Hamiltonian variational ansatz without barren plateaus
- URL: http://arxiv.org/abs/2302.08529v2
- Date: Wed, 24 Jan 2024 17:10:14 GMT
- Title: Hamiltonian variational ansatz without barren plateaus
- Authors: Chae-Yeun Park and Nathan Killoran
- Abstract summary: Variational quantum algorithms are one of the most promising applications of a near-term quantum computer.
Despite their huge potential, the utility of variational quantum algorithms beyond tens of qubits is still questioned.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Variational quantum algorithms, which combine highly expressive parameterized
quantum circuits (PQCs) and optimization techniques in machine learning, are
one of the most promising applications of a near-term quantum computer. Despite
their huge potential, the utility of variational quantum algorithms beyond tens
of qubits is still questioned. One of the central problems is the trainability
of PQCs. The cost function landscape of a randomly initialized PQC is often too
flat, asking for an exponential amount of quantum resources to find a solution.
This problem, dubbed barren plateaus, has gained lots of attention recently,
but a general solution is still not available. In this paper, we solve this
problem for the Hamiltonian variational ansatz (HVA), which is widely studied
for solving quantum many-body problems. After showing that a circuit described
by a time-evolution operator generated by a local Hamiltonian does not have
exponentially small gradients, we derive parameter conditions for which the HVA
is well approximated by such an operator. Based on this result, we propose an
initialization scheme for the variational quantum algorithms and a
parameter-constrained ansatz free from barren plateaus.
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