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Large gradients via correlation in random parameterized quantum circuits

Journal Article · · Quantum Science and Technology

Scaling of variational quantum algorithms to large problem sizes requires efficient optimization of random parameterized quantum circuits. For such circuits with uncorrelated parameters, the presence of exponentially vanishing gradients in cost function landscapes is an obstacle to optimization by gradient descent methods. In this work, we prove that reducing the dimensionality of the parameter space by utilizing circuit modules containing spatially or temporally correlated gate layers can allow one to circumvent the vanishing gradient phenomenon. Here, examples are drawn from random separable circuits and asymptotically optimal variational versions of Grover's algorithm based on the quantum alternating operator ansatz. In the latter scenario, our bounds on cost function variation imply a transition between vanishing gradients and efficient trainability as the number of layers is increased toward $$\mathcal{O}\left({2}^{n/2}\right)$$, the optimal oracle complexity of quantum unstructured search.

Research Organization:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
Grant/Contract Number:
89233218CNA000001
OSTI ID:
1764966
Report Number(s):
LA-UR--20-23818
Journal Information:
Quantum Science and Technology, Journal Name: Quantum Science and Technology Journal Issue: 2 Vol. 6; ISSN 2058-9565
Publisher:
IOPscienceCopyright Statement
Country of Publication:
United States
Language:
English

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Cited By (3)

The power of quantum neural networks journal June 2021
Adaptive pruning-based optimization of parameterized quantum circuits journal March 2021
Efficient trainability of linear optical modules in quantum optical neural networks text January 2020

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