# Quantum Algorithms for Structured Prediction

arXiv: https://arxiv.org/abs/1809.04091 · HTML: https://mlsanity.com/paper/1809.04091/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Sep 2018.

## Built on by (most cited first, 1 of 1)

- [Stochastic Security as a Performance Metric for Quantum-enhanced Generative AI](https://mlsanity.com/paper/2305.07973/) (2023)

## Abstract (arXiv)

We introduce two quantum algorithms for solving structured prediction problems. We first show that a stochastic gradient descent that uses the quantum minimum finding algorithm and takes its probabilistic failure into account solves the structured prediction problem with a runtime that scales with the square root of the size of the label space, and in widetilde Oleft(1/εright) with respect to the precision, ε, of the solution. Motivated by robust inference techniques in machine learning, we then introduce another quantum algorithm that solves a smooth approximation of the structured prediction problem with a similar quantum speedup in the size of the label space and a similar scaling in the precision parameter. In doing so, we analyze a variant of stochastic gradient descent for convex optimization in the presence of an additive error in the calculation of the gradients, and show that its convergence rate does not deteriorate if the additive errors are of the order O(√ε). This algorithm uses quantum Gibbs sampling at temperature Omega (ε) as a subroutine. Based on these theoretical observations, we propose a method for using quantum Gibbs samplers to combine feedforward neural networks with probabilistic graphical models for quantum machine learning. Our numerical results using Monte Carlo simulations on an image tagging task demonstrate the benefit of the approach.