A curated library of research on quantum, quantum-inspired, and classical methods for quantitative finance, assembled and maintained by Applied Quantum Software. 529 entries and growing.
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Christian Bayer, Denis Belomestny, Oleg Butkovsky, John Schoenmakers · arXiv:2203.01160 · 2024Stochastic Local Volatility (SLV / LSV)
Evaluates the mathematical error propagation and convergence guarantees of Guyon and Henry-Labordère's particle method, providing a formal convergence analysis of the interacting-particle limits used in LSV calibration.
M. Chowdhury · Imperial College London, MSc Thesis · 2019Stochastic Local Volatility (SLV / LSV)
A legible breakdown comparing traditional SLV with computationally efficient approximations such as Mixed Local Volatility (MLV) models, showing how discrete deterministic states can compress execution times by orders of magnitude.
Klaus Spanderen · QuantLib User Workshop 2014 · 2014Stochastic Local Volatility (SLV / LSV)
An excellent development tutorial mapping the concrete C++ implementation of a Heston SLV pricing engine in QuantLib. It lays out how to use 2D Alternating Direction Implicit (ADI) PDE solvers, operator-splitting schemes (Craig-Sneyd), and boundary-condition enforcement.
Martin Haugh · Columbia University, Continuous-Time Financial Engineering lecture notesStochastic Local Volatility (SLV / LSV)
A clear slide-deck tutorial that bridges pure local-volatility models (CEV, Dupire) to standard two-factor stochastic-volatility frameworks (Heston, Bates), detailing how each fails or succeeds at matching current market surfaces. A strong intuition-first resource for building a codebase without wading through deep measure theory.
Vladimir V. Piterbarg · SSRN Electronic Journal · 2006Stochastic Local Volatility (SLV / LSV)
Establishes the foundational theory of Markovian projection, used extensively to collapse multi-factor models into an effective one-factor local-volatility representation for calibration.
Julien Guyon, Pierre Henry-Labordère · Chapman & Hall/CRC (book) · 2013Stochastic Local Volatility (SLV / LSV)
Widely considered the practitioner's reference for SLV implementation. Chapter 11 systematically introduces the Particle Method, a Monte Carlo framework using interacting particle paths and non-parametric kernel density estimation (KDE) to calibrate the local leverage function dynamically forward in time.
Pierre Henry-Labordère · Risk Magazine, September 2009 · 2009Stochastic Local Volatility (SLV / LSV)
A major practical breakthrough for quantitative trading desks. It introduced a fast, highly accurate approximation using Markovian projection and Malliavin calculus to map multi-factor stochastic-volatility models (such as the two-factor log-normal or Bergomi models) to market smiles.
René Carmona, Sergey Nadtochiy · SSRN Electronic Journal · 2009Stochastic Local Volatility (SLV / LSV)
One of the earliest academic papers to rigorously unify and formalize SLV. It characterizes the dynamics of parametric local volatility under no-arbitrage constraints and outlines tracking the system under risk-neutral measures.
Bruno Dupire · Risk Magazine 7(1): 18-20 · 1994Stochastic Local Volatility (SLV / LSV)
Although it focuses strictly on pure local volatility, this paper introduced the fundamental forward equation linking option prices to a deterministic local-volatility surface, providing the blueprint for the baseline calibration layer of any SLV model.
Istvan Gyöngy · Stochastics 17(1-2): 11-40 · 1986Stochastic Local Volatility (SLV / LSV)
The mathematical bedrock of SLV. Gyöngy's theorem guarantees that for a given bounded, continuous stochastic process (such as an asset with stochastic volatility) there exists an SDE with deterministic coefficients (the local-volatility model) that yields the exact same one-dimensional marginal distributions.
Fredrik Hasselgren, Matthew L. Sims-Goh · arXiv:2610.03528 [quant-ph] · October 2, 2026Quantum state preparation / data loading
ASPIRE (Adaptive State Preparation by Iterative Removal of Entanglement) approximately compiles quantum state-preparation circuits for structured states such as matrix product states (MPS). Instead of the usual layered staircase of nearest-neighbour gates, it scores candidate qubit pairs by how much entanglement a gate between them would remove and assembles parallelised layers of long-range gates, while respecting the target processor's qubit connectivity and noise. Across Hamiltonian ground states and multivariate amplitude-encoded functions, in both NISQ and early fault-tolerant settings, ASPIRE reports higher fidelities and shallower circuits than existing methods for states with long-range entanglement, even after accounting for the classical optimisation cost, and is positioned for applications tolerant of imperfect fidelity such as guide states for quantum phase estimation. Relevant to AQS because loading classical data and distributions into a quantum computer is a central bottleneck to end-to-end quantum advantage in finance; efficient MPS state preparation is one route around it, and AQS's HQCS sidesteps the same bottleneck by learning the distribution into the circuit rather than loading it.
T. G. Draper · arXiv:quant-ph/0008033 · 2000Quantum circuit compilation & primitives
Cited as reference [41] in the AQS HQCS paper. T. G. Draper, arXiv:quant-ph/0008033.
Bergholm, Vartiainen, Mottonen, Salomaa · Phys. Rev. A 71, 052330 (2005) · 2005Quantum circuit compilation & primitives
Cited as reference [40] in the AQS HQCS paper. Bergholm, Vartiainen, Mottonen, Salomaa, Phys. Rev. A 71, 052330 (2005).
Funcke, Hartung, Jansen, Kuhn, Stornati · Quantum 5, 422 (2021) · 2021Barren plateaus & trainability
Cited as reference [39] in the AQS HQCS paper. Funcke, Hartung, Jansen, Kuhn, Stornati, Quantum 5, 422 (2021).
J. M. Lee · Graduate Texts in Mathematics, Vol. 218 (Springer, 2013) · 2013Mathematics
Cited as reference [38] in the AQS HQCS paper. J. M. Lee, Graduate Texts in Mathematics, Vol. 218 (Springer, 2013).
W. Xu · arXiv:2510.25557 · 2025Quantum recurrent & temporal models
Cited as reference [37] in the AQS HQCS paper. W. Xu, arXiv:2510.25557.
Markov, Rastunkov, Deshmukh, Fry, Stefanski · arXiv:2212.03796 · 2022Quantum recurrent & temporal models
Cited as reference [36] in the AQS HQCS paper. Markov, Rastunkov, Deshmukh, Fry, Stefanski, arXiv:2212.03796.
R. Mo, B. Zhang, Q. Zhuang · arXiv:2607.10055 · 2026Quantum generative modeling
Cited as reference [35] in the AQS HQCS paper. R. Mo, B. Zhang, Q. Zhuang, arXiv:2607.10055.
Arrasmith, Holmes, Cerezo, Coles · Quantum Sci. Technol. 7, 045015 (2022) · 2022Barren plateaus & trainability
Cited as reference [34] in the AQS HQCS paper. Arrasmith, Holmes, Cerezo, Coles, Quantum Sci. Technol. 7, 045015 (2022).
B. Zhang, Hu, Mo, Chen, Tureci, Q. Zhuang · Phys. Rev. X 16, 021027 (2026) · 2026Holographic & sequential quantum circuits
Cited as reference [33] in the AQS HQCS paper. B. Zhang, Hu, Mo, Chen, Tureci, Q. Zhuang, Phys. Rev. X 16, 021027 (2026).
Belyansky, Bienias, Kharkov, Gorshkov, Swingle · Phys. Rev. Lett. 125, 130601 (2020) · 2020Holographic & sequential quantum circuits
Cited as reference [32] in the AQS HQCS paper. Belyansky, Bienias, Kharkov, Gorshkov, Swingle, Phys. Rev. Lett. 125, 130601 (2020).
Kandala, Mezzacapo, Temme, Takita, Brink, Chow, Gambetta · Nature 549, 242 (2017) · 2017Quantum circuit compilation & primitives
Cited as reference [31] in the AQS HQCS paper. Kandala, Mezzacapo, Temme, Takita, Brink, Chow, Gambetta, Nature 549, 242 (2017).
Schuster, Haferkamp, Huang · Science 389, 92 (2025) · 2025Holographic & sequential quantum circuits
Cited as reference [30] in the AQS HQCS paper. Schuster, Haferkamp, Huang, Science 389, 92 (2025).
Zeng, Wu, Liu, Wang, Hu · Phys. Rev. A 99, 052306 (2019) · 2019Quantum generative modeling
Cited as reference [28] in the AQS HQCS paper. Zeng, Wu, Liu, Wang, Hu, Phys. Rev. A 99, 052306 (2019).
S. Lloyd and C. Weedbrook · Phys. Rev. Lett. 121, 040502 (2018) · 2018Quantum generative modeling
Cited as reference [27] in the AQS HQCS paper. S. Lloyd and C. Weedbrook, Phys. Rev. Lett. 121, 040502 (2018).
Rudolph, Lerch, Thanasilp, Kiss, Shaya, Vallecorsa, Grossi, Holmes · npj Quantum Information 10, 116 (2024) · 2024Quantum generative modeling
Cited as reference [26] in the AQS HQCS paper. Rudolph, Lerch, Thanasilp, Kiss, Shaya, Vallecorsa, Grossi, Holmes, npj Quantum Information 10, 116 (2024).
Gretton, Borgwardt, Rasch, Scholkopf, Smola · Journal of Machine Learning Research 13, 723 (2012) · 2012Copulas, MMD & statistics
Cited as reference [24] in the AQS HQCS paper. Gretton, Borgwardt, Rasch, Scholkopf, Smola, Journal of Machine Learning Research 13, 723 (2012).
Durante, Fernandez-Sanchez, Sempi · Applied Mathematics Letters 26, 945 (2013) · 2013Copulas, MMD & statistics
Cited as reference [23] in the AQS HQCS paper. Durante, Fernandez-Sanchez, Sempi, Applied Mathematics Letters 26, 945 (2013).
M. Sklar · Publ. Inst. Stat. Univ. Paris 8, 229 (1959) · 1959Copulas, MMD & statistics
Cited as reference [22] in the AQS HQCS paper. M. Sklar, Publ. Inst. Stat. Univ. Paris 8, 229 (1959).
Li, Wang, Han, Shi, Li, Shang, Zheng, Zhong, Gu · Neural Networks 166, 148 (2023) · 2023Quantum recurrent & temporal models
Cited as reference [20] in the AQS HQCS paper. Li, Wang, Han, Shi, Li, Shang, Zheng, Zhong, Gu, Neural Networks 166, 148 (2023).
Takaki, Mitarai, Negoro, Fujii, Kitagawa · Phys. Rev. A 103, 052414 (2021) · 2021Quantum recurrent & temporal models
Cited as reference [19] in the AQS HQCS paper. Takaki, Mitarai, Negoro, Fujii, Kitagawa, Phys. Rev. A 103, 052414 (2021).
Recio-Armengol, Ahmed, Bowles · arXiv:2503.02934 · 2025Quantum generative modeling
Cited as reference [16] in the AQS HQCS paper. Recio-Armengol, Ahmed, Bowles, arXiv:2503.02934.
Kasture, Kyriienko, Elfving · Phys. Rev. A 108, 042406 (2023) · 2023Quantum generative modeling
Cited as reference [15] in the AQS HQCS paper. Kasture, Kyriienko, Elfving, Phys. Rev. A 108, 042406 (2023).
B. Zhang and Q. Zhuang · Quantum Sci. Technol. 10, 015009 (2025) · 2025Barren plateaus & trainability
Cited as reference [14] in the AQS HQCS paper. B. Zhang and Q. Zhuang, Quantum Sci. Technol. 10, 015009 (2025).
McClean, Boixo, Smelyanskiy, Babbush, Neven · Nature Communications 9, 4812 (2018) · 2018Barren plateaus & trainability
Cited as reference [12] in the AQS HQCS paper. McClean, Boixo, Smelyanskiy, Babbush, Neven, Nature Communications 9, 4812 (2018).
Ransford, Allman, Arkinstall, et al. (Quantinuum) · arXiv:2511.05465 · 2025Quantum random circuit sampling & quantum advantage
Cited as reference [9] in the AQS HQCS paper. Ransford, Allman, Arkinstall, et al. (Quantinuum), arXiv:2511.05465.
Abanin, Acharya, et al. (Google Quantum AI) · Nature 646, 825 (2025) · 2025Quantum random circuit sampling & quantum advantage
Cited as reference [8] in the AQS HQCS paper. Abanin, Acharya, et al. (Google Quantum AI), Nature 646, 825 (2025).
DeCross, Haghshenas, Liu, Rinaldi, Gray, et al. (Quantinuum) · Phys. Rev. X 15, 021052 (2025) · 2025Quantum random circuit sampling & quantum advantage
Cited as reference [7] in the AQS HQCS paper. DeCross, Haghshenas, Liu, Rinaldi, Gray, et al. (Quantinuum), Phys. Rev. X 15, 021052 (2025).
Morvan, Villalonga, Mi, Mandra, et al. (Google Quantum AI) · Nature 634, 328 (2024) · 2024Quantum random circuit sampling & quantum advantage
Cited as reference [5] in the AQS HQCS paper. Morvan, Villalonga, Mi, Mandra, et al. (Google Quantum AI), Nature 634, 328 (2024).
Zhu, Cao, Chen, et al. · Science Bulletin 67, 240 (2022) · 2022Quantum random circuit sampling & quantum advantage
Cited as reference [4] in the AQS HQCS paper. Zhu, Cao, Chen, et al., Science Bulletin 67, 240 (2022).
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