Speaker
Description
The quantum circuit Born machine (QCBM) built from an instantaneous quantum polynomial-time (IQP) circuit is classically trainable, while sampling from it is believed to be classically intractable. It is known that the ancilla-free circuit is trainable under suitable initializations, but not universal. Adding ancilla qubits enables universality, yet whether the ancilla-augmented circuit is trainable remains open.
We propose the mixed IQP-QCBM to address these issues. The mixed IQP-QCBM generalizes the ancilla-augmented circuit into a mixture of "branches" (independent ancilla-free IQP circuits with free mixture weights). We establish that, based on the trainability of branches, the mixed IQP-QCBM can be trained with three initializations (data-agnostic, global, and cluster).
The mixed IQP-QCBM also shows what we call "mode separation": the mixture is more expressive than an ancilla-free circuit alone when the branches generate different distributions, each covering a distinct mode. Moreover, the ancilla parameters' gradients are proportional to the separations among branch distributions. In particular, the cluster initialization supplies gradients by assigning each branch to a distinct data distribution.
Experiments on targets including 16-bit Gaussian blobs, Ising models, 484-bit D-Wave data, and 784-bit MNIST images corroborate our analysis. Adding ancillas lowers the test maximum mean discrepancy on every benchmark, and mixed IQP-QCBMs outperform classical restricted Boltzmann machines throughout. On the 16-bit targets, mixed IQP-QCBMs learn the target distribution almost indistinguishably. The trained branches generate distinct distributions in every run, and stronger separation among them correlates with a better fit to the target.
| Topic | Hybrid quantum-classical approaches for learning and optimization |
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| Additional Topic | Quantum variational circuits and their applications |