A Unified Theory of Barren Plateaus for Deep Parametrized Quantum
Circuits
- URL: http://arxiv.org/abs/2309.09342v2
- Date: Wed, 20 Sep 2023 20:45:02 GMT
- Title: A Unified Theory of Barren Plateaus for Deep Parametrized Quantum
Circuits
- Authors: Michael Ragone, Bojko N. Bakalov, Fr\'ed\'eric Sauvage, Alexander F.
Kemper, Carlos Ortiz Marrero, Martin Larocca, and M. Cerezo
- Abstract summary: Variational quantum computing schemes have received considerable attention due to their high versatility and potential to make practical use of near-term quantum devices.
At their core, these models train a loss function by sending an initial state through a parametrized quantum circuit, and evaluating the expectation value of some operator at the circuit's output.
Despite their promise, the trainablity of these algorithms is hindered by barren plateaus induced by the expressiveness of the parametrized quantum circuit, entanglement of the input data, the locality of the observable, or the presence of hardware noise.
- Score: 37.84307089310829
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Variational quantum computing schemes have received considerable attention
due to their high versatility and potential to make practical use of near-term
quantum devices. At their core, these models train a loss function by sending
an initial state through a parametrized quantum circuit, and evaluating the
expectation value of some operator at the circuit's output. Despite their
promise, the trainablity of these algorithms is hindered by barren plateaus
induced by the expressiveness of the parametrized quantum circuit, the
entanglement of the input data, the locality of the observable, or the presence
of hardware noise. Up to this point, these sources of barren plateaus have been
regarded as independent and have been studied only for specific circuit
architectures. In this work, we present a general Lie algebraic theory that
provides an exact expression for the variance of the loss function of
sufficiently deep parametrized quantum circuits, even in the presence of
certain noise models. Our results unify under one single framework all
aforementioned sources of barren plateaus by leveraging generalized (and
subsystem independent) notions of entanglement and operator locality, as well
as generalized notions of algebraic decoherence due to noise. This theoretical
leap resolves a standing conjecture about a connection between loss
concentration and the dimension of the Lie algebra of the generators of the
parametrized circuit.
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