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  • Open Access

Resource-efficient shadow tomography using equatorial stabilizer measurements

Guedong Park, Yong Siah Teo*, and Hyunseok Jeong†

  • NextQuantum Innovation Research Center, Department of Physics and Astronomy, Seoul National University, Seoul 08826, Republic of Korea

  • *Contact author: ys_teo@snu.ac.kr
  • †Contact author: h.jeong37@gmail.com
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Phys. Rev. Research 7, 033097 – Published 28 July, 2025

DOI: https://doi.org/10.1103/9pbp-jzr9

Abstract

We propose a resource-efficient shadow-tomography scheme using equatorial-stabilizer measurements generated from subsets of Clifford unitaries. For n-qubit systems, equatorial-stabilizer-based shadow-tomography schemes can estimate M observables (up to an additive error ɛ) using O(log(M),poly(n),1/ɛ2) sampling copies for a large class of observables, including those with traceless parts possessing polynomially bounded Frobenius norms. For arbitrary quantum-state observables with a constant Frobenius norm, sampling complexity becomes n independent. Our scheme only requires an n-depth controlled-Z (CZ) circuit [O(n2) CZ gates] and Pauli measurements per sampling copy. Alternatively, our scheme is realizable with 2n-depth circuits comprising n2 nearest-neighboring cnot gates, exhibiting a smaller maximal gate count relative to previously known randomized-Clifford-based proposals. We numerically confirm our theoretically derived shadow-tomographic sampling complexities with random pure states and multiqubit graph states. Finally, we demonstrate that equatorial-stabilizer-based shadow tomography is more noise tolerant than randomized-Clifford-based schemes in terms of fidelity estimation for the Greenberger–Horne–Zeilinger state and W state.

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Phys. Rev. Research 7, 033097– Published 28 July, 2025
  • Received 2 April 2025
  • Accepted 25 June 2025
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