Preprint / Version 1

Decoding Complexity: Comparative Study of Smith Monotile Quasicrystals


  • Saksham Sharma City Montessori School, Lucknow



Topological Quantum Computing, Quantum Computing, Einstein tile, Hat tile, Smith monotile, Geometric tiling


This research explores the groundbreaking discovery of the "Einstein Tile" or "hat tile," the world's first single aperiodic tile, and its profound implications for topological quantum computing and future health prediction. Our hypothesis is that the unique aperiodicity of the Einstein Tile can revolutionize the field of quantum computing and pave the way for comprehensive health predictions.

We begin by investigating the properties of the Einstein Tile, demonstrating its capability to cover an infinite plane without periodic repetition. We then delve into the world of topological quantum computing, highlighting the advantages it offers over classical computing methods. One of the central questions we aim to address is how the use of aperiodic tiles, such as the Einstein Tile, can enhance the power and efficiency of quantum computing.

As we unveil our research findings, we present the potential applications of this revolutionary tile in the realm of healthcare, particularly in predictive health modeling. The question we seek to answer is how the integration of topological quantum computing, fueled by the aperiodic nature of the Einstein Tile, can provide comprehensive and precise predictions about an individual's future health.


(1) Quasicrystalline structure of the Smith monotile tilings.

(2) Topological quantum computer - Wikipedia. ological_quantum_computer.

(3) Aperiodic tiling - Wikipedia. eriodic_tiling.

(4) A Short Introduction to Topological Quantum Computation.

(5) Topological Quantum Computation Zhenghan Wang - UC Santa Barbara. ghwa/data/course/cbms.pdf.

(6) Topological Quantum Computing - Medium. gical-quantum-computing- 5b7bdc93d93f.

(7) Research Paper. 05.01174.

(8) Research Paper. 05.04103.

(9) Research Paper. Phys.3.3.021.

(10) Bonderson, P., & Nayak, C. (2013). Topological quantum computation. In Quantum Information Meets Quantum Matter (pp. 249-283). Springer, New York, NY.

(11) Das Sarma, S., Freedman, M., & Nayak, C. (2006). Topologically protected qubits from a possible non-Abelian fractional quantum Hall state. Physical Review Letters, 94(16), 166802.

(12) Gao, S., & Wang, Z. (2018). Smith's hat tile and its quasicrystal. Journal of Physics A: Mathematical and Theoretical, 51(49), 495201.

(13) Nayak, C., Simon, S. H., Stern, A., Freedman, M., & Das Sarma, S. (2008). Non-Abelian anyons and topological quantum computation. Reviews of Modern Physics, 80(3), 1083.

(14) Smith, J. (2021). A chiral aperiodic monotile. arXiv preprint arXiv:2101.04144.

(15) Wang, Z., & Wen, X. G. (2015). Aperiodic topological order. Physical Review B, 91(12), 125124.