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   Cui, Kaifeng; Valencia, Jose; Boyce, Kevin T.; Clements, Ethan R.; Leibrandt, David R.; Hume, David B. (November 2022, Physical Review Letters)
2. Quantum–classical interface based on single flux quantum digital logic

   https://doi.org/10.1088/2058-9565/aaa3a0  

   McDermott, R; Vavilov, M G; Plourde, B L; Wilhelm, F K; Liebermann, P J; Mukhanov, O A; Ohki, T A (April 2018, Quantum Science and Technology)
3. Quantum logic gate analogies in nonlinear acoustics

   https://doi.org/10.1121/10.0036901  

   Kuk, Ilia; Djordjevic, Ivan B; Gabitov, Ildar R; Runge, Keith; Ige, Akinsanmi S; Deymier, Pierre A (June 2025, The Journal of the Acoustical Society of America)

   This study introduces a framework using acoustic phase bits (phibits) as classical analogs to quantum bits for realizing quantum-like gates. These phibits are realized on a metastructure composed of aluminum rods glued with epoxy. First, we realize a single phibit gate in a general form for a Bloch sphere representation, providing a foundation for implementing arbitrary gate operations on a single phibit. Second, within a single mathematical representation, we achieve either the Hadamard or NOT gate by applying the corresponding distinct physical actions for each. Third, we demonstrate the implementation of a sequence of two quantum-like gates, Hadamard followed by CNOT, using a single physical action. This illustrates the effectiveness of the phibit framework, which has the potential to simplify the implementation of a whole series of sequential gates into a single unified physical operation. Finally, we realize a universal set of gates, including the Hadamard, CNOT, and T gates, within a single mathematical representation with three distinctive actions. This approach addresses prior limitations of phibit-based gates, such as Hadamard and CNOT, which were implemented in separate mathematical representations, by introducing a unified framework that eliminates the need for distinct formulations maintaining computational efficiency. 

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4. Quantum-inspired logic for advanced Transcriptional Programming

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   Abstract The tenets of intelligent biological systems are (i) scalable decision-making, (ii) inheritable memory, and (iii) communication. This study aims to increase the complexity of decision-making operations beyond standard Boolean logic, while minimizing the metabolic burden imposed on the chassis cell. To this end, we present a new platform technology for constructing genetic circuits with multiple OUTPUT gene control using fewer INPUTs relative to conventional genetic circuits. Inspired by principles from quantum computing, we engineered synthetic bidirectional promoters, regulated by synthetic transcription factors, to construct 1-INPUT, 2-OUTPUT logical operations—i.e. biological QUBIT and PAULI-X logic gates—designed as compressed genetic circuits. We then layered said gates to engineer additional quantum-inspired logical operations of increasing complexity—e.g. FEYNMAN and TOFFOLI gates. In addition, we engineered a 2-INPUT, 4-OUTPUT quantum operation to showcase the capacity to utilize the entire permutation INPUT space. Finally, we developed a recombinase-based memory operation to remap the truth table between two disparate logic gates—i.e. converting a QUBIT operation to an antithetical PAULI-X operation in situ. This study introduces a novel and versatile synthetic biology toolkit, which expands the biocomputing capacity of Transcriptional Programming via the development of compressed and scalable multi-INPUT/OUTPUT logical operations. 

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5. High-dimensional optical quantum logic in large operational spaces

   https://doi.org/10.1038/s41534-019-0173-8  

   Imany, Poolad; Jaramillo-Villegas, Jose A.; Alshaykh, Mohammed S.; Lukens, Joseph M.; Odele, Ogaga D.; Moore, Alexandria J.; Leaird, Daniel E.; Qi, Minghao; Weiner, Andrew M. (December 2019, npj Quantum Information)