Eric Anschuetz

Joshua Viszlai, Teague Tomesh, Pranav Gokhale et al.

Recent work has proposed and explored using coreset techniques for quantum algorithms that operate on classical data sets to accelerate the applicability of these algorithms on near-term quantum devices. We apply these ideas to Quantum Boltzmann Machines (QBM) where gradient-based steps which require Gibbs state sampling are the main computational bottleneck during training. By using a coreset in place of the full data set, we try to minimize the number of steps needed and accelerate the overall training time. In a regime where computational time on quantum computers is a precious resource, we propose this might lead to substantial practical savings. We evaluate this approach on 6x6 binary images from an augmented bars and stripes data set using a QBM with 36 visible units and 8 hidden units. Using an Inception score inspired metric, we compare QBM training times with and without using coresets.

Mikhail Mints, Eric Anschuetz

Hilbert space fragmentation is a phenomenon in which the Hilbert space of a quantum system is dynamically decoupled into exponentially many Krylov subspaces. We can define the Schur transform as a unitary operation mapping some set of preferred bases of these Krylov subspaces to computational basis states labeling them. We prove that this transformation can be efficiently learned via gradient descent from a set of training data using quantum neural networks, provided that the fragmentation is sufficiently strong such that the summed dimension of the unique Krylov subspaces is polynomial in the system size. To demonstrate this, we analyze the loss landscapes of random quantum neural networks constructed out of Hilbert space fragmented systems. We prove that in this setting, it is possible to eliminate barren plateaus and poor local minima, suggesting efficient trainability when using gradient descent. Furthermore, as the algebra defining the fragmentation is not known a priori and not guaranteed to have sparse algebra elements, to the best of our knowledge there are no existing efficient classical algorithms generally capable of simulating expectation values in these networks. Our setting thus provides a rare example of a physically motivated quantum learning task with no known dequantization.