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

Paper: arXiv 2611.01855

Authors: Doyeol “David” Ahn

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.

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a highly novel approach to computing long-term yields using quantum computing, grounded in advanced mathematical finance and quantum mechanics. It demonstrates strong empirical rigor through calibration to real market data and hardware experiments on NISQ platforms, showcasing practical applicability despite the theoretical complexity.

Research Flowchart

  flowchart TD
    A[Research Goal: Compute Long-term Yields of Short-Rate Models using VQE] --> B{Key Methodology: VQE for Feynman-Kac Ground State};
    B --> C{Models & Calibration Data};
    C --> D[Computational Process: Single-Setting Energy Estimation on NISQ Platforms];
    D --> E[Error Mitigation & Extrapolation];
    E --> F[Key Findings & Outcomes];

    C -- Models --> C1[Vasicek, CIR, Black-Karasinski];
    C -- Data --> C2[U.S. Treasury Curve (1985-2026)];
    D -- Platforms --> D1[IBM Cleveland, IonQ Forte Enterprise];
    F -- Yield Correlation --> F1[0.98 with 30-year Treasury yield];
    F -- VQE Accuracy --> F2[4-qubit estimates within 33-125 bp (models) & 23-67 bp (calibrated)];
    F -- Single-Setting Advantage --> F3[10x smaller errors vs. Pauli-measurement VQE];
    F -- On-Device Convergence --> F4[VQE converges from 4,939 bp to 130 bp];