![]() Nematic LCs are assemblies of aligned rod-like molecules. Our numerical results, combined with quantitative estimates of the typical energetic costs and time scales associated with physical nbit-manipulations, suggest that nbit-circuits can be implemented with existing LC technology.ĭefining and transforming single nbit states We confirm this prediction by demonstrating universal classical NAND and NOR gates as well as generalized continuous logic functions in simulations for experimentally feasible nematic LC parameters. Generalizing to multi-nbit states, we find that nematoelastic interactions can cause strong correlations in an ensemble of nbit pairs, suggesting that such interactions can be used to realize logic functions. By deriving a reduced dynamical description from electro-nematic LC theory ( 29, 30), we show how individual nbits, which correspond to points on the Poincaré-Bloch sphere ( 31), can be transformed in analogy with Pauli, Hadamard, and other typical single-qubit gates ( 32, 33) using electric fields. Building on recent theoretical work ( 28) that identified a direct relation between string-like LC defects and quaternions, we demonstrate here that such topological defects can be used as both classical binary and nonclassical continuous nematic bits (nbits Fig. Composed of rod-like molecules, LCs can host topological defects that are structurally robust against external perturbations, yet can be precisely manipulated through boundary conditions ( 25) and electric fields ( 26), as well as locally reconfigured with lasers ( 27). Independent of whether such nonstandard approaches will eventually result in scalable computing technologies, their exploration has generally led to a better experimental and theoretical understanding of the underlying physical, chemical, and biological systems.Ī widely studied class ( 22– 24) of continuous soft matter systems that can be accurately controlled experimentally ( 25, 26) but whose computational potential has not yet been systematically investigated are nematic liquid crystals (LCs). ![]() In parallel, several other promising information processing strategies in classical systems are currently also being explored, including DNA-based computation ( 11), analog-computing in cells ( 12), chemical computers ( 13, 14), microfluidic ( 15– 18) and mechanical ( 19) digital logic, or holonomic computation ( 20) in non-Abelian mechanical ( 21) systems. A popular example is quantum computers ( 8), which promise substantially faster search ( 9) and factoring ( 10) algorithms. Notwithstanding the historical success of classical bit-based computation, it has long been suggested that some practically relevant problems could be solved by performing parallel computations in larger or nondiscrete state spaces ( 2– 7). Accordingly, electronic digital circuits process information by manipulating deterministic bit sequences ![]() Similar to an idealized universal Turing machine ( 1), classical digital computers represent bits as two discrete voltage states, commonly labeled 0 and 1. These results open a route toward the implementation of classical digital and nonclassical continuous computation strategies in topological soft matter systems.īits are the fundamental units of binary digital computation and information storage. Last, we demonstrate the implementation of generalized logical functions that take values on the Poincaré-Bloch sphere. Using nematoelastic interactions, we show how four-nbit configurations can realize universal classical NOR and NAND gates. Through theory and simulations, we demonstrate how single-nbit operations can be implemented using electric fields, to construct LC analogs of Pauli, Hadamard, and other elementary logic gates. Here, we introduce the concept of nematic bits (nbits) by exploiting a quaternionic mapping from LC defects to the Poincaré-Bloch sphere. Although recent experimental progress enables precise control over nematic LC defects, their practical potential for information storage and processing has yet to be explored. Liquid crystals (LCs) can host robust topological defect structures that essentially determine their optical and elastic properties.
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