The Quantum Dynamics of Cost Accounting: Investigating WIP via the Time-Independent Schrödinger Equation

Authors

  • Maksym Lazirko Department of Accounting & Information System, Rutgers University, New Brunswick, NJ, United States Author

DOI:

https://doi.org/10.55578/jdso.2506.002

Keywords:

Managerial Accounting, Work in Progress, Quantum Information Theory, Accounting Information Systems, Continuous Audit

Abstract

The intersection of quantum theory and accounting presents an alternative way of understanding financial valuation and accounting practices. This paper applies quantum theory to cost accounting’s work-in-progress (WIP). WIP is conceptualized as in multiple states simultaneously, which provides probability amplitudes for different WIP values, and models interdependencies between various aspects of WIP. The study demonstrates how quantum concepts such as entanglement, superposition, measurement, teleportation , entropy , and tunnelling can be adapted to represent the dynamic nature of WIP. The primary contribution of this work is a more nuanced understanding of the uncertainties involved, which emerges by applying quantum phenomena to model the complexities and uncertainties inherent in managerial accounting. In contrast, previous works focus more on financial accounting or general accountancy.

References

1.Budd, C. S. (2010). Traditional measures in finance and accounting, problems, literature review, and TOC measures. Theory of Constraints Handbook, 335–372.

2.Frino, R. A. (2015). Quantum Superposition, Parallel Universes and Time Travel. viXra. https://consensus.app/papers/quantum-superposition-parallel-universes-time-travel-frino/ed44c9f2285955fdb31b8a4f108d200c/

3.Kovács, G. (2016). LOGISTICS AND PRODUCTION PROCESSES TODAY AND TOMORROW. Acta Logistica, 3(4), 1–5. https://doi.org/10.22306/al.v3i4.71

4.Myrelid, A., & Olhager, J. (2015). Applying modern accounting techniques in complex manufacturing. Industrial Management & Data Systems, 115(3), 402–418. https://doi.org/10.1108/IMDS-09-2014-0250

5.Demski, J. S., FitzGerald, S. A., Ijiri, Y., Ijiri, Y., & Lin, H. (2006). Quantum information and accounting information: Their salient features and conceptual applications. Journal of Accounting and Public Policy, 25(4), 435–464. https://doi.org/10.1016/j.jaccpubpol.2006.05.004

6.Kahyao, ğlu S. B. (2023). An evaluation of accounting and auditing framework within the quantum perspective. Southern African Journal of Accountability and Auditing Research, 25(1), 1–5. https://doi.org/10.10520/ejc-sajaar_v25_n1_a1

7.De Oliveira, K. V., & Lustosa, P. R. B. (2022). The entanglement of accounting goodwill: Einstein’s “spooky action at a distance.” Accounting Forum, 1–22. https://doi.org/10.1080/01559982.2022.2089319

8.Demski, J. S., FitzGerald, S. A., Ijiri, Y., Ijiri, Y., & Lin, H. (2006). Quantum information and accounting information: Their salient features and conceptual applications. Journal of Accounting and Public Policy, 25(4), 435-464.

9.Fellingham, J., Lin, H., & Schroeder, D. (2022). Entropy, Double Entry Accounting and Quantum Entanglement. Foundations and Trends® in Accounting, 16(4), 308–396. https://doi.org/10.1561/1400000069

10.Fellingham, J. C., Lin, H., & Schroeder, D. (2018). Quantum Entropy and Accounting. SSRN Electronic Journal. https://doi.org/10.2139/ssrn.3220892

11.Fellingham, J., & Schroeder, D. (2006). Quantum information and accounting. Journal of Engineering and Technology Management, 23(1–2), 33–53. https://doi.org/10.1016/j.jengtecman.2006.02.004

12.Demski, J. S., FitzGerald, S. A., Ijiri, Y., Ijiri, Y., & Lin, H. (2009). Quantum information and accounting information: Exploring conceptual applications of topology. Journal of Accounting and Public Policy, 28(2), 133–147. https://doi.org/10.151016/j.jaccpubpol.2009.01.002

13.Lazirko, M. (2023). Quantum Computing Standards & Accounting Information Systems (arXiv:2311.11925). arXiv. http://arxiv.org/abs/2311.11925.

14.Orrell, D. (2019). Quantum Financial Entanglement: The Case of Strategic Default. SSRN Electronic Journal. https://doi.org/10.2139/ssrn.3394550

15.Lee, R. S. (2021). Quantum finance forecast system with qu15antum anharmonic oscillator model for quantum price level modeling. International Advance Journal of Engineering Research, 4(02), 01–21.

16.Peres, A. (2000). Classical interventions in quantum systems. I. The measuring process. Physical Review A, 61(2), 022116. https://doi.org/10.1103/PhysRevA.61.022116

17.Wang, X.-L., Cai, X.-D., Su, Z.-E., Chen, M.-C., Wu, D., Li, L., Liu, N.-L., Lu, C.-Y., & Pan, J.-W. (2015). Quantum teleportation of multiple degrees of freedom of a single photon. Nature, 518(7540), 516–519. https://doi.org/10.1038/nature14246

18.Lee, S. M., Lee, S.-W., Jeong, H., & Park, H. S. (2020). Quantum Teleportation of Shared Quantum Secret. Physical Review Letters, 124(6), 060501. https://doi.org/10.1103/PhysRevLett.124.060501

19.Davis, M. J., & Heller, E. J. (1981). Quantum dynamical tunneling in bound states. The Journal of Chemical Physics, 75(1), 246–254. https://doi.org/10.1063/1.441832

20.Swieringa, R., Gibbins, M., Larsson, L., & Sweeney, J. L. (1976). Experiments in the Heuristics of Human Information Processing. Journal of Accounting Research, 14, 159. https://doi.org/10.2307/2490450

21.Meade, D. J., Kumar, S., & Kensinger, K. R. (2008). Investigating impact of the order activity costing method on product cost calculations. Journal of Manufacturing Systems, 27(4), 176–189. https://doi.org/10.1016/j.jmsy.2009.02.003

22.Almeida, R., Abrantes, R., Romão, M., & Proença, I. (2020). The Impact of Uncertainty in the Measurement of Progress in Earned Value Analysis. 457–467. https://doi.org/10.1016/J.PROCS.2021.01.191

23.Specogna, R., & Trevisan, F. (2011). A discrete geometric approach to solving time independent Schrödinger equation. Journal of Computational Physics, 230(4), 1370–1381. https://doi.org/10.1016/j.jcp.2010.11.007

24.CHENG, T. C. E. (1991). An Economic Order Quantity Model with Demand-Dependent Unit Production Cost and Imperfect Production Processes. IIE TRANSACTIONS. https://doi.org/10.1080/07408179108963838

25.Hussain, O., Dillon, T., Hussain, F. K., & Chang, E. (2011). Probabilistic assessment of financial risk in e-business associations. Simulation Modelling Practice and Theory, 19(2), 704–717. https://doi.org/10.1016/j.simpat.2010.10.007

26.Wróblewski, M. (2017). Nonlinear Schrödinger approach to European option pricing. Open Physics, 15(1), 280–291. https://doi.org/10.1515/phys-2017-0031

27.Ivancevic, V. G. (2010). Adaptive-Wave Alternative for the Black-Scholes Option Pricing Model. Cognitive Computation, 2(1), 17–30. https://doi.org/10.1007/s12559-009-9031-x

28.Chen, J. M. (2017). Econophysical Models of Finance: Baryonic Beta Dynamics and Beyond. SSRN Electronic Journal. https://doi.org/10.2139/ssrn.3059436

29.Arraut, I., Au, A., & Ching-biu Tse, A. (2020). Spontaneous symmetry breaking in quantum finance. Europhysics Letters, 131(6), 68003. https://doi.org/10.1209/0295-5075/131/68003

30.Arraut, I., Lobo Marques, J. A., & Gomes, S. (2021). The Probability Flow in the Stock Market and Spontaneous Symmetry Breaking in Quantum Finance. Mathematics, 9(21), Article 21. https://doi.org/10.3390/math9212777

31.Zheng, H., & Bai, J. (2024). Quantum Leap: A Price Leap Mechanism in Financial Markets. Mathematics, 12(2), Article 2. https://doi.org/10.3390/math12020315

32.Srokowski, T. (2001). Stochastic processes with finite correlation time: Modeling and application to the generalized Langevin equation. Physical Review E, 64(3), 031102. https://doi.org/10.1103/PhysRevE.64.031102

33.Korzh. R, & Р.в, К. (2024). Quantum economics: Key features and postulates. Economy and Entrepreneurship, 52, 17-26.https://doi.org/10.33111/EE.2024.52.

34.Ledinauskas, E., & Anisimovas, E. (2023). Scalable Imaginary Time Evolution with Neural Network Quantum States. SciPost Physics, 15(6), 229. https://doi.org/10.21468/SciPostPhys.15.6.229

35.Demeter, K., & Matyusz, Z. (2011). The impact of lean practices on inventory turnover. International Journal of Production Economics, 133(1), 154–163. https://doi.org/10.1016/j.ijpe.2009.10.031

36.Holster, A. (2021). Explaining Relativity: Summary of TAU - A Unified Theory. https://mail.vixra.org/abs/2108.0039

37.Majid, S. (1994). The quantum double as quantum mechanics. Journal of Geometry and Physics, 13(2), 169–202. https://doi.org/10.1016/0393-0440(94)90026-4

38.Li, L. (2025). Quantum Probability Theoretic Asset Return Modeling: A Novel Schrödinger-Like Trading Equation and Multimodal Distribution. Quantum Economics and Finance, 29767032251331075. https://doi.org/10.1177/29767032251331075

39.Osypanka, P., & Nawrocki, P. (2022). Resource Usage Cost Optimization in Cloud Computing Using Machine Learning. IEEE Transactions on Cloud Computing, 10, 2079–2089. https://doi.org/10.1109/TCC.2020.3015769

40.Zhao, T., Sun, C., Cohen, A., Stokes, J., & Veerapaneni, S. K. (2022). Quantum-inspired variational algorithms for partial differential equations: Application to financial derivative pricing. CoRR. https://openreview.net/forum?id=pxtos0Okgm&referrer=%5Bthe%20profile%20of%20Tianchen%20Zhao%5D(%2Fprofile%3Fid%3D~Tianchen_Zhao1)

41.Sato, Y., Kondo, R., Hamamura, I., Onodera, T., & Yamamoto, N. (2024). Hamiltonian simulation for hyperbolic partial differential equations by scalable quantum circuits. Physical Review Research, 6(3), 033246. https://doi.org/10.1103/PhysRevResearch.6.033246

42.Olajiga, O. K., Ani, E. C., Olu-lawal, K. A., Montero, D. J. P., & Adeleke, A. K. (2024). INTELLIGENT MONITORING SYSTEMS IN MANUFACTURING: CURRENT STATE AND FUTURE PERSPECTIVES. Engineering Science & Technology Journal. https://doi.org/10.51594/estj.v5i3.870

43.Cui, J., Brouwer, P. J. S. de, Herbert, S., Intallura, P., Kargi, C., Korpas, G., Krajenbrink, A., Shoosmith, W., Williams, I., & Zheng, B. (2024). Quantum Monte Carlo Integration for Simulation-Based Optimisation (arXiv:2410.03926). arXiv. https://doi.org/10.48550/arXiv.2410.03926

44.Wolf, M.-O., Ewen, T., & Turkalj, I. (2023). Quantum Architecture Search for Quantum Monte Carlo Integration via Conditional Parameterized Circuits with Application to Finance. 2023 IEEE International Conference on Quantum Computing and Engineering (QCE), 560–570. https://doi.org/10.1109/QCE57702.2023.00070

45.Christmann, J. (2025). From quantum-enhanced to quantum-inspired Monte Carlo. Physical Review A, 111(4). https://doi.org/10.1103/PhysRevA.111.042615

46.Buonaiuto, G., Gargiulo, F., De Pietro, G., Esposito, M., & Pota, M. (2023). Best practices for portfolio optimization by quantum computing, experimented on real quantum devices. Scientific Reports, 13(1), 19434. https://doi.org/10.1038/s41598-023-45392-w

47.Schneider, B. I., & Collins, L. A. (2005). The discrete variable method for the solution of the time-dependent Schrödinger equation. Journal of Non-Crystalline Solids, 351(18), 1551–1558. https://doi.org/10.1016/j.jnoncrysol.2005.03.028

Downloads

Published

2025-06-13

Data Availability Statement

No new data were created or analyzed in this study. Data sharing is not applicable to this article.

Issue

Section

Articles

How to Cite

The Quantum Dynamics of Cost Accounting: Investigating WIP via the Time-Independent Schrödinger Equation. (2025). Journal of Decision Science and Optimization, 1(1), 35-54. https://doi.org/10.55578/jdso.2506.002