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 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.

arXiv:2409.09919Advanced Quantum TechnologiesFeb 6, 202516 citations

Quantum Circuits

Colin P. Williams

Texts in computer scienceDec 6, 20100 citations

Possibilistic simulation of quantum circuits by classical circuits

Daochen Wang

In a breakthrough work, Bravyi, Gosset, and K\"onig (BGK) [Science 362, 308 (2018)] unconditionally proved that constant-depth quantum circuits are more powerful than their classical counterparts. Their result is equivalent to saying that a particular family of constant-depth quantum circuits takes classical circuits at least $\mathrm{\ensuremath{\Omega}}(logn)$ depth to ``simulate,'' in a certain sense. In our paper, we formalize their sense of simulation, which we call ``possibilistic simulation'' or `` $p$ -simulation,'' and construct explicit classical circuits that can $p$ -simulate any depth- $d$ quantum circuit with Clifford and $t\phantom{\rule{4pt}{0ex}}T$ -gates in depth $O(d+t)$ . Our classical circuits use ${\mathrm{NOT},\mathrm{AND},\mathrm{OR}}$ gates of fan-in $\ensuremath{\le}2$.In a breakthrough work, Bravyi, Gosset, and K\"onig (BGK) [Science 362, 308 (2018)] unconditionally proved that constant-depth quantum circuits are more powerful than their classical counterparts. Their result is equivalent to saying that a particular family of constant-depth quantum circuits takes classical circuits at least $\mathrm{\ensuremath{\Omega}}(logn)$ depth to ``simulate,'' in a certain sense. In our paper, we formalize their sense of simulation, which we call ``possibilistic simulation'' or ``$p$-simulation,'' and construct explicit classical circuits that can $p$-simulate any depth-$d$ quantum circuit with Clifford and $t\phantom{\rule{4pt}{0ex}}T$-gates in depth $O(d+t)$. Our classical circuits use ${\mathrm{NOT},\mathrm{AND},\mathrm{OR}}$ gates of fan-in $\ensuremath{\le}2$.

arXiv:1904.05282Physical Review ADec 22, 20224 citations

Quantum Circuits

WORLD SCIENTIFIC eBooksAug 27, 20260 citations

Classical Circuit Simulations for Superconducting Quantum Circuits

Alan M. Kadin

•Classical superconducting circuit simulators are powerful and available. •Include Josephson junction as basic element. •Provide efficient time-domain simulations of complex circuits. •May show effects otherwise attributed to quantum circuits. •Circuits of coupled superconducting qubits are being developed for quantum computing (QC). •Entangled quantum theory incompatible with classical simulators. •Quantum model difficult to simulate on conventional computers for complex circuits already being tested. •Classical circuit simulations should provide the baseline to compare with quantum effects, but this is seldom done. •Coupled oscillators are delocalized even in classical limit.•Classical superconducting circuit simulators are powerful and available. •Include Josephson junction as basic element. •Provide efficient time-domain simulations of complex circuits. •May show effects otherwise attributed to quantum circuits. •Circuits of coupled superconducting qubits are being developed for quantum computing (QC). •Entangled quantum theory incompatible with classical simulators. •Quantum model difficult to simulate on conventional computers for complex circuits already being tested. •Classical circuit simulations should provide the baseline to compare with quantum effects, but this is seldom done. •Coupled oscillators are delocalized even in classical limit.

Bulletin of the American Physical SocietyMar 1, 20210 citations

Quantum Circuits

Madhusudan Singh Irish Singh, Bharat S. Rawal

Springer eBooksJan 1, 20260 citations

p

-simulation,'' and construct explicit classical circuits that can

p

-simulate any depth-

d

quantum circuit with Clifford and

t\phantom{\rule{4pt}{0ex}}T

-gates in depth

O(d+t)

. Our classical circuits use

{\mathrm{NOT},\mathrm{AND},\mathrm{OR}}

gates of fan-in $\ensuremath{\le}2$.