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Advanced Intelligent Systems

Quantum Logic Gates Based on DNAtronics, RNAtronics, and Proteintronics

Sheh‐Yi Sheu, Hua-Yi Hsu, Dah‐Yen Yang

Published May 4, 2021• 5 citations
Publisher

Abstract

Quantum computers (QCs) adopt an n‐state quantum mechanical system to manipulate the superposition state. However, molecular transistors are not used to build up the quantum logic gate. Herein, it is demonstrated that DNA, RNA, and protein are promising media for QCs, and one uses residue pairs, including nucleotide base pairs and amino acid pairs, via proton‐coupled electron transfer to fabricate a quantum logic gate. In the residue pair, the proton transfer between donor and acceptor states fulfills a qubit. Both the DNA‐CG (3‐qubit) nucleobase pair and nucleotide base pair obey the Toffoli gate. AT (2‐qubit) nucleotide base pair behaves as a SWAP gate and a CNOT gate. Furthermore, the AU and RNA‐CG nucleotide base pairs follow the CNOT gate and Toffoli gate, respectively. In addition, a pair of amino acids achieves 1‐qubit and satisfies the Pauli‐X, ‐Y, and ‐Z gates. The generators of universal quantum logic gates are obtained.

DOI
10.1002/aisy.202000273

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Quantum computers (QCs) adopt an n‐state quantum mechanical system to manipulate the superposition state. However, molecular transistors are not used to build up the quantum logic gate. Herein, it is demonstrated that DNA, RNA, and protein are promising media for QCs, and one uses residue pairs, including nucleotide base pairs and amino acid pairs, via proton‐coupled electron transfer to fabricate a quantum logic gate. In the residue pair, the proton transfer between donor and acceptor states fulfills a qubit. Both the DNA‐CG (3‐qubit) nucleobase pair and nucleotide base pair obey the Toffoli gate. AT (2‐qubit) nucleotide base pair behaves as a SWAP gate and a CNOT gate. Furthermore, the AU and RNA‐CG nucleotide base pairs follow the CNOT gate and Toffoli gate, respectively. In addition, a pair of amino acids achieves 1‐qubit and satisfies the Pauli‐X, ‐Y, and ‐Z gates. The generators of universal quantum logic gates are obtained.
Biomolecular residue pairs have been utilized in constructing quantum logic gates (QLGs), significantly reducing the hardware size to the subnanoscale level. However, the development of molecular fault-tolerant topological quantum computers (TQCs) presents challenges in error reduction and hardware size minimization. This study presents the manipulation of molecular QLGs (MQLGs) by utilizing protein residue pairs as molecular transistors, enabling the construction of molecular topological QLGs. This innovative approach leverages molecular functionality in quantum computer (QC) designs to build sub-nanometer transistors that significantly reduce size, enhance efficiency, and accelerate computing. The transmission spectra of electron transfer in molecular junction systems were analyzed using the non-equilibrium Green’s function method. The molecular field effect led to the observation of four quantum states on a two-dimensional potential energy surface with two degrees of freedom—proton translation and molecular rotation. These states form a quaternary QLG, similar to a 2-qubit controlled-NOT logic gate. By applying the Kitaev honeycomb lattice model, MQLGs were employed to generate nonabelian anyons that adhere to fusion rules, such as Ising and Fibonacci anyons. Furthermore, quantum circuits incorporating nonabelian anyons and their fusion processes were developed for practical applications. These findings underscore the shift away from conventional atom-based silicon technology and highlight the potential for innovative applications of molecular universal QLGs, particularly in the advancement of sub-nanometer molecular fault-tolerance TQCs.
A quantum gate is the quantum analog of the classical logic gate of digital computers. It is a basic structural unit of a quantum circuit which operates on a small number of qubits to deliver a predefined output. A quantum circuit is a graphical representation of the sequence of the quantum gates used and the measurements performed in a quantum computation. Various quantum logic gates, namely, the Hadamard, T phase, NOT, Pauli-X, controlled NOT (CNOT), controlled-Z, SWAP and controlled phase gates as well as higher-level Toffoli and Fredkin gates are described. Conventions of reading quantum circuit diagrams are explained. Operation of a quantum full adder consisting of registers and gates is discussed, elaborating the role of the NOT gate, the sum calculation with CNOTgates and the carry C-out calculation with Toffoli gates. A primary tool used for performing arithmetic operations on a quantum computer is the quantum Fourier transform (QFT). The QFT adder and multiplier circuits are presented.
Abstract Protein design is a technique to engineer proteins by permuting amino acids in the sequence to obtain novel functionalities. However, exploring all possible combinations of amino acids is generally impossible due to the exponential growth of possibilities with the number of designable sites. The present work introduces circuits implementing a pure quantum approach, Grover’s algorithm, to solve protein design problems. Our algorithms can adjust to implement any custom pair-wise energy tables and protein structure models. Moreover, the algorithm's oracle is designed to consist of only adder functions. Quantum computer simulators validate the practicality of our circuits, containing up to 234 qubits. However, a smaller circuit is implemented on real quantum devices. Our results show that using O(N)\mathcal{O}\left(\sqrt{N}\right)O(N​) iterations, the circuits find the correct results among all N possibilities, providing the expected quadratic speed up of Grover's algorithm over classical methods (i.e., O(N)\mathcal{O}\text{(}N\text{)}O(N)).
Most problems and limitations associated with classical computing are eliminated in quantum computing. Despite the current methods of quantum computing which have to deal with the non-secondary problem of decoherence induced by the coupling of the system with the environment, biological systems use quantum physics at high temperature and in highly noise environments. As a consequence, taking inspiration from how DNA, enzymes and other biomolecules exploit quantum properties could help us find methods of quantum computation that could bypass the problems encountered in non-biological systems. In this paper, we shortly review bio-inspired qubits systems and how endonuclease restriction enzymes exploit quantum physics to solve searching problem, i.e., the identification of small sequences (4-6 nucleotides bases) in DNA (approximately 1 million nucleotides bases) complexes and its implication in developing universal quantum gates. The possible implications for quantum computation of this restriction enzyme feature is then briefly described
Protein design is a technique to engineer proteins by permuting amino acids in the sequence to obtain novel functionalities. However, exploring all possible combinations of amino acids is generally impossible due to the exponential growth of possibilities with the number of designable sites. The present work introduces circuits implementing a pure quantum approach, Grover's algorithm, to solve protein design problems. Our algorithms can adjust to implement any custom pair-wise energy tables and protein structure models. Moreover, the algorithm's oracle is designed to consist of only adder functions. Quantum computer simulators validate the practicality of our circuits, containing up to 234 qubits. However, a smaller circuit is implemented on real quantum devices. Our results show that using [Formula: see text] iterations, the circuits find the correct results among all N possibilities, providing the expected quadratic speed up of Grover's algorithm over classical methods (i.e., [Formula: see text]).