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Abstract

Quantum computers and simulators can potentially outperform classical
computers in finding ground states of classical and quantum Hamiltonians.
However, if this advantage can persist in the presence of noise without error
correction remains unclear. In this paper, by exploiting the principle of
Lagrangian duality, we develop a numerical method to classically compute a
certifiable lower bound on the minimum energy attainable by the output state of
a quantum circuit in the presence of depolarizing noise. We provide theoretical
and numerical evidence that this approach can provide circuit-architecture
dependent bounds on the performance of noisy quantum circuits.