A Sc2C2@C88-cluster-based ultra-compact multilevel probabilistic bit for matrix multiplication
Source abstract
Abstract
Information units are progressively approaching the fundamental physical limits of integration density, including in terms of extremely small sizes, multistates and probabilistic traversal. However, simultaneously encompassing all of these characteristics in a unit remains elusive. Here, via real-time in situ electrical monitoring, we clearly observed stochastic alterations of multiple conductance states in Sc2C2@C88. The true random bit sequence generated exhibited an autocorrelation function whose confidence interval fell within ±0.02, demonstrating high-quality randomness. The alterations of multiple conductance states are controllable, that is, whose probability distributions could traverse from 0 to 1, enabling us to factorize 551 into its prime factors. Furthermore, we proposed a matrix-chain multiplication scheme and experimentally verified the multiplication of two 4 × 4 state-transition matrices with a small maximum error of <0.05. Combined with theoretical calculations, the stochastic but controllable multistates are probably attributed to the rich energy landscape, which could be stepwise changed by the electric field. Our findings reveal extremely small multilevel probabilistic bit for matrix multiplication, which pave the way for ultra-compact intelligent electronic devices.
Source: europepmc · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Quantum Computing Algorithms and Architecture · Quantum and electron transport phenomena · Quantum many-body systems
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (64)
Show source-provided references
1. Markov, I. L. Limits on fundamental limits to computation. Nature 512, 147–154 (2014).10.1038/nature13570 ↗
2. Wang, H. et al. Scientific discovery in the age of artificial intelligence. Nature 620, 47–60 (2023).10.1038/s41586-023-06221-2 ↗
3. Adleman, L. M. Molecular computation of solutions to combinatorial problems. Science 266, 1021–1024 (1994).10.1126/science.7973651 ↗
4. Cherry, K. M. & Qian, L. Scaling up molecular pattern recognition with DNA-based winner-take-all neural networks. Nature 559, 370–376 (2018).10.1038/s41586-018-0289-6 ↗
5. Woods, D. et al. Diverse and robust molecular algorithms using reprogrammable DNA self-assembly. Nature 567, 366–372 (2019).10.1038/s41586-019-1014-9 ↗
6. Lv, H. et al. DNA-based programmable gate arrays for general-purpose DNA computing. Nature 622, 292–300 (2023).10.1038/s41586-023-06484-9 ↗
7. Schirm, C. et al. A current-driven single-atom memory. Nat. Nanotechnol. 8, 645–648 (2013).10.1038/nnano.2013.170 ↗
8. Donati, F. et al. Magnetic remanence in single atoms. Science 352, 318–321 (2016).10.1126/science.aad9898 ↗
9. Kalff, F. E. et al. A kilobyte rewritable atomic memory. Nat. Nanotechnol. 11, 926–929 (2016).10.1038/nnano.2016.131 ↗
10. Natterer, F. D. et al. Reading and writing single-atom magnets. Nature 543, 226–228 (2017).10.1038/nature21371 ↗
11. Hus, S. M. et al. Observation of single-defect memristor in an MoS2 atomic sheet. Nat. Nanotechnol. 16, 58–62 (2021).10.1038/s41565-020-00789-w ↗
12. Vincent, R., Klyatskaya, S., Ruben, M., Wernsdorfer, W. & Balestro, F. Electronic read-out of a single nuclear spin using a molecular spin transistor. Nature 488, 357–360 (2012).10.1038/nature11341 ↗
13. Thiele, S. et al. Electrically driven nuclear spin resonance in single-molecule magnets. Science 344, 1135–1138 (2014).10.1126/science.1249802 ↗
14. Goodwin, C. A. P., Ortu, F., Reta, D., Chilton, N. F. & Mills, D. P. Molecular magnetic hysteresis at 60 kelvin in dysprosocenium. Nature 548, 439–442 (2017).10.1038/nature23447 ↗
15. Kato, C. et al. Giant hysteretic single-molecule electric polarisation switching above room temperature. Angew. Chem. Int. Ed. 57, 13429–13432 (2018).10.1002/anie.201806803 ↗
16. Zhang, K. et al. A Gd@C82 single-molecule electret. Nat. Nanotechnol. 15, 1019–1024 (2020).10.1038/s41565-020-00778-z ↗
17. Li, J. et al. Room-temperature logic-in-memory operations in single-metallofullerene devices. Nat. Mater. 21, 917–923 (2022).10.1038/s41563-022-01309-y ↗
18. Athmanathan, A., Stanisavljevic, M., Papandreou, N., Pozidis, H. & Eleftheriou, E. Multilevel-cell phase-change memory: a viable technology. IEEE J. Emerg. Sel. Topics Circuits Syst. 6, 87–100 (2016).10.1109/JETCAS.2016.2528598 ↗
19. Goswami, S. et al. Decision trees within a molecular memristor. Nature 597, 51–56 (2021).10.1038/s41586-021-03748-0 ↗
20. Rao, M. et al. Thousands of conductance levels in memristors integrated on CMOS. Nature 615, 823–829 (2023).10.1038/s41586-023-05759-5 ↗
21. Sharma, D. et al. Linear symmetric self-selecting 14-bit kinetic molecular memristors. Nature 633, 560–566 (2024).10.1038/s41586-024-07902-2 ↗
22. Correll, J. M. et al. An 8-bit 20.7 TOPS/W multilevel cell ReRAM macro with ADC-assisted bit-serial processing. IEEE J. Solid-State Circuits 60, 2995–3008 (2025).10.1109/JSSC.2025.3540114 ↗
23. Borders, W. A. et al. Integer factorization using stochastic magnetic tunnel junctions. Nature 573, 390–393 (2019).10.1038/s41586-019-1557-9 ↗
24. Roques-Carmes, C. et al. Biasing the quantum vacuum to control macroscopic probability distributions. Science 381, 205–209 (2023).10.1126/science.adh4920 ↗
25. Wang, K. et al. Single skyrmion true random number generator using local dynamics and interaction between skyrmions. Nat. Commun. 13, 722 (2022).10.1038/s41467-022-28334-4 ↗
26. Wang, Y. et al. Superior probabilistic computing using operationally stable probabilistic-bit constructed by a manganite nanowire. Natl Sci. Rev. 12, nwae338 (2025).10.1093/nsr/nwae338 ↗
27. Chandler, H. J., Stefanou, M., Campbell, E. E. B. & Schaub, R. Li@C60 as a multi-state molecular switch. Nat. Commun. 10, 2283 (2019).10.1038/s41467-019-10300-2 ↗
28. Huang, T. et al. A molecular switch based on current-driven rotation of an encapsulated cluster within a fullerene cage. Nano Lett. 11, 5327–5332 (2011).10.1021/nl2028409 ↗
29. Auwärter, W. et al. A surface-anchored molecular four-level conductance switch based on single proton transfer. Nat. Nanotechnol. 7, 41–46 (2012).10.1038/nnano.2011.211 ↗
30. Wang, F. et al. Electrically controlled nonvolatile switching of single-atom magnetism in a Dy@C84 single-molecule transistor. Nat. Commun. 15, 2450 (2024).10.1038/s41467-024-46854-z ↗
31. Yuan, X. H. et al. Arbitrary modulation of average dwell time in discrete-time Markov chains based on tunneling magnetoresistance effect. IEEE Electron Device Lett. 45, 1349–1352 (2024).10.1109/LED.2024.3394711 ↗
32. Larimian, S., Mahmoodi, M. R. & Strukov, D. B. Lightweight integrated design of PUF and TRNG security primitives based on eFlash memory in 55-nm CMOS. IEEE Trans. Electron Devices 67, 1586–1592 (2020).10.1109/TED.2020.2976632 ↗
33. Ding, Q. et al. Unified 0.75 pJ/bit TRNG and attack resilient 2F2/bit PUF for robust hardware security solutions with 4-layer stacking 3D NbOx threshold switching array. IEDM 39, 1–4 (2021).
34. Shen, B. et al. Harnessing microcomb-based parallel chaos for random number generation and optical decision making. Nat. Commun. 14, 4590 (2023).10.1038/s41467-023-40152-w ↗
35. Ravichandran, H. et al. A stochastic encoder using point defects in two-dimensional materials. Nat. Commun. 15, 10562 (2024).10.1038/s41467-024-54283-1 ↗
36. Preston, R. J., Kershaw, V. F. & Kosov, D. S. Current-induced atomic motion, structural instabilities, and negative temperatures on molecule-electrode interfaces in electronic junctions. Phys. Rev. B 101, 155415 (2020).10.1103/PhysRevB.101.155415 ↗
37. Rudge, S. L. & Kosov, D. S. Distribution of waiting times between electron cotunneling events. Phys. Rev. B 98, 245402 (2018).10.1103/PhysRevB.98.245402 ↗
38. Rudge, S. L. & Kosov, D. S. Fluctuating-time and full counting statistics for quantum transport in a system with internal telegraphic noise. Phys. Rev. B 100, 235430 (2019).10.1103/PhysRevB.100.235430 ↗
39. Niazi, S. et al. Training deep Boltzmann networks with sparse Ising machines. Nat. Electron. 7, 610–619 (2024).10.1038/s41928-024-01182-4 ↗
40. Tian, H. et al. A hardware Markov chain algorithm realized in a single device for machine learning. Nat. Commun. 9, 4305 (2018).10.1038/s41467-018-06644-w ↗
41. Sun, Z. et al. Solving matrix equations in one step with cross-point resistive arrays. Proc. Natl Acad. Sci. USA 116, 4123–4128 (2019).10.1073/pnas.1815682116 ↗
42. Duan, X. G. et al. Memristor-based neuromorphic chips. Adv. Mater. 36, 2310704 (2024).10.1002/adma.202310704 ↗
43. Cai, F. X. et al. A fully integrated reprogrammable memristor-CMOS system for efficient multiply-accumulate operations. Nat. Electron. 2, 290–299 (2019).10.1038/s41928-019-0270-x ↗
44. Jeong, H. et al. Self-supervised video processing with self-calibration on an analogue computing platform based on a selector-less memristor array. Nat. Electron. 8, 168–178 (2025).
45. Zhang, W. B. et al. Edge learning using a fully integrated neuro-inspired memristor chip. Science 381, 1205–1211 (2023).10.1126/science.ade3483 ↗
46. Kim, Y. & Song, H. Noise spectroscopy of molecular electronic junctions. Appl. Phys. Rev. 8, 011303 (2021).10.1063/5.0027602 ↗
47. Guo, Y. et al. Emergent complexity of quantum rotation tunneling. Sci. Adv. 11, eads0503 (2025).10.1126/sciadv.ads0503 ↗
48. Dulić, D. et al. Controlled stability of molecular junctions. Angew. Chem. Int. Ed. 48, 8273–8276 (2009).10.1002/anie.200902168 ↗
49. Kihira, Y., Shimada, T., Matsuo, Y., Nakamura, E. & Hasegawa, T. Random telegraphic conductance fluctuation at Au−pentacene−Au nanojunctions. Nano Lett. 9, 1442–1446 (2009).10.1021/nl803284t ↗
50. Park, Y. et al. Atomic-precision control of plasmon-induced single-molecule switching in a metal–semiconductor nanojunction. Nat. Commun. 15, 6709 (2024).10.1038/s41467-024-51000-w ↗
51. Kim, Y., Song, H., Kim, D., Lee, T. & Jeong, H. Noise characteristics of charge tunneling via localized states in metal−molecule−metal junctions. ACS Nano 4, 4426–4430 (2010).10.1021/nn100255b ↗
52. Arielly, R., Vadai, M., Kardash, D., Noy, G. & Selzer, Y. Real-time detection of redox events in molecular junctions. J. Am. Chem. Soc. 136, 2674–2680 (2014).10.1021/ja412668f ↗
53. Chen, C.-H. et al. Zigzag Sc2C2 carbide cluster inside a [88]fullerene cage with one heptagon, Sc2C2@Cs(hept)-C88: a kinetically trapped fullerene formed by C2 insertion? J. Am. Chem. Soc. 138, 13030–13037 (2016).10.1021/jacs.6b07912 ↗
54. Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994).10.1103/PhysRevB.50.17953 ↗
55. Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1775 (1999).10.1103/PhysRevB.59.1758 ↗
56. Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).10.1103/PhysRevB.54.11169 ↗
57. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).10.1103/PhysRevLett.77.3865 ↗
58. Grimme, S., Antony, J., Ehrlich, S. & Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 132, 154104 (2010).10.1063/1.3382344 ↗
59. Hong, J. et al. Exploring atomic defects in molybdenum disulphide monolayers. Nat. Commun. 6, 6293 (2015).10.1038/ncomms7293 ↗
60. Qiao, J., Kong, X., Hu, Z.-X., Yang, F. & Ji, W. High-mobility transport anisotropy and linear dichroism in few-layer black phosphorus. Nat. Commun. 5, 4475 (2014).10.1038/ncomms5475 ↗
61. Qiao, J. et al. Few-layer tellurium: one-dimensional-like layered elementary semiconductor with striking physical properties. Sci. Bull. 63, 159–168 (2018).10.1016/j.scib.2018.01.010 ↗
62. Zhao, Y. et al. Extraordinarily strong interlayer interaction in 2D layered PtS2. Adv. Mater. 28, 2399–2407 (2016).10.1002/adma.201504572 ↗
63. Boltzmann, L. Studies on the balance of living force between moving material points. Wiener Ber. 58, 517–560 (1868).
64. Zierenberg, J., Schierz, P. & Janke, W. Canonical free-energy barrier of particle and polymer cluster formation. Nat. Commun. 8, 14546 (2017).10.1038/ncomms14546 ↗