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Parameterized Quantum Circuits (PQC) are drawing increasing research interestthanks to its potential to achieve quantum advantages on near-term NoisyIntermediate Scale Quantum (NISQ) hardware. In order to achieve scalable PQClearning, the training process needs to be offloaded to real quantum machinesinstead of using exponential-cost classical simulators. One common approach toobtain PQC gradients is parameter shift whose cost scales linearly with thenumber of qubits. We present QOC, the first experimental demonstration ofpractical on-chip PQC training with parameter shift. Nevertheless, we find thatdue to the significant quantum errors (noises) on real machines, gradientsobtained from naive parameter shift have low fidelity and thus degrading thetraining accuracy. To this end, we further propose probabilistic gradientpruning to firstly identify gradients with potentially large errors and thenremove them. Specifically, small gradients have larger relative errors thanlarge ones, thus having a higher probability to be pruned. We perform extensiveexperiments with the Quantum Neural Network (QNN) benchmarks on 5classification tasks using 5 real quantum machines. The results demonstratethat our on-chip training achieves over 90% and 60% accuracy for 2-class and4-class image classification tasks. The probabilistic gradient pruning bringsup to 7% PQC accuracy improvements over no pruning. Overall, we successfullyobtain similar on-chip training accuracy compared with noise-free simulationbut have much better training scalability. The QOC code is available in theTorchQuantum library.

QOC: Quantum On-Chip Training with Parameter Shift and Gradient Pruning