Computer Science

Analog Simulation of the Quantum Bit

[Source: AI, Public Domain]

Theory and design of analog circuit that simulates probability behaviors and spherical position of a quantum bit. The circuit will compute the position of a qubit state on the Bloch sphere in 3D space, as well as simulate measurement of the qubit. We will review the basic principles of a qubit and the Bloch sphere representation. We will discuss the principles informing the analog computer design. The circuit can be physically built, or run on your computer. I have made available in a SPICE circuit simulation that anyone can run or tinker with.

Example Circuit Output. Movement on the Block Sphere. [Image by Author]

Quick Review of Qubits

Informally, a qubit q is a vector of two complex numbers. The two numbers describe a probability distribution of two possible values, “0” or “1”.

q ∈ ℂ²

That is, q = <α, β> where
α = x + yi,
β = w + zi

A qubit can only every have two distinct outcomes when measured. The amplitudes α and β describe the probability of getting either answer:

Prob(“0”) = |α|²
Prob(“1”) = |b|²