Jun 16, 2021

Diagnosing barren plateaus with tools from quantum optimal control

Date: June 16, 2021 | 3:00 pm – 4:00 pm
Speaker: Martin Larocca, FCEyN, Universidad de Buenos Aires, Argentina
Location: Online on Zoom

Variational Quantum Algorithms (VQAs) have received considerable attention due to their potential for achieving near-term quantum advantage. However, more work is needed to understand their scalability. One known scaling result for VQAs is barren plateaus, where certain circumstances lead to exponentially vanishing gradients. It is common folklore that problem-inspired ansatzes avoid barren plateaus, but in fact, very little is known about their gradient scaling. In this work we employ tools from quantum optimal control to develop a framework that can diagnose the presence or absence of barren plateaus for problem-inspired ansatzes. Such ansatzes include the Quantum Alternating Operator Ansatz (QAOA), the Hamiltonian Variational Ansatz (HVA), and others. With our framework, we prove that avoiding barren plateaus for these ansatzes is not always guaranteed. Specifically, we show that the gradient scaling of the VQA depends on the controllability of the system, and hence can be diagnosed through the dynamical Lie algebra $\mathfrak{g}$ obtained from the generators of the ansatz. We analyze the existence of barren plateaus in QAOA and HVA ansatzes, and we highlight the role of the input state, as different initial states can lead to the presence or absence of barren plateaus. Taken together, our results provide a framework for trainability-aware ansatz design strategies that do not come at the cost of extra quantum resources. Moreover, we prove no-go results for obtaining ground states with variational ansatzes for controllable systems such as spin glasses. We finally provide evidence that barren plateaus can be linked to the dimension of $\mathfrak{g}$

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https://istaustria.zoom.us/j/99477145630?pwd=WjdhRTdvZmNTdkJoaGFhVWFjSTNNUT09

Meeting ID: 994 7714 5630

Passcode: 555461

More Information:

Date:
June 16, 2021
3:00 pm – 4:00 pm

Speaker:
Martin Larocca, FCEyN, Universidad de Buenos Aires, Argentina

Location:
Online on Zoom

Contact:

Maksym Serbyn

Email:
maksym.serbyn@ist.ac.at

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