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arXiv:2409.09919 · Advanced Quantum Technologies

Engineering Topological States and Quantum‐Inspired Information Processing Using Classical Circuits

Tian Chen, Weixuan Zhang, Deyuan Zou, Yifan Sun, Xiangdong Zhang

Published Feb 6, 2025• 16 citations
arXivHTMLPDF

Abstract

Abstract Based on the correspondence between circuit Laplacian and Schrodinger equations, recent investigations have shown that classical electric circuits can be used to simulate various topological physics and Schrödinger's equation. Furthermore, a series of quantum‐inspired information processing has been implemented by using classical electric circuit networks. In this review, the similarity between the circuit Laplacian and the lattice Hamiltonian is analyzed, with topological physics introduced based on classical circuits. Subsequently, reviews of the research progress in quantum‐inspired information processing based on the electric circuit are provided, including discussions of topological quantum computing with classical circuits, quantum walk based on classical circuits, quantum combinational logics based on classical circuits, electric‐circuit realization of fast quantum search, implementing unitary transforms and so on.

DOI
10.1002/qute.202400448

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Abstract Based on the correspondence between circuit Laplacian and Schrodinger equations, recent investigations have shown that classical electric circuits can be used to simulate various topological physics and Schrödinger's equation. Furthermore, a series of quantum‐inspired information processing has been implemented by using classical electric circuit networks. In this review, the similarity between the circuit Laplacian and the lattice Hamiltonian is analyzed, with topological physics introduced based on classical circuits. Subsequently, reviews of the research progress in quantum‐inspired information processing based on the electric circuit are provided, including discussions of topological quantum computing with classical circuits, quantum walk based on classical circuits, quantum combinational logics based on classical circuits, electric‐circuit realization of fast quantum search, implementing unitary transforms and so on.
ABSTRACT Universal quantum computation that consists of producing arbitrary input states and executing universal unitary gates is an important goal for the future information field. However, realizing a device that performs practical universal quantum computation is tricky. This is because it requires a scalable qubit system with long coherence time and good controls, which is harsh for most current platforms. Here, we provide a novel scheme to emulate the universal quantum computer by designing a classical circuit network. In the circuit network, we encode information using correlated electrical signals. The information processing elements that correspond to the universal quantum gate set are designed and embedded into the circuit network, which gives the classical circuit networks processing functions similar to that of universal quantum computation. Taking the analogy of two‐qubit processor as an example, we experimentally verify that our proposal works well. Because classical circuit networks possess good scalability and stability, the present scheme is expected to avoid some problems faced by the quantum schemes. Thus, our findings are advantageous for information processing in the era of big data.
Quantum search algorithm, which can search an unsorted database quadratically faster than any known classical algorithms, has become one of the most impressive showcases of quantum computation. It has been implemented using various quantum schemes. Here, we demonstrate both theoretically and experimentally that such a fast search algorithm can also be realized using classical electric circuits. The classical circuit networks to perform such a fast search have been designed. It has been shown that the evolution of electric signals in the circuit networks is analogies of quantum particles randomly walking on graphs described by quantum theory. The searching efficiencies in our designed classical circuits are the same to the quantum schemes. Because classical circuit networks possess good scalability and stability, the present scheme is expected to avoid some problems faced by the quantum schemes. Thus, our findings are advantageous for information processing in the era of big data.
The key obstacle to the realization of a scalable quantum computer is overcoming environmental and control errors. Topological quantum computation has attracted great attention because it has emerged as one of the most promising approaches to solving these problems. Various theoretical schemes for building topological quantum computation have been proposed. However, experimental implementation has always been a great challenge because it has proved to be extremely difficult to create and manipulate topological qubits in real systems. Therefore, topological quantum computation has not been realized in experiments yet. Here, we report the first experimental realization of topological quantum computation with electric circuits. Based on our proposed new scheme with circuits, Majorana-like edge states are not only observed experimentally, but also T junctions are constructed for the braiding process. Furthermore, we demonstrate the feasibility of topological quantum computing through a set of one- and two-qubit unitary operations. Finally, our implementation of Grover's search algorithm demonstrates that topological quantum computation is ideally suited for such tasks.
The key obstacle to the realization of a scalable quantum computer is overcoming environmental and control errors. Topological quantum computation attracts great attention because it emerges as one of the most promising approaches to solving these problems. Various theoretical schemes for building topological quantum computation have been proposed. However, experimental implementation has always been a great challenge because it has proved to be extremely difficult to create and manipulate topological qubits in real systems. Therefore, topological quantum computation has not been realized in experiments yet. Herein, the first experimental simulation of topological quantum computation with classical circuits is reported. Based on the proposed new scheme with circuits, not only Majorana‐like edge states are simulated experimentally, but also T junctions are constructed for simulating the braiding process. Furthermore, the feasibility of simulated topological quantum computing through a set of one‐ and two‐qubit unitary operations is demonstrated. Finally, the simulation of Grover's search algorithm demonstrates that simulated topological quantum computation is ideally suited for such tasks. The developed circuit‐based topological quantum‐computing simulator can provide important references for developing future topological quantum circuits.
Quantum computation requires controlled engineering of quantum states to perform tasks that go beyond those possible with classical computers. Topological quantum computation aims to achieve this goal by using non-Abelian quantum phases of matter. Such phases allow for quantum information to be stored and manipulated in a nonlocal manner, which protects it from imperfections in the implemented protocols and from interactions with the environment. Recently, substantial progress in this field has been made on both theoretical and experimental fronts. We review the basic concepts of non-Abelian phases and their topologically protected use in quantum information processing tasks. We discuss different possible realizations of these concepts in experimentally available solid-state systems, including systems hosting Majorana fermions, their recently proposed fractional counterparts, and non-Abelian quantum Hall states.
Abstract Classical combinational logic circuits (CCLCs) are widely used in various fields. Corresponding to the CCLCs, here schemes are given for some quantum combinational logic circuits (QCLCs) based on the quantum NAND tree. Three typical circuits, adder, comparator, and seven‐segment display decoder, are discussed in detail as examples. All the designs of the schemes are based on the quantum random walk theory. Furthermore, these QCLCs are mapped onto the classical circuit networks and design new types of CCLCs, and take advantage of the fact that there is a good correspondence between the voltage in the circuit satisfying Kirchhoff's law and the system wave function satisfying the Schrodinger equation. These CCLCs that are designed have exponential speedup functions compared with conventional ones, which have been demonstrated experimentally. Because classical circuit networks possess good scalability and stability, the realization of QCLCs on classical circuits is expected to have potential applications for information processing in the era of big data.