 Feb 2025.

## Builds on (most cited first, 18 of 18)

- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Optimal Best Arm Identification with Fixed Confidence](https://mlsanity.com/paper/1602.04589/) (2016)
- [Connecting ansatz expressibility to gradient magnitudes and barren plateaus](https://mlsanity.com/paper/2101.02138/) (2021)
- [Estimating means of bounded random variables by betting](https://mlsanity.com/paper/2010.09686/) (2020)
- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [Quantum circuit architecture search for variational quantum algorithms](https://mlsanity.com/paper/2010.10217/) (2020)
- [Effect of barren plateaus on gradient-free optimization](https://mlsanity.com/paper/2011.12245/) (2020)
- [Does provable absence of barren plateaus imply classical simulability?](https://mlsanity.com/paper/2312.09121/) (2023)
- [Non-Asymptotic Pure Exploration by Solving Games](https://mlsanity.com/paper/1906.10431/) (2019)
- [Lipschitz Bandits: Regret Lower Bounds and Optimal Algorithms](https://mlsanity.com/paper/1405.4758/) (2014)
- [A Survey on Practical Applications of Multi-Armed and Contextual Bandits](https://mlsanity.com/paper/1904.10040/) (2019)
- [Escaping from the Barren Plateau via Gaussian Initializations in Deep Variational Quantum Circuits](https://mlsanity.com/paper/2203.09376/) (2022)
- [Challenges and Opportunities in Quantum Optimization](https://mlsanity.com/paper/2312.02279/) (2023)
- [Multi-armed Bandits with Application to 5G Small Cells](https://mlsanity.com/paper/1510.00627/) (2015)
- [Pure Exploration in Bandits with Linear Constraints](https://mlsanity.com/paper/2306.12774/) (2023)
- [Adaptive-treed bandits](https://mlsanity.com/paper/1302.2489/) (2013)
- [Learning pure quantum states (almost) without regret](https://mlsanity.com/paper/2406.18370/) (2024)
- [Certified Multi-Fidelity Zeroth-Order Optimization](https://mlsanity.com/paper/2308.00978/) (2023)

## Built on by (most cited first, 2 of 2)

- [Generative flow-based warm start of the variational quantum eigensolver](https://mlsanity.com/paper/2507.01726/) (2025)
- [Balancing Expressivity and Learnability in Quantum Kernel Bandit Optimization](https://mlsanity.com/paper/2607.01080/) (2026)

## Abstract (arXiv)

We introduce a novel approach to variational Quantum algorithms (VQA) via continuous bandits. VQA are a class of hybrid Quantum-classical algorithms where the parameters of Quantum circuits are optimized by classical algorithms. Previous work has used zero and first order gradient based methods, however such algorithms suffer from the barren plateau (BP) problem where gradients and loss differences are exponentially small. We introduce an approach using bandits methods which combine global exploration with local exploitation. We show how VQA can be formulated as a best arm identification problem in a continuous space of arms with Lipschitz smoothness. While regret minimization has been addressed in this setting, existing methods for pure exploration only cover discrete spaces. We give the first results for pure exploration in a continuous setting and derive a fixed-confidence, information-theoretic, instance specific lower bound. Under certain assumptions on the expected payoff, we derive a simple algorithm, which is near-optimal with respect to our lower bound. Finally, we apply our continuous bandit algorithm to two VQA schemes: a PQC and a QAOA quantum circuit, showing that we significantly outperform the previously known state of the art methods (which used gradient based methods).