Journal
QUANTUM SCIENCE AND TECHNOLOGY
Volume 7, Issue 4, Pages -Publisher
IOP Publishing Ltd
DOI: 10.1088/2058-9565/ac7d06
Keywords
barren plateau; quantum computing; quantum machine learning; narrow gorge; variational algorithm
Funding
- U.S. Department of Energy (DOE), Office of Science, Office of High Energy Physics QuantISED program [DE-AC52-06NA25396]
- Los Alamos National Laboratory (LANL) ASC Beyond Moore's Law project
- Center for Nonlinear Studies at LANL
- U.S. DOE, Office of Science, Office of Advanced Scientific Computing Research, under the Accelerated Research in Quantum Computing (ARQC) program
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This research investigates the relationship between cost function landscapes of parameterized quantum circuits (PQCs). It is analytically proven that the phenomena of exponentially vanishing gradients, exponential cost concentration about the mean, and the exponential narrowness of minima occur together. The key implication of this result is that BPs can be diagnosed numerically through cost differences instead of computationally expensive gradients.
Optimizing parameterized quantum circuits (PQCs) is the leading approach to make use of near-term quantum computers. However, very little is known about the cost function landscape for PQCs, which hinders progress towards quantum-aware optimizers. In this work, we investigate the connection between three different landscape features that have been observed for PQCs: (1) exponentially vanishing gradients (called barren plateaus (BPs)), (2) exponential cost concentration about the mean, and (3) the exponential narrowness of minima (called narrow gorges). We analytically prove that these three phenomena occur together, i.e., when one occurs then so do the other two. A key implication of this result is that one can numerically diagnose BPs via cost differences rather than via the computationally more expensive gradients. More broadly, our work shows that quantum mechanics rules out certain cost landscapes (which otherwise would be mathematically possible), and hence our results could be interesting from a quantum foundations perspective.
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