Quantum teleportation is one of basis study of quantum computing algorithms mostly used in quantum communication. This algorithm has so far been implemented using a variety of quantum realization models. In this study, quantum teleportation algorithm is realized experimentally using classical LC circuits. In addition, electrical simulation of some quantum gates such as Hadamard and CNOT gates used in algorithm are also given. The importance of implementation of such quantum algorithms onto classical electrical circuit is that it is being inexpensive and can work at room temperature. This study can contribute greatly to the experimental teaching of the emerging quantum technology revolution to students.
Quantum computation may well be performed with the use of electric circuits. Especially, the Schrödinger equation can be simulated by the lumped-element model of transmission lines, which is applicable to low-frequency electric circuits. In this paper, we show that the Dirac equation is simulated by the distributed-element model, which is applicable to high-frequency electric circuits. Then, a set of universal quantum gates (the Hadamard, phase-shift and CNOT gates) are constructed by networks made of transmission lines. We demonstrate Shor's prime factorization based on electric circuits. It will be possible to simulate any quantum algorithms simply by designing networks of metallic wires.
In this work, we investigate the Harrow-Hassidim-Lloyd (HHL) quantum algorithm for the solution of electric field integral equation (EFIE)-based matrix equation system for analyzing electromagnetic scattering from three-dimensional (3D) perfect electrically conducting (PEC) objects. The HHL algorithm is one of the representative quantum algorithms for the solution of linear equation systems. Numerical experiments are presented to investigate the computational cost and accuracy of the HHL algorithm for solving the EFIE matrix equation system executed on the virtual simulator on the classical computers.
We introduce a quantum algorithm for simulating the dynamics of electrical circuits consisting of resistors, inductors and capacitors (aka RLC circuits) along with power sources. Given oracle access to the connectivity of the circuit and values of the electrical elements, our algorithm prepares a quantum state that encodes voltages and current values either at a specified time or the history of their evolution over a time-interval. For an RLC circuit with
N components, our algorithm runs in time
polylog(N) under mild assumptions on the connectivity of the circuit and values of its components. This provides an exponential speed-up over classical algorithms that take
poly(N) time in the worst-case. Our algorithm can be used to estimate energy across a set of components or dissipated power in
polylog(N) time, a problem that we prove is BQP-hard and therefore unlikely to be efficiently solved by classical algorithms. The main challenge in simulating the dynamics of RLC circuits is that they are governed by differential-algebraic equations (DAEs), a coupled system of differential equations with hidden algebraic constraints. Consequentially, existing quantum algorithms for ordinary differential equations cannot be directly utilized. We therefore develop a quantum DAE solver for simulating the time-evolution of linear DAEs. For RLC circuits, we employ modified nodal analysis to create a system of DAEs compatible with our quantum algorithm. We establish BQP-hardness by demonstrating that any network of classical harmonic oscillators, for which an energy-estimation problem is known to be BQP-hard, is a special case of an LC circuit. Our work gives theoretical evidence of quantum advantage in simulating RLC circuits and we expect that our quantum DAE solver will find broader use in the simulation of dynamical systems.