Virtual mitigation of coherent non-adiabatic transitions by echo verification

Benjamin F. Schiffer1, Dyon van Vreumingen2,3, Jordi Tura4, and Stefano Polla4,5

1Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching, Germany
2Institute of Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
3QuSoft, Centrum Wiskunde & Informatica (CWI), Science Park 123, 1098 XG Amsterdam, The Netherlands
4Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands
5Google Quantum AI, 80636 München, Germany

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Abstract

Transitions out of the ground space limit the performance of quantum adiabatic algorithms, while hardware imperfections impose stringent limitations on the circuit depth. We propose an adiabatic echo verification protocol which mitigates both coherent and incoherent errors, arising from non-adiabatic transitions and hardware noise, respectively. Quasi-adiabatically evolving forward and backward allows for an echo-verified measurement of any observable. In addition to mitigating hardware noise, our method uses positive-time dynamics only. Crucially, the estimator bias of the observable is reduced when compared to standard adiabatic preparation, achieving up to a quadratic improvement.

The adiabatic algorithm is a powerful state preparation technique in quantum computation, and one of the few algorithms successfully implemented on devices with up to hundreds of qubits. However, its performance is limited by non-adiabatic transitions, which arise due to a limited circuit depth. Our work addresses this challenge by adapting error mitigation techniques to the adiabatic algorithm. We introduce an Adiabatic Echo Verification (AEV) scheme, demonstrating up to a quadratic suppression of errors caused by non-adiabatic transitions while also mitigating hardware noise. Notably, our protocol requires the simulation of Hamiltonian evolution for positive times only, making it appealing for analog quantum simulators.

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