Enhancing Circuit Trainability with Selective Gate Activation Strategy

TL;DR

This work tackles the challenge of training variational quantum circuits under the tension between expressibility and trainability, a problem exacerbated by barren plateaus. It introduces selective gate activation strategies, with a novel Magnitude-based activation that prioritizes gates with larger parameter magnitudes, and compares it against fully random and gate-type random activations. Through 10-qubit VQE experiments on molecular Hamiltonians generated with PennyLane, Magnitude-based activation consistently achieves faster convergence and lower energy gaps, demonstrating robustness across activation percentages and minimal reliance on warm-up. The findings suggest that carefully choosing which gates to train can mitigate barren plateaus and enable more scalable quantum optimization on NISQ devices, with future work exploring adaptive and multi-gate activation schemes.

Abstract

Hybrid quantum-classical computing relies heavily on Variational Quantum Algorithms (VQAs) to tackle challenges in diverse fields like quantum chemistry and machine learning. However, VQAs face a critical limitation: the balance between circuit trainability and expressibility. Trainability, the ease of optimizing circuit parameters for problem-solving, is often hampered by the Barren Plateau, where gradients vanish and hinder optimization. On the other hand, increasing expressibility, the ability to represent a wide range of quantum states, often necessitates deeper circuits with more parameters, which in turn exacerbates trainability issues. In this work, we investigate selective gate activation strategies as a potential solution to these challenges within the context of Variational Quantum Eigensolvers (VQEs). We evaluate three different approaches: activating gates randomly without considering their type or parameter magnitude, activating gates randomly but limited to a single gate type, and activating gates based on the magnitude of their parameter values. Experiment results reveal that the Magnitude-based strategy surpasses other methods, achieving improved convergence.

Figures (4)

• Figure 1: An illustration of (a) fully random activation, (b) gate random activation strategy, and (c) magnitude-based activation where red-colored gates indicate selected gate. In (b), the RX gate is selected as the activated gate type, and in (c), the parameters with darker blue have a larger magnitude.
• Figure 2: Performance of strategies when $k$ varies from 10, 50, and 90. The shaded regions indicate one standard deviation ($[\mu-\sigma/2, \mu+\sigma/2]$). RA failed to train as more gates were activated, whereas Mag remained trainable even with up to $50\%$ gate usage.
• Figure 3: Performance of different strategies when $10\%$ of gates are selected. The shaded regions indicate one standard deviation ($[\mu-\sigma/2, \mu+\sigma/2]$).
• Figure 4: Convergence of Mag with different warm-up iteration numbers, 0, 100, 200, and 500. The shaded regions indicate one standard deviation ($[\mu-\sigma/2, \mu+\sigma/2]$).