A Shadow Enhanced Greedy Quantum Eigensolver
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910027238866944 |
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| author | Erle, Jona Koczor, Balint |
| author_facet | Erle, Jona Koczor, Balint |
| contents | While ground-state preparation is expected to be a primary application of quantum computers, it is also an essential subroutine for many fault-tolerant algorithms. In early fault-tolerant regimes, logical measurements remain costly, motivating adaptive, shot-frugal state-preparation strategies that efficiently utilize each measurement. We introduce the Shadow Enhanced Greedy Quantum Eigensolver (SEGQE) as a greedy, shadow-assisted framework for measurement-efficient ground-state preparation. SEGQE uses classical shadows to evaluate, in parallel and entirely in classical post-processing, the energy reduction induced by large collections of local candidate gates, greedily selecting at each step the gate with the largest estimated energy decrease. We derive rigorous worst-case per-iteration sample-complexity bounds for SEGQE, exhibiting logarithmic dependence on the number of candidate gates. Numerical benchmarks on finite transverse-field Ising models and ensembles of random local Hamiltonians demonstrate convergence in a number of iterations that scales approximately linearly with system size, while maintaining high-fidelity ground-state approximations and competitive energy estimates. Together, our empirical scaling laws and rigorous per-iteration guarantees establish SEGQE as a measurement-efficient state-preparation primitive well suited to early fault-tolerant quantum computing architectures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_17615 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Shadow Enhanced Greedy Quantum Eigensolver Erle, Jona Koczor, Balint Quantum Physics While ground-state preparation is expected to be a primary application of quantum computers, it is also an essential subroutine for many fault-tolerant algorithms. In early fault-tolerant regimes, logical measurements remain costly, motivating adaptive, shot-frugal state-preparation strategies that efficiently utilize each measurement. We introduce the Shadow Enhanced Greedy Quantum Eigensolver (SEGQE) as a greedy, shadow-assisted framework for measurement-efficient ground-state preparation. SEGQE uses classical shadows to evaluate, in parallel and entirely in classical post-processing, the energy reduction induced by large collections of local candidate gates, greedily selecting at each step the gate with the largest estimated energy decrease. We derive rigorous worst-case per-iteration sample-complexity bounds for SEGQE, exhibiting logarithmic dependence on the number of candidate gates. Numerical benchmarks on finite transverse-field Ising models and ensembles of random local Hamiltonians demonstrate convergence in a number of iterations that scales approximately linearly with system size, while maintaining high-fidelity ground-state approximations and competitive energy estimates. Together, our empirical scaling laws and rigorous per-iteration guarantees establish SEGQE as a measurement-efficient state-preparation primitive well suited to early fault-tolerant quantum computing architectures. |
| title | A Shadow Enhanced Greedy Quantum Eigensolver |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2602.17615 |