[Paper Review] A quantum algorithm to train neural networks using low-depth circuits

Guillaume Verdon, Michael Broughton+1 more|arXiv (Cornell University)|Dec 14, 2017

Quantum Computing Algorithms and ArchitectureComputer Science1 references83 citations

TL;DR

The paper introduces the Quantum Approximate Boltzmann Machine (QABoM) that uses low-depth QAOA-based circuits to generate approximate Gibbs samples for training quantum Boltzmann machines on noisy near-term devices, with randomized clamping improving learning.

ABSTRACT

Can near-term gate model based quantum processors offer quantum advantage for practical applications in the pre-fault tolerance noise regime? A class of algorithms which have shown some promise in this regard are the so-called classical-quantum hybrid variational algorithms. Here we develop a low-depth quantum algorithm to generative neural networks using variational quantum circuits. We introduce a method which employs the quantum approximate optimization algorithm as a subroutine in order produce then sample low-energy distributions of Ising Hamiltonians. We sample these states to train neural networks and demonstrate training convergence for numerically simulated noisy circuits with depolarizing errors of rates of up to $4\%$.

Motivation & Objective

• Motivate the use of classical-quantum hybrid variational algorithms for practical learning on pre-fault-tolerance quantum devices.
• Develop a low-depth quantum algorithm (QABoM) to generate approximate thermal distributions for neural network training.
• Demonstrate training convergence under depolarizing noise in numerically simulated circuits.
• Compare regular clamping with quantum randomized clamping (QRC) for improved learning performance.

Proposed method

• Use Quantum Approximate Optimization Algorithm (QAOA) as a subroutine to sample low-energy distributions of Ising Hamiltonians.
• Define a quantum variational thermalization objective via free energy minimization to approximate thermal states.
• Implement unclamped and clamped Gibbs sampling with full and partial cost/mixer Hamiltonians, respectively.
• Train Quantum Boltzmann Machines by updating weights with a bound-based rule derived from clamped/unclamped expectations.
• Introduce Quantum Randomized Clamping (QRC) to batch data using QRAM or classical randomization to accelerate training.
• Report numerical experiments simulating depolarizing noise and compare QABoM variations.

Experimental results

Research questions

• RQ1 Can near-term circuit-model quantum computers train neural networks by sampling approximate thermal distributions of Ising Hamiltonians?
• RQ2 Does a low-depth QAOA-based approach (QABoM) provide robust learning on noisy quantum devices compared to traditional clamping?
• RQ3 What is the impact of quantum randomized clamping (QRC) on training quality and convergence under realistic noise?
• RQ4 How do unclamped and clamped Gibbs sampling strategies compare in estimating gradients for Boltzmann-machine training?

Key findings

• QABoM enables training convergence for numerically simulated noisy circuits with depolarizing errors up to 4%.
• QRC outperforms regular clamping by producing weight updates that better approximate the KL gradient.
• Increasing measurements improves quantum expectation estimation accuracy, while deeper QAOA can be detrimental under fixed optimization effort in noisy regimes.
• Training with depolarizing noise at modest levels (≤1%) shows signs of convergence across tested scenarios.
• The approach demonstrates robustness of near-term quantum devices for energy-based neural network training in the RBM setting.