Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session B64: Quantum Algorithms for Optimization
11:30 AM–1:54 PM,
Monday, March 6, 2023
Room: Room 415
Sponsoring
Unit:
DQI
Chair: Matthew DeCross, Quantinuum
Abstract: B64.00005 : Performances and limitations of variational quantum algorithms under realistic noise models*
12:18 PM–12:30 PM
Presenter:
Marco Schumann
(Forschungszentrum Jülich)
Authors:
Marco Schumann
(Forschungszentrum Jülich)
Frank Wilhelm-Mauch
(Forschungszentrum Jülich)
Alessandro Ciani
(Forschungszentrum Jülich)
We consider the performances of VQAs under more realistic noise models, like dephasing and/or amplitude-damping noise, focusing on the Quantum Approximate Optimization Algorithm (QAOA) for MaxCut problems. We show how sampling over random circuit parameters, and in the limit of weak noise, the output state of the quantum circuit approaches with high probability the completely mixed state exponentially in the circuit depth. This, in turn, implies exponential decay also of the gradient of the cost function. We show how this exponential decay can be explained as a unitary 2-design property of the QAOA circuit, which effectively turns the noise into a global depolarizing one. While it is known that some QAOA circuits give rise to universal unitaries [2], we show numerically that for our examples the noise is well described by the global depolarizing channel, even for single parameter sets.
*We would like to acknowledge the financial support from QSolid(DBA02121) and QAI2(DBA01967).
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