Constant-Depth Quantum Barrier Option Pricing via a Static Bivariate Oracle Framework
Abstract
Quantum amplitude estimation offers a theoretical quadratic speedup over classical Monte Carlo methods for financial derivative pricing. However, extending gate-based algorithms to path-dependent barrier options has historically been hampered by sequential path discretization, where tracking price paths across d monitoring dates incurs a linear escalation in qubit footprint and gate depth (𝒪(d)), posing severe coherence challenges for near-term quantum processors. In this work, we present a constant-depth quantum pricing framework that fundamentally eliminates the temporal dependency of barrier monitoring. Leveraging the Brownian reflection principle and Girsanov theorem, we project the continuous supremum dynamics onto a static bivariate joint distribution of the terminal price ST and running supremum MT. This allows decoupling dynamic boundary checks into a static bivariate oracle comprising two parallel comparators and a dual-controlled rotation gate. We prove this architecture reduces circuit depth and comparator complexity from 𝒪(d) to an invariant 𝒪(1), while supporting discrete monitoring via zero-quantum-cost boundary corrections. Transpilation benchmarks for daily monitoring (d = 252) show our framework slashes physical CNOT count by 98.59% (from 2262 to 32) and compresses two-qubit depth by 98.02% (from 1514 to 30 layers). Under a realistic 127-qubit IBM Eagle noise model, the shallow circuit achieves a 7.84% relative valuation error with M3 readout mitigation. Finally, the framework seamlessly extends to nonlinear exotic payoffs lacking analytical solutions, establishing a noise-resilient pathway toward practical quantum advantage in computational finance.
Related
- Pricing of graph-based quantum portfolios from first principles
- Quantum bivariate bicycle codes with weight-8 checks surpassing the BB benchmark
- Reducing the arithmetic cost of quantum derivative pricing with language-model circuit design
- Lowering the implementation barrier of neutral-atom quantum computing with agentic workflows
- Constant-round quantum advantage in communication complexity for total functions
BibTeX
@misc{mo2026constantdepth,
title = {{Constant-Depth Quantum Barrier Option Pricing via a Static Bivariate Oracle Framework}},
author = {Ji-Hui Mo and Yuan-Hong Tao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27929},
eprint = {2610.27929},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27929},
}
RIS
TY - UNPB
TI - Constant-Depth Quantum Barrier Option Pricing via a Static Bivariate Oracle Framework
AU - Ji-Hui Mo
AU - Yuan-Hong Tao
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.27929
UR - https://arxiv.org/abs/2610.27929
AB - Quantum amplitude estimation offers a theoretical quadratic speedup over classical Monte Carlo methods for financial derivative pricing. However, extending gate-based algorithms to path-dependent barrier options has historically been hampered by sequential path discretization, where tracking price paths across d monitoring dates incurs a linear escalation in qubit footprint and gate depth (𝒪(d)), posing severe coherence challenges for near-term quantum processors. In this work, we present a constant-depth quantum pricing framework that fundamentally eliminates the temporal dependency of barrier monitoring. Leveraging the Brownian reflection principle and Girsanov theorem, we project the continuous supremum dynamics onto a static bivariate joint distribution of the terminal price S_T and running supremum M_T. This allows decoupling dynamic boundary checks into a static bivariate oracle comprising two parallel comparators and a dual-controlled rotation gate. We prove this architecture reduces circuit depth and comparator complexity from 𝒪(d) to an invariant 𝒪(1), while supporting discrete monitoring via zero-quantum-cost boundary corrections. Transpilation benchmarks for daily monitoring (d = 252) show our framework slashes physical CNOT count by 98.59% (from 2262 to 32) and compresses two-qubit depth by 98.02% (from 1514 to 30 layers). Under a realistic 127-qubit IBM Eagle noise model, the shallow circuit achieves a 7.84% relative valuation error with M3 readout mitigation. Finally, the framework seamlessly extends to nonlinear exotic payoffs lacking analytical solutions, establishing a noise-resilient pathway toward practical quantum advantage in computational finance.
ER -