Breaking the Shot-Noise Barrier: Cached Recycled Variance-Reduced Gradients for Quantum Optimization

arXiv:2609.38800 · quant-ph, math.OC · Submitted 2026-09-30 · Read on arXiv

quant-ph, math.OC

Submitted: 2026-09-30

Updated: 2026-09-30

Terminology

• Sample Complexity — 22× in this paper · explained in 15 episodes
• Parameter-Shift Rule — 11× in this paper
• Benchmark — 10× in this paper · explained in 2 episodes
• Objective Function — 10× in this paper · explained in 2 episodes
• Variational Quantum Algorithm — 9× in this paper
• Cached Recycled Variance-Reduced Gradient — 5× in this paper
• Simultaneous Perturbation Stochastic Approximation — 4× in this paper
• Stochastic Gradient Descent — 4× in this paper
• Accuracy — 3× in this paper · explained in 1 episode
• Robustness — 3× in this paper · explained in 5 episodes
• Variational Quantum Eigensolver — 3× in this paper
• Fisher Information — 2× in this paper · explained in 3 episodes
• Maximum Independent Set — 2× in this paper
• Quantum Approximate Optimization Algorithm — 2× in this paper
• Quantum Circuits — 2× in this paper · explained in 2 episodes
• Sequential Minimal Optimization — 2× in this paper
• Variational Quantum Eigensolver (VQE) — 2× in this paper · explained in 5 episodes
• Approximation Ratio (AR) — 1× in this paper · explained in 1 episode
• Combinatorial Optimization — 1× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Core — 1× in this paper · explained in 2 episodes
• Higher-order derivatives — 1× in this paper · explained in 2 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Lyapunov function — 1× in this paper · explained in 2 episodes
• Noisy Intermediate-Scale Quantum — 1× in this paper
• Quantum Physics — 1× in this paper · explained in 10 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Sample Complexity Scaling — 1× in this paper · explained in 2 episodes
• Stochastic Gradient Descent (SGD) — 1× in this paper · explained in 5 episodes
• Theoretical Guarantees — 1× in this paper · explained in 2 episodes
• Trace — 1× in this paper · explained in 2 episodes

Sources

• Operator Sampling for Shot-frugal Optimization in Variational Algorithms
• A Quantum Approximate Optimization Algorithm

Related papers

• Reconquering Bell sampling on qudits: stabilizer learning and testing, quantum pseudorandomness bounds, and more
• Encrypted clones can leak: Classification of informative subsets in Quantum Encrypted Cloning
• Polynomial-time classical and quantum simulation of quantum impurity models
• Theory of quantum-enhanced interferometry with general Markovian light sources
• A convergent hierarchy of spectral gap certificates for qubit Hamiltonians
• Universal Bound and Phase Transition in Many-Body Fermionic Non-Gaussianity