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3216. From barren plateaus through fertile valleys: Conic extensions of parameterised quantum circuits

Invited abstract in session MD-42: Optimization in Quantum Information, stream Quantum Computing Optimization.

Monday, 14:30-16:00
Room: 98 (building: 306)

Authors (first author is the speaker)

1. Timo Ziegler
Institut für theoretische Physik - AG Quanteninformation, Leibniz Universität Hannover
2. Gereon Koßmann
RWTH Aachen

Abstract

Unconstrained optimization problems such as integer linear programs can be relaxed
to the task of finding the ground state of a physical system described by a quantum
state. In the realm of quantum devices having comparably low numbers in qubits
prone to noise, quantum circuits consisting of a sequence of parameterised unitary
gates controlled by classical optimization methods are the prevalent technique of
near-term quantum algorithms. However, the omnipresent phenomenon of barren
plateaus - parameter regions with vanishing gradients - sets a persistent hurdle that
drastically diminishes their success in practice.
In this work, we introduce an approach -based on non-unitary operations - that
favours jumps out of a barren plateau into a fertile valley. These operations are con-
structed from conic extensions of parameterised unitary quantum circuits, relying on
mid-circuit measurements and a small ancilla system. We further reduce the prob-
lem of finding optimal jump directions to a low-dimensional generalised eigenvalue
problem.
As a proof of concept we incorporate jumps within state-of-the-art implementa-
tions of the Quantum Approximate Optimisation Algorithm (QAOA) - a prominent
descendant of the class of variational quantum algorithms. We demonstrate the ex-
tensions' effectiveness on QAOA through extensive simulations, showcasing robust-
ness against barren plateaus and highly improved sampling probabilities of optimal
solutions.

Keywords

Status: accepted


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