We've seen that a qubit lives in a complex vector space of dimension 2, whose basis is given by \((\ket0, \ket1)\). Let's call this vector space \(E\). Now, how do we describe the state of 2 qubits? We introduce the tensor product of \(E\) with itself, deno…

Having seen what a qubit is, let's look at the basic operations that can be applied to it. The operators used in quantum computation are all unitary (with the exception of measurements, which mathematically correspond to orthogonal projectors), and theref…

Here's a correction of the second Maths composition in MP for the X competitive entrance exam. It's a very difficult subject, in 4 parts. The main object is the study of linear differential equations with periodic coefficients: we are looking for class \…

With the competitive entrance exam season in full swing, today we turn our attention to the prestigious X competitive entrance exam, with this problem A section MP common to the Ecole Normale competitive entrance exam. Linear algebra is really reduced …

A classical bit can contain either 0 or 1; a quantum bit (qubit) can be in an intermediate state, which is neither 0 nor 1, or both at the same time, a superposition of the two states. Mathematically modeled by: \[ \ket\psi = \alpha\ket0 + \beta\ket1 …