Skip to main content
. 2024 Jul 18;19(7):e0304317. doi: 10.1371/journal.pone.0304317

Table 7. Research themes in quantum finance.

Quantum finance approaches Pubs Authors
1 Financial markets (risk, crisis, time series predictions) 43 Aboussalah, AM; Chi, C; Lee, CG (2023); Alcazar, J; Leyton-Ortega, V; Perdomo-Ortiz, A (2020); An, D et al (2021); Araújo R.D.A., De Oliveira A.L.I., Soares S.C.B. (2010a); Araujo, R.D.A.; de Oliveira, A.L.I.; Soares, S.C.B. (2010b); Arraut, I; Au, A; Tse, ACB (2020); Baaquie, B.E. (2007); Bai, L et al (2020); Barad, G (2012); Chang B.R., Tsai H.F. (2006a); Chang, B.R.; Tsai, HF (2006b); Chang, BR; Tsai, HF (2009); Cruz, P; Cruz, H (2020); Ding, YC et al (2023); Gomez, A et al (2022); Goncalves, CP (2011); Griffin, P; Sampat, R (2021); Hanauske, M et al (2010); Henkel, C (2017); Hwang J.H. (2015); Kaneko, K et al (2021); Kim, MJ et al (2011); Manjunath C., Marimuthu B., Ghosh B. (2023); Mugel S., Lizaso E., Orús R. (2020); Nastasiuk, VA (2014); Nastasiuk, VA (2015); Orús R., Mugel S., Lizaso E. (2019); Orus, R; Mugel, S; Lizaso, E (2018); Paquet, E; Soleymani, F (2022); Racorean O. (2013); Romero J.M., Lavana U., Miranda E.M. (2014); Schaden, M (2002); Wang, CF; Yang, YK; Xu, LL; Wong, A (2023); Wilkens, S; Moorhouse, J (2023);
Financial Time Series Forecasting 14
Volatility models, price volatility, The Greeks, volatility clustering effect, chaotic volatility 10
Systematic risk, risk management, value at risk (VaR), financial risk, risk analysis 7
Financial shock, financial crisis, prediction of financial crashes 5
NGARCH Composite Model (nonlinear type of generalized autoregressive 2
Dynamic Time Warping (DTW) 2
Other topics (Random Walk Dilemma, Time Phase Distortions Adjustment, Generative models) 3
2 Models for financial derivatives 65 An, D et al (2021); Araújo R.D.A., De Oliveira A.L.I., Soares S.C.B. (2010a); Araujo, R.D.A.; de Oliveira, A.L.I.; Soares, S.C.B. (2010b); Baaquie B.E. (2008a); Baaquie, B.E. (2018); Baaquie, B.E. (2007); Baaquie, B.E. (2013); Baaquie, B.E. (2010); Baaquie, B.E. (2009); Baaquie, B.E. (2008b); Baaquie, BE; Du, X; Tang, P; Cao, Y (2014); Baaquie, BE; Liang, C (2007a); Baaquie, BE; Liang, C (2007b); Baaquie, BE; Pan, T (2011); Baaquie, BE; Tang, P (2012); Baaquie, BE; Yang, C (2009); Baaquie, BE; Yu, M; Bhanap, J (2018); Bagheri, A; Peyhani, HM; Akbari, M (2014); Barad, G (2012); Darbyshire, P (2005); Doriguello J.F. et al (2022); Fernandez-Lorenzo, S; Porras, D; Garcia-Ripoll, JJ (2021); Fontanela, F; Jacquier, A; Oumgari, M (2019); Gomez, A et al (2022); Hellstem, G (2021); Ingber L. (2015); Khrennikov, A (2007); Kim, MJ et al (2011); Manjunath C., Marimuthu B., Ghosh B. (2023); Martin, A et al (2019); Melnyk S.I., Tuluzov I.G. (2008); Orús R., Mugel S., Lizaso E. (2019); Paquet, E; Soleymani, F (2022); Rebentrost, P; Gupt, B; Bromley, TR (2018); Romero, JM; Miranda, EM; Lavana, U (2014); Stamatopoulos, N et al (2021); Wilkens, S; Moorhouse, J (2023);
Interest rate options, interest rate swap, swap options, Libor, forward interest rate, accrual swap, caplet 13
Hybrid model
11
European options on coupon bonds, index-linked coupon bonds, American options on coupon bond 10
Financial Derivatives
9
Option pricing model
8
Heath, Jarrow and Morton (HJM) model 3
Barrier options
3
BGM–Jamshidian model 2
Black’s caplet formula 2
Other topics (sukuk, options on stocks, automatic differentiation, options on foreign exchange) 4
3 Financial mathematics 68 An, D et al (2021); Arraut, I; Au, A; Tse, ACB (2020); Arraut, I; Marques, JAL; Gomes, S (2021); Baaquie, B.E. (2018); Baaquie, B.E. (2009); Baaquie, B.E. (2008b); Baaquie, BE; Du, X; Tang, P; Cao, Y (2014); Bagheri, A; Peyhani, HM; Akbari, M (2014); Barad, G (2012); Biesner, D et al (2022); Cruz, P; Cruz, H (2020); Darbyshire, P (2005); Doriguello J.F. et al (2022); Farinelli S., Takada H. (2022); Fontanela, F; Jacquier, A; Oumgari, M (2019); Gomez, A et al (2022); Haven E. (2007); Henkel, C (2017); Kaneko, K et al (2021); Martin, A et al (2019); Melnyk S.I., Tuluzov I.G. (2008); Nastasiuk, VA (2014); Nastasiuk, VA (2015); Orús R., Mugel S., Lizaso E. (2019); Orus, R; Mugel, S; Lizaso, E (2018); Racorean O. (2013); Rebentrost, P; Gupt, B; Bromley, TR (2018); Romero J.M., Lavana U., Miranda E.M. (2014); Romero, JM; Miranda, EM; Lavana, U (2014); Schaden, M (2002); Stamatopoulos, N et al (2021); Tahmasebi, F et al (2015); Tang, YH et al (2022); Yaghobipour, S; Yarahmadi, M (2018); Yaghobipour, S; Yarahmadi, M (2020); Yeşiltaş Ö. (2023)
Black—Scholes equations, Black-Scholes Quantum formula 13
Hamiltonian approach
13
Monte Carlo methods
12
Schrodinger Equation 8
Stochastic differential equations (SDEs), stochastic Taylor expansion, Ito calculus 6
Martingale condition 3
Merton-Garman equations 2
Spontaneous symmetry breaking 2
Other topics (fractals, Fisher information approach, Hilbert Space, Poisson Jump Process, Hull-White model, Wavelet Transform (WT), Hopf algebra, Hamilton–Jacobi–Bellman (HJB) equation, subset sum) 9
4 Quantum optimization techniques 20 Aboussalah, AM; Chi, C; Lee, CG (2023); Alcazar, J; Leyton-Ortega, V; Perdomo-Ortiz, A (2020); Bagheri, A; Peyhani, HM; Akbari, M (2014); Biesner, D et al (2022); Ding, YC et al (2023); Fernandez-Lorenzo, S; Porras, D; Garcia-Ripoll, JJ (2021); Griffin, P; Sampat, R (2021); Mugel S., Lizaso E., Orús R. (2020); Nakaji, K et al (2021); Orús R., Mugel S., Lizaso E. (2019); Orus, R; Mugel, S; Lizaso, E (2018); Pan, WT et al (2021); Piotrowski, EW; Sladkowski, J (2001); Qiu Y., Liu R., Lee R.S.T. (2021); Sun, J; Xu, WB; Fang, W (2010); Tang, YH et al (2022); Yaghobipour, S; Yarahmadi, M (2018); Yaghobipour, S; Yarahmadi, M (2020);
Optimization model, quadratic unconstrained binary optimization (QUBO), Fruit Fly Optimization Algorithm (QFOA), Bee Colony Optimization Algorithm (QABC), Quantum-behaved Particle Swarm Optimization (QPSO), Ant Colony Optimization (QACO), a higher-order unconstrained binary optimization (HUBO) 10
Portofolio optimization 9
Variational quantum algorithms (VQAs) 1
5 Quantum mechanics / theory 110 Aboussalah, AM; Chi, C; Lee, CG (2023); Alcazar, J; Leyton-Ortega, V; Perdomo-Ortiz, A (2020); Araújo R.D.A., De Oliveira A.L.I., Soares S.C.B. (2010a); Araujo, R.D.A.; de Oliveira, A.L.I.; Soares, S.C.B. (2010b); Baaquie, B.E. (2007); Baaquie, BE; Liang, C (2007a); Baaquie, BE; Liang, C (2007b); Bagheri, A; Peyhani, HM; Akbari, M (2014); Bai, L et al (2020); Biesner, D et al (2022); Chang B.R., Tsai H.F. (2006a); Chang, B.R.; Tsai, HF (2006b); Chang, BR; Tsai, HF (2009); Chen, CM; Tso, GKF; He, KJ (2023); Choustova O. (2007a); Choustova O. (2007b); Choustova, O (2009); Choustova, OA (2007c); Covers O., Doeland M. (2020); Coyle, B et al (2020); Cruz, P; Cruz, H (2020); Darbyshire, P (2005); Ding, YC et al (2023); Dupoyet, B; Fiebig, HR; Musgrove, DP (2010); Farinelli S., Takada H. (2022); Feng, XN et al (2022); Ghosh B., Kozarevic E. (2018); Gomez, A et al (2022); Goncalves, CP (2011); Griffin, P; Sampat, R (2021); Hanauske, M et al (2010); Haven E. (2007); Haven E. (2019); Hellstem, G (2021); Henkel, C (2017); Ingber L. (2015); Khrennikov, A (2007); Khrennikova P. (2019); Kim, MJ et al (2011); Mancilla, J; Pere, C (2022); Manjunath C., Marimuthu B., Ghosh B. (2023); Martin, A et al (2019); Nakaji, K et al (2021); Nakayama, Y (2009); Nastasiuk, VA (2014); Orús R., Mugel S., Lizaso E. (2019); Orus, R; Mugel, S; Lizaso, E (2018); Paquet, E; Soleymani, F (2022); Petrenko, K; Mashatan, A; Shirazi, F (2019); Piotrowski, EW; Sladkowski, J (2004); Piotrowski, EW; Sladkowski, J (2001); Pistoia, M et al (2021); Qiu Y., Liu R., Lee R.S.T. (2021); Sarkissian, J (2020); Schaden, M (2002); Singh, S; Subrahmanya, MHB (2021); Stamatopoulos, N et al (2021); Tahmasebi, F et al (2015); Tang, YH et al (2022); Wang, CF; Yang, YK; Xu, LL; Wong, A (2023); Wilkens, S; Moorhouse, J (2023); Yaghobipour, S; Yarahmadi, M (2018); Yeşiltaş Ö. (2023)
Behavioral financial model, artificial neural network, quantum neural network, Hopfield networks, mobile behavior 14
Quantum mechanics 12
Quantum machine learning 9
Noisy intermediate-scale quantum (NISQ) 7
Bohmian Mechanics, pilot wave model 6
Quantum game theory, Hawk–dove game 5
Bohm-Vigier model, stochastic mechanics 4
Quantum probabilistic model, quantum probability 4
Restricted Boltzmann machines (RBMs) 3
Quantum Inspired Evolutionary Algorithm (QIEA) 3
Feynmann diagrams / perturbation 3
Quantum minimization 3
BPNN-weighted GREY-C3LSP prediction 3
Quantum cryptography, cyber security, cryptographyc algorithms 3
Approximate Amplitude Encoding, quantum amplitude estimation 3
Quantum circuit Born mashines (QCBMs) 2
Quibit MultiLayer Perceptron (QuMLP) 2
Lattice theory 2
D-Wave 2000Q quantum annealer, quantum annealers, D-Wave machine 2
Quantum Social Science (QSS), quantum world in social phenomena 2
Support Vector Machine (SVM) 2
Other topics (Quantum partitioning, Weak-value, Double slit experiment, Adaptive Network-based Fuzzy Inference System (ANFIS), Quantum Entropy, continuous-time quantum walk (CTQW), Tight-binding methods, Gauge invariance, quantum blind signature, Khrennikov Quantum Potential Quantum-like Approach, quantum path-integral, quantum data encoding, Reggeon field theory, Quantum Zeno effect, Deep Reinforcement Learning (DRL), Quantum coupled-wave theory) 16