Electric-circuit simulation of the Schrödinger equation and non-Hermitian quantum walks

Abstract

Recent progress has witnessed that various topological physics can be simulated by electric circuits under alternating current. However, it is still a nontrivial problem if it is possible to simulate the dynamics subject to the Schrödinger equation based on electric circuits. In this work, we reformulate the Kirchhoff law in one dimension in the form of the Schrödinger equation. As a typical example, we investigate quantum walks in $LC$ circuits. We also investigate how quantum walks are different in topological and trivial phases by simulating the Su-Schrieffer-Heeger model in electric circuits. We then generalize them to include dissipation and nonreciprocity by introducing resistors, which produce non-Hermitian effects. We point out that the time evolution of one-dimensional quantum walks is exactly solvable with the use of the generating function made of the Bessel functions.

5 pages, 5 figures

References in corpus (16)

• Universal computation by quantum walk
• Quantum walks of correlated particles
• Spatial search by quantum walk
• Realization of quantum walks with negligible decoherence in waveguide lattices
• Hybrid higher-order skin-topological modes in non-reciprocal systems
• Topological Transition in a Non-Hermitian Quantum Walk
• Universal computation by multi-particle quantum walk
• Interplay of non-Hermitian skin effects and Anderson localization in non-reciprocal quasiperiodic lattices
• Chiral voltage propagation in a self-calibrated topolectrical Chern circuit
• Higher-order topological electric circuits and topological corner resonance on the breathing Kagome and pyrochlore lattices
• Non-Hermitian higher-order topological states in nonreciprocal and reciprocal systems with their electric-circuit realization
• Non-Hermitian boundary and interface states in nonreciprocal higher-order topological metals and electrical circuits
• Braiding of Majorana corner states in electric circuits and its non-Hermitian generalization
• Electric circuits for non-Hermitian Chern insulators
• Phase Transitions in Dissipative Quantum Transport and Mesoscopic Nuclear Spin Pumping
• Topological Transitions and Bulk Wavefunctions in the SSH Model

Cited by in corpus (27)

• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• Magnetic suppression of non-Hermitian skin effects
• Engineering of topological state transfer and topological beam splitter in an even-size Su-Schrieffer-Heeger chain
• Nonlinear non-Hermitian higher-order topological laser
• Non-Hermitian Topological Metamaterials with Odd Elasticity
• Systematic construction of square-root topological insulators and superconductors
• Dynamical nonlinear higher-order non-Hermitian skin effects and topological trap-skin phase
• Non-Hermitian Kibble-Zurek mechanism with tunable complexity in single-photon interferometry
• Bound states and photon emission in non-Hermitian nanophotonics
• Electric circuits for universal quantum gates and quantum Fourier transformation
• Topological Toda lattice and nonlinear bulk-edge correspondence
• Topolectrical-circuit realization of quadrupolar surface semimetals
• Quench dynamics and bulk-edge correspondence in nonlinear mechanical systems
• Coexistence of stable and unstable population dynamics in a nonlinear non-Hermitian mechanical dimer
• Interplay of nonreciprocity and nonlinearity on mean-field energy and dynamics of a Bose-Einstein condensate in a double-well potential
• Universal quantum gates, artificial neurons and pattern recognition simulated by \textit{LC} resonators
• Variational Quantum Support Vector Machine based on $\Gamma$ matrix expansion and Variational Universal-Quantum-State Generator
• Nonlinear topological phase diagram in dimerized sine-Gordon model
• Dirac formulation for universal quantum gates and Shor's integer factorization in high-frequency electric circuits
• Two-level Quantum Walkers on Directed Graphs I: Universal Quantum Computing
• Integral Transforms and $\mathcal{P}\mathcal{T}$-symmetric Hamiltonians
• Defect production due to time-dependent coupling to environment in the Lindblad equation
• Cavity-induced topological edge and corner states
• Non-Hermitian Topoelectrical Circuits: Expedient Tools for Topological State Engineering with Gain-Loss Modulation
• Beyond characteristic equations: A unified one-dimensional non-Bloch band theory via wavefunction data
• Nonlinear Anderson localization in Toda lattices