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arXiv · 2206.01982

Avoiding barren plateaus via transferability of smooth solutions in Hamiltonian Variational Ansatz

Antonio Anna Mele·Glen Bigan Mbeng·Giuseppe Ernesto Santoro·Mario Collura·Pietro Torta
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Abstract

A large ongoing research effort focuses on Variational Quantum Algorithms (VQAs), representing leading candidates to achieve computational speed-ups on current quantum devices. The scalability of VQAs to a large number of qubits, beyond the simulation capabilities of classical computers, is still debated. Two major hurdles are the proliferation of low-quality variational local minima, and the exponential vanishing of gradients in the cost function landscape, a phenomenon referred to as barren plateaus. Here we show that by employing iterative search schemes one can effectively prepare the ground state of paradigmatic quantum many-body models, circumventing also the barren plateau phenomenon. This is accomplished by leveraging the transferability to larger system sizes of iterative solutions, displaying an intrinsic smoothness of the variational parameters, a result that does not extend to other solutions found via random-start local optimization. Our scheme could be directly tested on near-term quantum devices, running a refinement optimization in a favorable local landscape with non-vanishing gradients.

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Antonio Anna Mele, Glen Bigan Mbeng, Giuseppe Ernesto Santoro, Mario Collura, Pietro Torta. 2023-01-02. Avoiding barren plateaus via transferability of smooth solutions in Hamiltonian Variational Ansatz. https://doi.org/10.1103/physreva.106.l060401

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