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We present, QP-SBGD, a novel layer-wise stochastic optimiser tailored towardstraining neural networks with binary weights, known as binary neural networks(BNNs), on quantum hardware. BNNs reduce the computational requirements andenergy consumption of deep learning models with minimal loss in accuracy.However, training them in practice remains to be an open challenge. Most knownBNN-optimisers either rely on projected updates or binarise weightspost-training. Instead, QP-SBGD approximately maps the gradient onto binaryvariables, by solving a quadratic constrained binary optimisation. Underpractically reasonable assumptions, we show that this update rule convergeswith a rate of $\mathcal{O}(1 / \sqrt{T})$. Moreover, we show how the$\mathcal{NP}$-hard projection can be effectively executed on an adiabaticquantum annealer, harnessing recent advancements in quantum computation. Wealso introduce a projected version of this update rule and prove that if afixed point exists in the binary variable space, the modified updates willconverge to it. Last but not least, our algorithm is implemented layer-wise,making it suitable to train larger networks on resource-limited quantumhardware. Through extensive evaluations, we show that QP-SBGD outperforms or ison par with competitive and well-established baselines such as BinaryConnect,signSGD and ProxQuant when optimising the Rosenbrock function, training BNNs aswell as binary graph neural networks.

Projected Stochastic Gradient Descent with Quantum Annealed Binary Gradients