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Journal of Physics A Mathematical and Theoretical

Classical Boolean logic gates with quantum systems

Nicolas Renaud, Christian Joachim

Published Mar 18, 2011• 15 citations
Publisher

Abstract

An analytical method is proposed to implement any classical Boolean function in a small quantum system by taking the advantage of its electronic transport properties. The logical input, α = {α1, ..., αN}, is used to control well-identified parameters of the Hamiltonian of the system noted . The logical output is encoded in the tunneling current intensity passing through the quantum system when connected to conducting electrodes. It is demonstrated how to implement the six symmetric two-input/one-output Boolean functions in a quantum system. This system can be switched from one logic function to another by changing its structural parameters. The stability of the logic gates is discussed, perturbing the Hamiltonian with noise sources and studying the effect of decoherence.

DOI
10.1088/1751-8113/44/15/155302

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An analytical method is proposed to implement any classical Boolean function in a small quantum system by taking the advantage of its electronic transport properties. The logical input, α = {α1, ..., αN}, is used to control well-identified parameters of the Hamiltonian of the system noted . The logical output is encoded in the tunneling current intensity passing through the quantum system when connected to conducting electrodes. It is demonstrated how to implement the six symmetric two-input/one-output Boolean functions in a quantum system. This system can be switched from one logic function to another by changing its structural parameters. The stability of the logic gates is discussed, perturbing the Hamiltonian with noise sources and studying the effect of decoherence.
Abstract Quantum Hamiltonian Computing is a recent approach that uses quantum systems, in particular a single molecule, to perform computational tasks. Within this approach, we present explicit methods to construct logic gates using two different designs, where the logical outputs are encoded either at fixed energy and spatial positioning of the quantum states, or at different energies. We use these results to construct quantum Boolean adders involving a minimal number of quantum states with the two designs. We also establish a matrix algebra giving an analogy between classical Boolean logic gates and quantum ones, and assess the possibilities of both designs for more complex gates.
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This paper explores a novel approach to logic gate design based on the phenomenon of quantum tunneling. Traditional logic gates rely on classical electron flow controlled by transistors. We propose a fundamentally different architecture leveraging the probabilistic nature of quantum tunneling to perform logical operations. The core concept involves designing structures that exploit controlled tunneling events to dictate electronic pathways, effectively creating a logic circuit. This approach challenges the established design paradigm of logic gates and offers a potentially scalable route to quantum computation using readily accessible quantum phenomena. We detail the theoretical framework, outline potential gate designs, and discuss key considerations for realizing such a system. The core claim is the feasibility of utilizing quantum tunneling effects to implement logic gate functionalities. The core mechanism centers around controlling electron flow through quantum tunneling for logical operations. This work represents a new design strategy for logic gates, differing from conventional transistor-based approaches.
Quantum phase slip (QPS) junction can act as a superconductor switch when a voltage pulse larger than its critical voltage is applied to it. As a result, a current pulse with an area equal to 2e(or multiples of 2e) flows across the junction, and the junction switches from zero to one in the charge-base logic. For having a proper operation simulation of the QPS junction, it should be overdamped, and the damping factor should be less than one. Physical parameters of the QPS junction, namely, the normal resistance, the kinetic inductance, and the critical voltage, can affect the overdamping condition and switching behavior of the junction, as well as the damping factor. The basic block for designing the QPS logic gates is the charge island. By different and proper connections of the charge islands, basic QPSand, or, andxorlogic gates are designed. Generally, each of these gates has its own circuit and junction parameters for proper operation. In this manuscript, a universal QPS logic gate is proposed that can perform basicand, or, andxorBoolean functions by proper selection of parameters for QPS junctions in the case of each Boolean function. This universal QPS logic gate can simplify the design the complicated QPS logic circuits, since only the parameters of each junction have to be properly selected for achieving the desired Boolean function, and the gate circuit topology remains unchanged.
We propose a new concept for quantum thermal logic gates -- analogous to classical electronic logic gates -- that exploit the heat current in a coupled quantum-dot system tunnel-coupled to metallic thermal reservoirs for logic operations in quantum circuits. We obtained a remarkable one-to-one correspondence with the structure of classical electronic logic gate circuits. An experimental setup is presented that demonstrates a realizable nano-electronic quantum circuit architecture for implementing such quantum thermal logic operations.