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Diagonal state designs with reconfigurable real-time circuits

Yizhi Shen1,*, Katherine Klymko2, Eran Rabani3,4,5, Norm M. Tubman6, Daan Camps2, Roel Van Beeumen1, and Michael Lindsey7

  • *Contact author: yizhis@lbl.gov
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Phys. Rev. Research 8, 013042 – Published 15 January, 2026

DOI: https://doi.org/10.1103/nb7c-d6kk

Abstract

Unitary designs are widely used in quantum computation, but in many practical settings it suffices to construct a diagonal state design generated with unitary gates diagonal in the computational basis. In this work, we introduce a simple and efficient diagonal state 3-design based on real-time evolutions under 2-local Hamiltonians. Our construction is inspired by the classical Girard-Hutchinson trace estimator in that it involves the stochastic preparation of many random-phase states. Though the exact Girard-Hutchinson states are not tractably implementable on a quantum computer, we can construct states that match the statistical moments of the Girard-Hutchinson states with real-time evolution. Importantly, our random states are all generated using the same Hamiltonians for real-time evolution, with the randomness arising solely from stochastic variations in the durations of the evolutions. In this sense, the circuit is fully reconfigurable and thus suited for near-term realizations on both digital and analog platforms. Moreover, we show how to extend our construction to achieve diagonal state designs of arbitrarily high order.

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Phys. Rev. Research 8, 013042– Published 15 January, 2026
  • Received 27 September 2024
  • Accepted 29 September 2025
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