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Error-mitigated nonorthogonal quantum eigensolver via shadow tomography

Hang Ren1,2,3, Yipei Zhang1,2,3, Wendy M. Billings1,2,3, Rebecca Tomann1,2,3, Nikolay V. Tkachenko1,2,3, Mingyu Kang1,2,3, Martin Head-Gordon2,3, and K. Birgitta Whaley1,2,3,*

  • 1Berkeley Center for Quantum Information and Computation, Berkeley, California 94720, USA
  • 2Department of Chemistry, University of California, Berkeley, California 94720, USA
  • 3Challenge Institute for Quantum Computation, Berkeley, California 94720, USA

  • *Contact author: whaley@berkeley.edu
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Phys. Rev. Research 8, 013268 – Published 10 March, 2026

DOI: https://doi.org/10.1103/7c5b-3v56

Abstract

We present a shadow-tomography-enhanced nonorthogonal quantum eigensolver (NOQE) for more efficient and accurate electronic structure calculations on near-term quantum devices. By integrating shadow tomography into the NOQE, the measurement cost scales linearly rather than quadratically with the number of reference states, while also reducing the required qubits and circuit depth by half. This approach enables extraction of all matrix elements via randomized measurements and classical postprocessing. We analyze its sample complexity and show that, for small systems, it remains constant in the high-precision regime, while for larger systems, it scales linearly with the system size. We further apply shadow-based error mitigation to suppress noise-induced bias without increasing quantum resources. Demonstrations on the hydrogen molecule in the strongly correlated regime achieve chemical accuracy under realistic noise, showing that our method is both resource-efficient and noise-resilient for practical quantum chemistry simulations in the near term.

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Phys. Rev. Research 8, 013268– Published 10 March, 2026
  • Received 22 April 2025
  • Accepted 30 December 2025
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