Simple Diagonal State Designs with Reconfigurable Real-Time Circuits
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.
Keywords
Cite
@article{arxiv.2401.04176,
title = {Simple Diagonal State Designs with Reconfigurable Real-Time Circuits},
author = {Yizhi Shen and Katherine Klymko and Eran Rabani and Norm M. Tubman and Daan Camps and Roel Van Beeumen and Michael Lindsey},
journal= {arXiv preprint arXiv:2401.04176},
year = {2026}
}