Reducing the arithmetic cost of quantum derivative pricing with language-model circuit design
Abstract
Quantum amplitude estimation can estimate expected discounted payoffs with quadratically fewer oracle calls than Monte Carlo, but each call requires coherent computation. We use language-model-assisted circuit design to reduce reversible payoff arithmetic for a three-asset worst-of autocallable and a target accrual redemption forward (TARF). The constructions retain compact integer representations of market paths alongside contract history, reconstructing quantities temporarily for contract decisions and payoff-angle evaluation. Relative to matched internal references, the factor-sum autocallable and windowed TARF circuits reduce the product of Toffoli count and peak logical qubits (NTof Qmax) by factors of 2.39 and 4.84, respectively. At a second autocallable setting, fresh search recovers a 1.35-fold saving after the tested fixed adaptation loses its advantage. For the factor-sum circuit, we prove exact coherent execution of its integer specification for every input, incoming accumulator and measurement record, with clean workspace and phase cancellation. A separate lattice calculation gives a numerical angle-tolerance-violation probability of 6.248e-8 and evaluates pricing bias under the declared loading law, with bounded omission but no certified numerical enclosure. The results connect compact representations to lower-cost payoff arithmetic and separately assessed logical and financial correctness. Their resource scope excludes loading, payoff rotation and estimation.
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BibTeX
@misc{sharma2026reducing,
title = {{Reducing the arithmetic cost of quantum derivative pricing with language-model circuit design}},
author = {Monit Sharma and Hoong Chun Lau},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04431},
eprint = {2611.04431},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04431},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Reducing the arithmetic cost of quantum derivative pricing with language-model circuit design
AU - Monit Sharma
AU - Hoong Chun Lau
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04431
UR - https://arxiv.org/abs/2611.04431
AB - Quantum amplitude estimation can estimate expected discounted payoffs with quadratically fewer oracle calls than Monte Carlo, but each call requires coherent computation. We use language-model-assisted circuit design to reduce reversible payoff arithmetic for a three-asset worst-of autocallable and a target accrual redemption forward (TARF). The constructions retain compact integer representations of market paths alongside contract history, reconstructing quantities temporarily for contract decisions and payoff-angle evaluation. Relative to matched internal references, the factor-sum autocallable and windowed TARF circuits reduce the product of Toffoli count and peak logical qubits (N_Tof Q_max) by factors of 2.39 and 4.84, respectively. At a second autocallable setting, fresh search recovers a 1.35-fold saving after the tested fixed adaptation loses its advantage. For the factor-sum circuit, we prove exact coherent execution of its integer specification for every input, incoming accumulator and measurement record, with clean workspace and phase cancellation. A separate lattice calculation gives a numerical angle-tolerance-violation probability of 6.248e-8 and evaluates pricing bias under the declared loading law, with bounded omission but no certified numerical enclosure. The results connect compact representations to lower-cost payoff arithmetic and separately assessed logical and financial correctness. Their resource scope excludes loading, payoff rotation and estimation.
ER -