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

• URL: http://arxiv.org/abs/2206.01982v2
• Date: Mon, 2 Jan 2023 11:18:46 GMT
• Title: Avoiding barren plateaus via transferability of smooth solutions in Hamiltonian Variational Ansatz
• Authors: Antonio Anna Mele, Glen Bigan Mbeng, Giuseppe Ernesto Santoro, Mario Collura, Pietro Torta
• Abstract summary: Variational Quantum Algorithms (VQAs) represent leading candidates to achieve computational speed-ups on current quantum devices. Two major hurdles are the proliferation of low-quality variational local minima, and the exponential vanishing of gradients in the cost function landscape. Here we show that by employing iterative search schemes one can effectively prepare the ground state of paradigmatic quantum many-body models.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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