{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,4]],"date-time":"2026-08-04T04:45:51Z","timestamp":1785818751763,"version":"3.56.0"},"reference-count":25,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006467","name":"Research Institute of Electrical Communication, Tohoku University","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100006467","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Quantum circuit simulation is usually evaluated through final numerical accuracy, while the dynamics of stochastic execution itself are less explicitly characterized. This work presents a precision-elastic persistent stochastic execution framework based on integral stochastic computing (ISC), where execution behavior is controlled by stream length N and ISC multiplicity m, where m represents the number of aggregated stochastic sub-streams per cycle (standard SC corresponds to m = 1). We focus on correlation-sensitive propagation under persistent reuse, and show that this regime produces circuit-dependent stochastic behavior and execution uncertainty patterns that are not captured by stage-wise re-encoded execution alone. To characterize this behavior, we use high-m tail descriptors, including the circuit-dependent coefficient \u03b3c, as compact indicators of persistent stochastic sensitivity. Across benchmark circuits, persistent execution exhibits reproducible tail regimes and structured cross-circuit variability, while deterministic reduced-precision baselines are used only as trend-consistency references. We further demonstrate adaptive stochastic precision scheduling, where circuit-dependent (N,m) settings satisfy a target fidelity with reduced stochastic workload. These results position persistent ISC as a configurable stochastic execution framework for analyzing execution-induced uncertainty propagation and correlation-sensitive behavior in quantum circuits.<\/jats:p>","DOI":"10.3390\/e28080862","type":"journal-article","created":{"date-parts":[[2026,8,3]],"date-time":"2026-08-03T15:51:23Z","timestamp":1785772283000},"page":"862","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Precision-Elastic Persistent Stochastic Execution for Quantum Circuit Simulation"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4855-7081","authenticated-orcid":false,"given":"Naoya","family":"Onizawa","sequence":"first","affiliation":[{"name":"Research Institute of Electrical Communication, Tohoku University, Sendai 980-8577, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8754-0701","authenticated-orcid":false,"given":"Martin","family":"Lukac","sequence":"additional","affiliation":[{"name":"Graduate School of Information Sciences, Hiroshima City University, Hiroshima 731-3194, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4783-7487","authenticated-orcid":false,"given":"Shinobu","family":"Nagayama","sequence":"additional","affiliation":[{"name":"Graduate School of Information Sciences, Hiroshima City University, Hiroshima 731-3194, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4397-8290","authenticated-orcid":false,"given":"Takahiro","family":"Hanyu","sequence":"additional","affiliation":[{"name":"Research Institute of Electrical Communication, Tohoku University, Sendai 980-8577, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,1]]},"reference":[{"key":"ref_1","unstructured":"Nielsen, M.A., and Chuang, I.L. (2010). Quantum Computation and Quantum Information, Cambridge University Press. [10th anniversary ed.]."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"963","DOI":"10.1137\/050644756","article-title":"Simulating quantum computation by contracting tensor networks","volume":"38","author":"Markov","year":"2008","journal-title":"SIAM J. Comput."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"147902","DOI":"10.1103\/PhysRevLett.91.147902","article-title":"Efficient classical simulation of slightly entangled quantum computations","volume":"91","author":"Vidal","year":"2003","journal-title":"Phys. Rev. Lett."},{"key":"ref_4","unstructured":"(2026, February 25). Google Quantum AI; Quantumlib Contributors. qsim. High-Performance Quantum Circuit Simulator. Available online: https:\/\/github.com\/quantumlib\/qsim."},{"key":"ref_5","unstructured":"Qiskit Development Team (2026, February 25). Qiskit Aer. High-Performance Quantum Circuit Simulators. Available online: https:\/\/github.com\/Qiskit\/qiskit-aer."},{"key":"ref_6","unstructured":"NVIDIA (2026, February 25). NVIDIA cuQuantum SDK. GPU-Accelerated Quantum Simulation Libraries. Available online: https:\/\/developer.nvidia.com\/cuquantum-sdk."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1145\/3550488","article-title":"QASMBench: A low-level QASM benchmark suite for NISQ evaluation and simulation","volume":"4","author":"Li","year":"2023","journal-title":"ACM Trans. Quantum Comput."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"130232","DOI":"10.1109\/ACCESS.2025.3589746","article-title":"AEQUAM: Accelerating Quantum Algorithm Validation through FPGA-Based Emulation","volume":"13","author":"Lagostina","year":"2025","journal-title":"IEEE Access"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Liang, S., Lu, Y., Guo, C., Luk, W., and Kelly, P.H.J. (2024, January 5\u20138). PCQ: Parallel Compact Quantum Circuit Simulation. Proceedings of the 32nd IEEE Annual International Symposium on Field-Programmable Custom Computing Machines (FCCM), Orlando, FL, USA.","DOI":"10.1109\/FCCM60383.2024.00013"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1145\/2465787.2465794","article-title":"Survey of stochastic computing","volume":"12","author":"Alaghi","year":"2013","journal-title":"ACM Trans. Embed. Comput. Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2688","DOI":"10.1109\/TVLSI.2017.2654298","article-title":"VLSI Implementation of Deep Neural Network Using Integral Stochastic Computing","volume":"25","author":"Ardakani","year":"2017","journal-title":"IEEE Trans. Very Large Scale Integr. (VLSI) Syst."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Gross, W.J., and Gaudet, V.C. (2019). Accuracy and Correlation in Stochastic Computing. Stochastic Computing: Techniques and Applications, Springer.","DOI":"10.1007\/978-3-030-03730-7"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Lee, V.T., Alaghi, A., and Ceze, L. (2018). Correlation Manipulating Circuits for Stochastic Computing. arXiv.","DOI":"10.23919\/DATE.2018.8342234"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Wang, M., Tannu, S., and Nair, P.J. (2025). Accelerating Simulation of Quantum Circuits under Noise via Computational Reuse. Proceedings of the 52nd Annual International Symposium on Computer Architecture, Tokyo, Japan, 21\u201325 June 2025, Association for Computing Machinery. ISCA \u201925.","DOI":"10.1145\/3695053.3730992"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Gr\u00fcrl, T., Kueng, R., Fu\u00df, J., and Wille, R. (2020). Stochastic Quantum Circuit Simulation Using Decision Diagrams. arXiv.","DOI":"10.23919\/DATE51398.2021.9474135"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"662","DOI":"10.1063\/1.4822960","article-title":"Diffusion Quantum Monte Carlo","volume":"4","author":"Reynolds","year":"1990","journal-title":"Comput. Phys."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Yang, Y., Lu, B.N., and Li, Y. (2021). Accelerated quantum Monte Carlo with mitigated error on noisy quantum computers. arXiv.","DOI":"10.1103\/PRXQuantum.2.040361"},{"key":"ref_18","first-page":"1737","article-title":"Deep learning with limited numerical precision","volume":"Volume 37","author":"Gupta","year":"2015","journal-title":"Proceedings of the 32nd International Conference on Machine Learning, Lille, France, 7\u20139 July 2015"},{"key":"ref_19","unstructured":"Micikevicius, P., Narang, S., Alben, J., Diamos, G., Elsen, E., Garc\u00eda, D., Ginsburg, B., Houston, M., Kuchaiev, O., and Venkatesh, G. (May, January 30). Mixed precision training. Proceedings of the International Conference on Learning Representations (ICLR), Vancouver, BC, Canada."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Han, J., and Orshansky, M. (2013, January 27\u201330). Approximate computing: An emerging paradigm for energy-efficient design. Proceedings of the 2013 18th IEEE European Test Symposium (ETS), Avignon, France.","DOI":"10.1109\/ETS.2013.6569370"},{"key":"ref_21","first-page":"031014","article-title":"Stochastic p-bits for invertible logic","volume":"7","author":"Camsari","year":"2017","journal-title":"Phys. Rev. X"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3102823","DOI":"10.1109\/TQE.2026.3681202","article-title":"Grover Adaptive Search-Based Hybrid Benders Decomposition for Mixed-Integer Linear Programs","volume":"7","author":"Zheng","year":"2026","journal-title":"IEEE Trans. Quantum Eng."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Osca, J., and Vala, J. (2023). SOQCS: A Stochastic Optical Quantum Circuit Simulator. arXiv.","DOI":"10.1016\/j.softx.2023.101603"},{"key":"ref_24","unstructured":"Onizawa, N. (2026, February 25). Persistent ISC Quantum Simulation. Available online: https:\/\/github.com\/nonizawa\/persistent-isc-quantum-sim."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Lukac, M., Onizawa, N., and Nagayama, S. (2026, January 19\u201321). A Stochastic-Computing-Based Framework for Quantum Circuit Simulation. Proceedings of the IEEE International Symposium on Multiple-Valued Logic (ISMVL), Sendai, Japan.","DOI":"10.1109\/ISMVL68998.2026.00035"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/8\/862\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,4]],"date-time":"2026-08-04T04:20:08Z","timestamp":1785817208000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/8\/862"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8,1]]},"references-count":25,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2026,8]]}},"alternative-id":["e28080862"],"URL":"https:\/\/doi.org\/10.3390\/e28080862","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,8,1]]}}}