GENIE: learned quantum circuits as embedding impurity solvers, and why compactness, not correlation strength, decides when they work
Abstract
Sample-based quantum diagonalization has been used as an impurity solver in density matrix embedding theory (DMET), but always with fixed-form circuits and without comparison to classical selection at the same subspace size. We introduce GENIE, a DMET impurity solver in which a generative transformer learns the sampling circuit, trained on the quantum-selected configuration interaction energy. On N2, hydrogen chains, water and a hydrogen ring, we compare GENIE at equal determinant budget with classical selected configuration interaction (CIPSI, ASCI, heat-bath CI) and with DMET combined with sample-based quantum diagonalization (SQD). GENIE selects: for N2 at 200 determinants it is within a factor of 1.7 of CIPSI and 25 to 1000 times more accurate than the determinants a fixed circuit actually samples, while standard SQD reaches good energies mainly by filling the subspace. GENIE does not beat the best classical selection, and its circuits require fault-tolerant hardware. Its failures are governed by the compactness of the wavefunction relative to the budget, not by correlation strength. A cheap estimate from coupled-cluster amplitudes predicts this compactness. A router built on it never recommended GENIE where it then failed, apart from seed-to-seed variance, and it transferred unchanged to a blind test on new systems. We also identify two benchmarking pitfalls that can create apparent quantum advantages of one to two orders of magnitude.
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BibTeX
@misc{loharkar2026genie,
title = {{GENIE: learned quantum circuits as embedding impurity solvers, and why compactness, not correlation strength, decides when they work}},
author = {Awadhoot Vijay Loharkar and Arcesio Castañeda Medina},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41957},
eprint = {2610.41957},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41957},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - GENIE: learned quantum circuits as embedding impurity solvers, and why compactness, not correlation strength, decides when they work
AU - Awadhoot Vijay Loharkar
AU - Arcesio Castañeda Medina
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41957
UR - https://arxiv.org/abs/2610.41957
AB - Sample-based quantum diagonalization has been used as an impurity solver in density matrix embedding theory (DMET), but always with fixed-form circuits and without comparison to classical selection at the same subspace size. We introduce GENIE, a DMET impurity solver in which a generative transformer learns the sampling circuit, trained on the quantum-selected configuration interaction energy. On N2, hydrogen chains, water and a hydrogen ring, we compare GENIE at equal determinant budget with classical selected configuration interaction (CIPSI, ASCI, heat-bath CI) and with DMET combined with sample-based quantum diagonalization (SQD). GENIE selects: for N2 at 200 determinants it is within a factor of 1.7 of CIPSI and 25 to 1000 times more accurate than the determinants a fixed circuit actually samples, while standard SQD reaches good energies mainly by filling the subspace. GENIE does not beat the best classical selection, and its circuits require fault-tolerant hardware. Its failures are governed by the compactness of the wavefunction relative to the budget, not by correlation strength. A cheap estimate from coupled-cluster amplitudes predicts this compactness. A router built on it never recommended GENIE where it then failed, apart from seed-to-seed variance, and it transferred unchanged to a blind test on new systems. We also identify two benchmarking pitfalls that can create apparent quantum advantages of one to two orders of magnitude.
ER -