Cristopher Pérez

This are my quantum computing notes and resources. (03/Februar/2026)

I had read in book that quantum mechanics are way more easies than classical mechanics (mathematically), but classical are conceptually easier than quantum mechanics

(09/februar/2026)

• The state of a quantum object is completelly specified by a single wave function Ψ(x) which is a Complex number

  
• P(x) = |Ψ(x)|^2 determinates the probability-density that the object in state Ψ(x) will be found at x

• Given two possible configurations of a quantum system corresponding to two wave functions 1) Ψ(x) and 2) Ψ(x), the system can also be in a SUPERPOSITION of these: Ψ(x) = α Ψ_1(x) + β Ψ_2(x) where: α,β are Complex

  Quantum states live in a complex vector space (Hilbert space).

  SUPERPOSITION means: The particle is in a state that is literally neither 1 nor 2.

  Any wave funciton Ψ(x) can be expressed as a SUPERPOSITION in the form:

  

  of states w/ defINITE momentum p=ℏk

• (next one is in stand by)

(12/februar/2026)

Experiments in quantum mechanics are never gentle. Here "not gentle" means:

• Looking at a planet
• Reading a thermometer
• Weighting something

Why? because it's impossible in principle. Measurements are interactions strong enough to:

• Project wavefunctions Ψ(x)
• Destroy phase relations
• Select one outcome from a SUPERPOSITION

Those interactions must transfer: Energy, Momentum and Phase Information

Here's my github repot with quantum stuff: quantum stuff

(21/februar/2026)

this is more mathematical: vector spaces to define quantum mechanical states are called Hilbert Spaces

Motivating example: Euclidean vector space

another wonderful idea of Hilbert spaces is that they are abstract mathematical areas to track probabilities of a quantum state

Inner Product

Dot product on steroids.

While standard dot"+product tells the angle between two lines. in a Hilbert space the inner product tells the overlap (or similarity) between two quantum states

(22/februar/2026)

State of Spin in quantum mechanics describes the intrinsic angular momentum of a particle and the probabilities of measuring specific spin values along a chosen axis

(15/März/2026)

• state = vector a single qubit e.g.: psi = [a, b]
• observable = Hermitian operator value = psi† A psi
• gate = unitary operator psi' = U psi
• evolution = linear differential equation i dpsi/dt = H psi
• measurement = spectral decomposition p_i = <psi|P_i|psi>
• conservation of probability = continuity + divergence What comes out of one point goes into another → constant total probability.
• simulation = exponential of operators exp(-iHt) = I - iHt + (-iHt)^2/2! + (-iHt)^3/3! + ...

(13/07/2026)

I realized I need to know classical mechanics in order to study QM