Introducing Non-Linearity into Quantum Generative Models
- URL: http://arxiv.org/abs/2205.14506v1
- Date: Sat, 28 May 2022 18:59:49 GMT
- Title: Introducing Non-Linearity into Quantum Generative Models
- Authors: Kaitlin Gili, Mykolas Sveistrys, Chris Ballance
- Abstract summary: We introduce a model that adds non-linear activations via a neural network structure onto the standard Born Machine framework.
We compare our non-linear QNBM to the linear Quantum Circuit Born Machine.
We show that while both models can easily learn a trivial uniform probability distribution, the QNBM achieves an almost 3x smaller error rate than a QCBM.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The evolution of an isolated quantum system is linear, and hence quantum
algorithms are reversible, including those that utilize quantum circuits as
generative machine learning models. However, some of the most successful
classical generative models, such as those based on neural networks, involve
highly non-linear and thus non-reversible dynamics. In this paper, we explore
the effect of these dynamics in quantum generative modeling by introducing a
model that adds non-linear activations via a neural network structure onto the
standard Born Machine framework - the Quantum Neuron Born Machine (QNBM). To
achieve this, we utilize a previously introduced Quantum Neuron subroutine,
which is a repeat-until-success circuit with mid-circuit measurements and
classical control. After introducing the QNBM, we investigate how its
performance depends on network size, by training a 3-layer QNBM with 4 output
neurons and various input and hidden layer sizes. We then compare our
non-linear QNBM to the linear Quantum Circuit Born Machine (QCBM). We allocate
similar time and memory resources to each model, such that the only major
difference is the qubit overhead required by the QNBM. With gradient-based
training, we show that while both models can easily learn a trivial uniform
probability distribution, on a more challenging class of distributions, the
QNBM achieves an almost 3x smaller error rate than a QCBM with a similar number
of tunable parameters. We therefore show that non-linearity is a useful
resource in quantum generative models, and we put forth the QNBM as a new model
with good generative performance and potential for quantum advantage.
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