Measurement-induced landscape transitions in hybrid variational quantum circuits

• URL: http://arxiv.org/abs/2312.09135v1
• Date: Thu, 14 Dec 2023 17:07:24 GMT
• Title: Measurement-induced landscape transitions in hybrid variational quantum circuits
• Authors: Sonny Rappaport, Gaurav Gyawali, Tiago Sereno, Michael J. Lawler
• Abstract summary: We show two transitions, a measurement-induced landscape transition (MILT) and a measurement-induced phase transition (MIPT) Our results show there are two transitions, a measurement-induced landscape transition (MILT) that seems universal across different VQA ansatzes and appears at a lower probability of measurements, and the MIPT that appears at a higher probability of measurements.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The entanglement-induced barren plateau phenomenon is an exponential vanishing of the parameter gradients with system size that limits the use of variational quantum algorithms(VQA). Recently, it was observed that a landscape transition from a barren plateau to no barren plateau occurs if the volume-law growth of entanglement is suppressed by adding measurements with post-selection. This suppression appears to coincide with a measurement-induced phase transition (MIPT) that measurements are known to cause in monitored circuits. From an information theory perspective, we argue that these are different transitions. We back this hypothesis with a numerical study of the cost landscape of such hybrid variational quantum circuits with extensive results on the behavior of cost-gradient variances with and without post-selection, direct visualizations of optimization runs for specific local quantum circuits, and a mutual information measure we introduce and compare with entanglement measures used in the study of MIPT. Specifically, our results show there are two transitions, a measurement-induced landscape transition (MILT) that seems universal across different VQA ansatzes and appears at a lower probability of measurements, and the MIPT that appears at a higher probability of measurements and appears at an ansatz specific location. Finally, to reap the benefits of MILT for optimization, our numerical simulations suggest the necessity of post-selecting measurement outcomes.

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