Harnessing LC Oscillators for Quantum Entanglement and Quantum Operations

We emulate quantum entanglement and Bell states in classical electrical circuits by representing quantum states as voltage oscillations of LC oscillators. In general, an N-qubit quantum system is modeled using 2^N LC resonators and quantum operations performed by applying time-dependent perturbations to the resonator and connecting capacitors. We demonstrate how such perturbations can be used to perform the Hadamard and CNOT operations to generate maximally perturbed states in a two-qubit Bell state circuit. The emergence of entangled and Bell states are manifested in the time-evolution behavior of the voltage states in which the first and third resonators exhibit in-phase sinusoidal voltage oscillations with 70.7% reduced amplitudes compared to the initial oscillations while the voltages of the other two LC oscillators remain negligible. We analyze the probability distribution and statevector representation of the Bell states through circuit simulations and IBM Quantum Composer tools and confirm the successful realization of quantum entanglement in the electrical circuit. This research opens the door to utilizing classical electrical components for simulating quantum phenomena with potential applications in quantum cryptography and quantum computing paradigms.