Journal
PHYSICAL REVIEW B
Volume 100, Issue 19, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.100.195125
Keywords
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Funding
- NSERC
- Canada Research Chair program
- Perimeter Institute for Theoretical Physics
- government of Canada through the Department of Innovation, Science and Economic Development Canada
- province of Ontario through the Ministry of Economic Development, Job Creation and Trade
- Simons Foundation
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Generative modeling with machine learning has provided a new perspective on the data-driven task of reconstructing quantum states from a set of qubit measurements. As increasingly large experimental quantum devices are built in laboratories, the question of how these machine learning techniques scale with the number of qubits is becoming crucial. We empirically study the scaling of restricted Boltzmann machines (RBMs) applied to reconstruct ground-state wave functions of the one-dimensional transverse-field Ising model from projective measurement data. We define a learning criterion via a threshold on the relative error in the energy estimator of the machine. With this criterion, we observe that the number of RBM weight parameters required for accurate representation of the ground state in the worst case - near criticality - scales quadratically with the number of qubits. By pruning small parameters of the trained model, we find that the number of weights can be significantly reduced while still retaining an accurate reconstruction. This provides evidence that overparametrization of the RBM is required to facilitate the learning process.
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