Long-term yields of short-rate models as Feynman-Kac ground states: a variational quantum eigensolver with single-setting energy estimation on two NISQ platforms
Abstract
We show that the long-term yield of a short-rate model is the ground-state energy of a Schrodinger operator obtained from the Feynman-Kac bond-pricing equation, so that it can be computed by a variational quantum eigensolver (VQE). We treat the Vasicek, Cox-Ingersoll-Ross and Black-Karasinski models; the last has no closed form. Calibrated monthly to the U.S. Treasury curve from 1985 to 2026, the long-term yield follows the 30-year yield with an in-sample correlation of 0.98. The Hamiltonian is stoquastic, so its ground state is positive and the energy can be estimated from computational-basis samples with a single measurement setting. On ibm_cleveland, gate noise appears mainly as bit flips of the high-order qubits. A bit-flip deconvolution with a tail set fixed by a WKB criterion, combined with readout mitigation and zero-noise extrapolation, gives four-qubit estimates within 33-125 bp of the grid ground-state energies for all three models, and within 23-67 bp for Treasury-calibrated parameters. On IonQ Forte Enterprise the same analysis reduces the error in the same proportions. On the same circuits, a Pauli-measurement VQE deviates by 791-1,129 bp, so the single-setting estimator gives about ten times smaller errors with one setting instead of nine. An on-device VQE converges from 4,939 bp to 130 bp.
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BibTeX
@misc{ahn2026longterm,
title = {{Long-term yields of short-rate models as Feynman-Kac ground states: a variational quantum eigensolver with single-setting energy estimation on two NISQ platforms}},
author = {Doyeol "David" Ahn},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01855},
eprint = {2611.01855},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01855},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Long-term yields of short-rate models as Feynman-Kac ground states: a variational quantum eigensolver with single-setting energy estimation on two NISQ platforms
AU - Doyeol "David" Ahn
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01855
UR - https://arxiv.org/abs/2611.01855
AB - We show that the long-term yield of a short-rate model is the ground-state energy of a Schrodinger operator obtained from the Feynman-Kac bond-pricing equation, so that it can be computed by a variational quantum eigensolver (VQE). We treat the Vasicek, Cox-Ingersoll-Ross and Black-Karasinski models; the last has no closed form. Calibrated monthly to the U.S. Treasury curve from 1985 to 2026, the long-term yield follows the 30-year yield with an in-sample correlation of 0.98. The Hamiltonian is stoquastic, so its ground state is positive and the energy can be estimated from computational-basis samples with a single measurement setting. On ibm_cleveland, gate noise appears mainly as bit flips of the high-order qubits. A bit-flip deconvolution with a tail set fixed by a WKB criterion, combined with readout mitigation and zero-noise extrapolation, gives four-qubit estimates within 33-125 bp of the grid ground-state energies for all three models, and within 23-67 bp for Treasury-calibrated parameters. On IonQ Forte Enterprise the same analysis reduces the error in the same proportions. On the same circuits, a Pauli-measurement VQE deviates by 791-1,129 bp, so the single-setting estimator gives about ten times smaller errors with one setting instead of nine. An on-device VQE converges from 4,939 bp to 130 bp.
ER -