Classical analog circuit emulation of quantum Grover search algorithm

TL;DR

This paper presents an analog electronic circuit framework that emulates quantum gates and algorithms, including Grover search, using classical components to mimic quantum behavior without decoherence.

Contribution

It introduces a novel classical analog circuit approach to emulate quantum gates and algorithms, including entanglement and Grover search, without quantum decoherence.

Findings

Successfully emulated 3-qubit Grover search algorithm

Circuit outputs matched theoretical predictions

Framework can serve as components in quantum computing systems

Abstract

We construct a completely analog framework that emulates universal quantum gates and quantum algorithms. It is based on electronic circuits made of operational amplifiers, resistors and capacitors. In these circuits, input and output lines represent the computational basis states (CBSs) and thus $2^n$ lines are required to represent $n$ qubits. An operation of the circuits is based on classical evolution and interference of complex amplitudes associated with each CBS. The framework can emulate entangled states and is free from decoherence, measurements are classical and do not collapse states. Similar to physical quantum computers, emulated quantum algorithms can be constructed as a sequence of the gates belonging to a universal set (phase shift, Hadamard, controlled-NOT), as a unitary matrix and as combinations of the two. Circuits representing the universal gates have been made and tested. We also have made a matrix-based emulator of a 3-qubit Grover search algorithm. We tested it by searching for one and two particular states with one and two iterations and found that its outputs accurately match predicted values. We anticipate that the emulators can work as sub-components of physical quantum computers. On their own, the emulators can be used for operations that require a few qubits or operations that can be split into independent (and perhaps weakly entangled) blocks of qubits.