Fundamental Scaling Constraints for Equilibrium Molecular Computing
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916968094760960 |
|---|---|
| author | Crawley, Erin Zhu, Qian-Ze Brenner, Michael P. |
| author_facet | Crawley, Erin Zhu, Qian-Ze Brenner, Michael P. |
| contents | Molecular computing promises massive parallelization to explore solution spaces, but so far practical implementations remain limited due to off-target binding and exponential proliferation of competing structures. Here, we investigate the theoretical limits of equilibrium self-assembly systems for solving computing problems, focusing on the directed Hamiltonian Path Problem (HPP) as a benchmark for NP-complete problems. The HPP is encoded via particles with directional lock-key patches, where self-assembled chains form candidate solution paths. We determine constraints on the required energy gap between on-target and off-target binding for the HPP to be encoded and solved. We simultaneously examine whether components with the required energy gap can be designed. Combining these results yields a phase diagram identifying regions where HPP instances are both encodable and solvable. These results establish fundamental upper bounds on equilibrium molecular computation and highlight the necessity of non-equilibrium approaches for scalable molecular computing architectures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_20526 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fundamental Scaling Constraints for Equilibrium Molecular Computing Crawley, Erin Zhu, Qian-Ze Brenner, Michael P. Soft Condensed Matter Statistical Mechanics Molecular computing promises massive parallelization to explore solution spaces, but so far practical implementations remain limited due to off-target binding and exponential proliferation of competing structures. Here, we investigate the theoretical limits of equilibrium self-assembly systems for solving computing problems, focusing on the directed Hamiltonian Path Problem (HPP) as a benchmark for NP-complete problems. The HPP is encoded via particles with directional lock-key patches, where self-assembled chains form candidate solution paths. We determine constraints on the required energy gap between on-target and off-target binding for the HPP to be encoded and solved. We simultaneously examine whether components with the required energy gap can be designed. Combining these results yields a phase diagram identifying regions where HPP instances are both encodable and solvable. These results establish fundamental upper bounds on equilibrium molecular computation and highlight the necessity of non-equilibrium approaches for scalable molecular computing architectures. |
| title | Fundamental Scaling Constraints for Equilibrium Molecular Computing |
| topic | Soft Condensed Matter Statistical Mechanics |
| url | https://arxiv.org/abs/2509.20526 |