## Abstract

Adiabatic quantum algorithms solve computational problems by slowly evolving a trivial state to the desired solution. On an ideal quantum computer, the solution quality improves monotonically with increasing circuit depth. By contrast, increasing the depth in current noisy computers introduces more noise and eventually deteriorates any computational advantage. What is the optimal circuit depth that provides the best solution Here, we address this question by investigating an adiabatic circuit that interpolates between the paramagnetic and ferromagnetic ground states of the one-dimensional quantum Ising model. We characterize the quality of the final output by the density of defects d, as a function of the circuit depth N and noise strength σ. We find that d is well described by the simple form dideal+dnoise, where the ideal case dideal∼N-1/2 is controlled by the Kibble-Zurek mechanism, and the noise contribution scales as dnoise∼Nσ2. It follows that the optimal number of steps minimizing the number of defects goes as ∼σ-4/3. We implement this algorithm on a noisy superconducting quantum processor and find that the dependence of the density of defects on the circuit depth follows the predicted nonmonotonous behavior and agrees well with noisy simulations. Our work allows one to efficiently benchmark quantum devices and extract their effective noise strength σ.

Original language | English |
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Article number | 125127 |

Journal | Physical Review B |

Volume | 107 |

Issue number | 12 |

DOIs | |

State | Published - 15 Mar 2023 |

### Bibliographical note

Publisher Copyright:© 2023 American Physical Society.

### Funding

This work was supported by Rigetti Computing. D.A. and E.G.D.T. were supported by the Israel Science Foundation, Grants No. 151/19 and No. 154/19. The experimental results presented here are based upon work supported by the Defense Advanced Research Projects Agency (DARPA) under Agreement No. HR00112090058.

Funders | Funder number |
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Defense Advanced Research Projects Agency | HR00112090058 |

Israel Science Foundation | 151/19, 154/19 |