High-precision and low-depth quantum algorithm design for eigenstate problems
File(s)
Published version
Author(s)
Kim, Myungshik
Sun, Jinzhao
Type
Journal Article
Abstract
Estimating the eigenstate properties of quantum systems is a long-standing, challenging problem for both classical and quantum computing. Existing universal quantum algorithms typically rely on ideal and efficient query models (e.g. time evolution operator or block encoding of the Hamiltonian), which, however, become suboptimal for actual implementation at the quantum circuit level. Here, we present a full-stack design of quantum algorithms for estimating the eigenenergy and eigenstate properties, which can achieve high precision and good scaling with system size. The gate complexity per circuit for estimating generic Hamiltonians’ eigenstate properties is O(˜ log 𝜺¯¹), which has a logarithmic dependence on the inverse precision 𝜺. For lattice Hamiltonians, the circuit depth of our design achieves near-optimal system-size scaling, even with local qubit connectivity. Our full-stack algorithm has low overhead in circuit compilation, which thus results in a small actual gate count (cnot and non-Clifford gates) for lattice and molecular problems compared to advanced eigenstate algorithms. The algorithm is implemented on IBM quantum devices using up to 2,000 two-qubit gates and 20,000 single-qubit gates, and achieves high-precision eigenenergy estimation for Heisenberg-type Hamiltonians, demonstrating its noise robustness.
Date Issued
2026-01-01
Date Acceptance
2025-11-26
Citation
Science Advances, 2026, 12 (3)
ISSN
2375-2548
Publisher
American Association for the Advancement of Science (AAAS)
Journal / Book Title
Science Advances
Volume
12
Issue
3
Copyright Statement
Copyright © 2026 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution License 4.0 (CC BY). This is an open-access article distributed under the terms of the Creative Commons Attribution license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
License URL
Publication Status
Published
Date Publish Online
2026-01-16