Table 8. Future research directions in quantum finance.

Authors	Future research directions
Alcazar, J; Leyton-Ortega, V; Perdomo-Ortiz, A (2020)	expansion of quantum simulations to more qubits while employing target distribution samples as a training set for both classical and quantum models.
An, D; Linden, N; Liu, JP; Montanaro, A; Shao, CP; Wang, JS (2021)	provision of other meaningful characteristics of stochastic processes, finding more practical quantum input-output models for potential applications in finance
Arraut, I; Au, A; Tse, ACB; Segovia, C (2019)	modeling the uncertainties in the prices of the options by using the double-slit approach and the concept of weak-value
Arraut, I; Marques, JAL; Gomes, S (2021)	using symmetry arguments to analyze the flow of information in the stock market and its visualizations
Baaquie, BE (2018)	to research the situation in which the tenor, principal payments, and quantity of the coupon payments are all subject to stochastic variation
Baaquie, BE; Yu, M; Bhanap, J (2018)	to study Malaysian forward interest rates
Bagheri, A; Peyhani, HM; Akbari, M (2014)	to construct a real-time warning system by using the suggested method on shorter timescales.
Biesner, D; Gerlach, T; Sifa, R; Bauckhage, C; Kliem, B (2022)	to create an algorithm for smart auditing software
Chen, CM; Tso, GKF; He, KJ (2023)	optimization directions for their model: other quantum population selection techniques can be tested; the introduction of profit-based measures in their solution; performance and cost tradeoff analysis of the proposed method on many targets or labels scenario
Covers O., Doeland M. (2020)	to deal with the threats associated with quantum computing,
Coyle, B; Henderson, M; Le, JCJ; Kumar, N; Paini, M; Kashefi, E (2020)	to increase Born Machine training efficiency, to increase performance by considering quantum-specific optimizers for the model and training, expanding the range of classical model comparison, and researching ways to divide the classical-quantum resources in the learning process
Cruz, P; Cruz, H (2020)	to study the possibility of having a moving indicator based on a quantum mechanical tool
Doriguello J.F., Luongo A., Bao J., Rebentrost P., Santha M. (2022)	how and when their algorithm can find application in practice
Dupoyet, B; Fiebig, HR; Musgrove, DP (2010)	examination of the lattice characteristics of the model’s parameters, including looking for phase transitions or spontaneous symmetry-breaking
Feng, XN; Wu, HY; Zhou, XL; Yao, Y (2022)	the creation of a quantum blind signature system to address the noise situation and complete the design
Fontanela, F; Jacquier, A; Oumgari, M (2019)	to design an efficient ansatz for more complex financial products, or in the development of an ansatz-free approach
Ghosh B., Kozarevic E. (2018)	utilization by policymakers of the financial Reynolds number as an indicator of market volatility
Gomez, A; Leitao, A; Manzano, A; Musso, D; Nogueiras, MR; Ordonez, G; Vazquez, C (2022)	to discover effective unitary transform-based mathematical representations of payoff functions that can be readily implemented in a quantum circuit, as well as efficient methods for loading probability distributions into quantum registers
Griffin, P; Sampat, R (2021)	to improve quantum hardware, processing speeds, and data volumes that quantum offers
Hellstem, G (2021)	to develop hybrid quantum networks
Henkel, C (2017)	to find solutions of stochastic differential delay equations
Kaneko, K; Miyamoto, K; Takeda, N; Yoshino, K (2021)	to explore the possibility of making quantum algorithm for Monte Carlo more efficient
Khrennikova P. (2019)	to apply the theory of quantum probability’s utility to the financial market considering behavioral anomalies and state-dependent preferences
Mancilla, J; Pere, C (2022)	to expand the method to include additional datasets (with more attributes) in additional domains to establish a benchmark through a broad application
Nakaji, K; Uno, S; Suzuki, Y; Raymond, R; Onodera, T; Tanaka, T; Tezuka, H; Mitsuda, N; Yamamoto, N (2021)	to test their algorithm with a real quantum computing device.
Nastasiuk, VA (2015)	to find analytically solvable equations and use widely available financial data
Orús R., Mugel S., Lizaso E. (2019)	to research the applications of quantum simulators in finance, the impact of quantum cryptography on the security of financial transactions, and how quantum technologies can be relevant to the blockchain and cryptocurrencies
Orus, R; Mugel, S; Lizaso, E (2018)	to identify ways of improving the efficiency and accuracy of their procedure, to deal with other financial equilibrium problems
Pan, WT; Liu, Y; Jiang, H; Chen, YT; Liu, T; Qing, Y; Huang, GH; Li, R (2021)	to suggest additional strategies for improving the four algorithms, including wavelet or chaos theory
Piotrowski, EW; Sladkowski, J (2004)	markets cleared by quantum algorithms (computers)
Pistoia, M; Ahmad, SF; Ajagekar, A; Buts, A; Chakrabarti, S; Herman, D; Hu, SH; Jena, A; Minssen, P; Niroula, P; Rattew, A; Sun, Y; Yalovetzky, R (2021)	enhancing the financial sector with quantum machine learning methods in the NISQ era
Qiu Y., Liu R., Lee R.S.T. (2021)	to develop a multi-agent mechanism
Racorean O. (2013)	to see particle physics effects in the stock market
Rebentrost, P; Gupt, B; Bromley, TR (2018)	investigating the promising advantages of the continuous variable quantum computation setting in a financial context
Sarkissian, J (2020)	understanding financial processes progresses from a basic analogy-based level to a level based on physical nature.
Stamatopoulos, N; Mazzola, G; Woerner, S; Zeng, WJ (2021)	a detailed comparison of the performance between the quantum gradient algorithms and AD methods