{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Representando los estados de un qubit.\n", "\n", "Por lo comentado en el tema anterior, ya sabes algo sobre bits y sobre cómo funcionan nuestros conocidos ordenadores digitales. Todas las variables complejas, objetos y estructuras de datos que se utilizan en el software moderno son, básicamente, grandes montones de bits. Los que trabajan en computación cuántica las llaman *variables clásicas* y a los ordenadores que las utilizan, como el que estás usando para leer este artículo, los llamamos *ordenadores clásicos*.\n", "\n", "En los ordenadores cuánticos, la variable básica es el _qubit:_ una variante cuántica del bit. Tienen exactamente las mismas restricciones que los bits normales: sólo pueden almacenar una única pieza binaria de información y sólo pueden darnos una salida de \"0\" o \"1\". Sin embargo, también pueden manipularse de forma que sólo puede describir la mecánica cuántica. Esto nos da nuevas puertas con las que jugar y nos permite encontrar nuevas formas de diseñar algoritmos.\n", "\n", "Para entender bien estas nuevas puertas, primero tenemos que entender cómo se escriben los estados de los qubits. Para ello utilizaremos las matemáticas de vectores, matrices y [números complejos](complejos). Aunque introduciremos estos conceptos a medida que avancemos, lo mejor es que ya te sientas cómodo con ellos. Se pueden encontrar los conceptos necesarios de álgebra matricial en este enlace (en inglés).\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. Classical vs Quantum Bits \n", "\n", "(statevector)=\n", "### Statevectors o vector de estados.\n", "\n", "```{index} statevectors\n", "```\n", "\n", "En física cuántica utilizamos _vectores de estado_(o statevectors) para describir el estado de nuestro sistema. Digamos que queremos describir la posición de un coche a lo largo de una pista, este es un sistema clásico por lo que podríamos utilizar un número $x$:\n", "\n", "![tracking a car with scalars](images/car_1.PNG)\n", "\n", "$$ x=4 $$\n", "\n", "Alternativamente, podríamos utilizar una colección de números en un vector llamado _vector de estado._ Cada elemento del vector de estado contiene la *probabilidad de encontrar el coche en un lugar determinado*:\n", "\n", "![tracking a car with vectors](images/car_2.PNG)\n", "\n", "$$\n", "|x\\rangle = \\begin{bmatrix} 0\\\\ \\vdots \\\\ 0 \\\\ 1 \\\\ 0 \\\\ \\vdots \\\\ 0 \\end{bmatrix} \n", " \\begin{matrix} \\\\ \\\\ \\\\ \\leftarrow \\\\ \\\\ \\\\ \\\\ \\end{matrix}\n", " \\begin{matrix} \\\\ \\\\ \\text{Probabilidad} \\\\ \\text{coche esté en} \\\\ \\text{posición 4} \\\\ \\\\ \\\\ \\end{matrix} \n", "$$\n", "\n", "Esto no se limita a la posición, también podríamos mantener un vector de estado de todas las posibles velocidades que podría tener el coche y todos los posibles colores que pudiera tener. Con los sistemas clásicos (como el ejemplo del coche anterior), esto es una tontería, ya que requiere mantener vectores enormes cuando en realidad sólo necesitamos un número. Pero como veremos en este capítulo, los vectores de estado (statevectors) resultan ser una forma muy buena de llevar la cuenta de los sistemas cuánticos, incluidos los ordenadores cuánticos.\n", "\n", "\n", "### 1.2 Qubit Notation \n", "\n", "Los bits clásicos siempre tienen un estado completamente bien definido: o son \"0\" o son \"1\" en cada momento del cálculo. No podemos añadir más detalles al estado de un bit. Para escribir el estado de un bit clásico (c), basta con utilizar estos dos valores binarios. Por ejemplo:\n", "\n", " c = 0\n", "\n", "Esta restricción desaparece en el caso de los bits cuánticos. Para obtener un \"0\" o un \"1\" de un qubit, sólo es necesario que esté bien definido cuando se realiza una medición para extraer un resultado. En ese momento, debe comprometerse con una de estas dos opciones. El resto del tiempo, su estado será algo más complejo que un simple valor binario.\n", "\n", "Para ver cómo describirlos, podemos centrarnos primero en los dos casos más sencillos. Como vimos en la última sección, es posible preparar un qubit en un estado para el que definitivamente da el resultado `0` cuando se mide.\n", "\n", "Necesitamos un nombre para este estado. Seamos poco imaginativos y llamémoslo $0$ . Del mismo modo, existe un estado qubit que tiene la certeza de producir un \"1\". Lo llamaremos $1$. Estos dos estados se excluyen mutuamente. O bien el qubit da un 0, o bien da un 1. No hay solapamiento. Una forma de representar esto con las matemáticas es utilizar dos vectores ortogonales.\n", "\n", "\n", "$$\n", "|0\\rangle = \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix} \\, \\, \\, \\, |1\\rangle =\\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix}.\n", "$$\n", "\n", "Esto es mucha notación para asimilar de golpe. En primer lugar, vamos a desentrañar los extraños símbolos utilizados: $|$ y $\\rangle$. Su función consiste básicamente en recordarnos que estamos hablando de los vectores que representan los estados de los qubits etiquetados con $0$ y $1$. Esto nos ayuda a distinguirlos de cosas como los valores de bits 0 y 1 o los números 0 y 1. Forma parte de la *notación bra-ket*, introducida por Dirac.\n", "\n", "Si no estás familiarizado con los vectores, puedes pensar en ellos como listas de números que manipulamos siguiendo ciertas reglas. Si estás familiarizado con los vectores por tus clases de física en el instituto, sabrás que estas reglas hacen que los vectores sean muy adecuados para describir cantidades con una magnitud y una dirección. Por ejemplo, la velocidad de un objeto se describe perfectamente con un vector. Sin embargo, la forma en que utilizamos los vectores para los estados cuánticos es ligeramente distinta a ésta, así que no te aferres demasiado a tu intuición anterior. ¡Es hora de hacer algo nuevo!.\n", "\n", "Con los vectores podemos describir estados más complejos que $|0\\rangle$ y $|1\\rangle$. Por ejemplo, consideremos el vector\n", "\n", "\n", "$$\n", "|q_0\\rangle = \\begin{bmatrix} \\tfrac{1}{\\sqrt{2}} \\\\ \\tfrac{i}{\\sqrt{2}} \\end{bmatrix} .\n", "$$\n", "\n", "Para entender lo que significa este estado, tendremos que utilizar las reglas matemáticas para manipular vectores. En concreto, tendremos que entender cómo sumar vectores y cómo multiplicarlos por escalares.\n", "\n", "\n", "\n", "\n", "Como los estados $|0\\rangle$ y $|1\\rangle$ forman una base ortonormal, podemos representar cualquier vector 2D con una combinación de estos dos estados. Esto nos permite escribir el estado de nuestro qubit en la forma alternativa:\n", "\n", "$$ |q_0\\rangle = \\tfrac{1}{\\sqrt{2}}|0\\rangle + \\tfrac{i}{\\sqrt{2}}|1\\rangle $$\n", "\n", "Este vector, $|q_0\\rangle$ se llama _vector de estado_ del qubit, y nos dice todo lo que podemos saber sobre este qubit. Por ahora, sólo podemos sacar algunas conclusiones sencillas sobre este ejemplo particular de vector de estado: no es enteramente $|0\\rangle$ ni enteramente $|1\\rangle$. En su lugar, se describe mediante una combinación lineal de ambos. En mecánica cuántica, solemos describir este tipo de combinaciones lineales con la palabra \"superposición\".\n", "\n", "Aunque nuestro estado de ejemplo $|q_0\\rangle$ puede expresarse como una superposición de $|0\\rangle$ y $|1\\rangle$, no deja de ser un estado qubit definido y bien definido. Para ver esto, podemos empezar a explorar cómo se puede manipular un qubit.\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Explorando Qubits con Qiskit \n", "\n", "En primer lugar, tenemos que importar todas las herramientas que vamos a necesitar:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "tags": [ "thebelab-init" ] }, "outputs": [], "source": [ "from qiskit import QuantumCircuit, assemble, Aer\n", "from qiskit.visualization import plot_histogram, plot_bloch_vector\n", "from math import sqrt, pi" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "```{index} QuantumCircuit, Inicializar qubit\n", "```\n", "\n", "En Qiskit, utilizamos el objeto `QuantumCircuit` para almacenar nuestros circuitos, esto es esencialmente una lista de las operaciones cuánticas en nuestro circuito y los qubits a los que se aplican." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "qc = QuantumCircuit(1) # Creamos un circuito cuántico con un qubit." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "```{index} initialize\n", "```\n", "\n", "En nuestros circuitos cuánticos, nuestros qubits siempre comienzan por defecto en el estado $|0\\rangle$. Podemos utilizar el método `initialize()` para transformar esto en cualquier estado. Le damos a `initialize()` el vector que queremos en forma de lista, y le decimos qué qubit(s) queremos inicializar en este estado:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(1) # Create a quantum circuit with one qubit\n", "initial_state = [0,1] # Define initial_state as |1>\n", "qc.initialize(initial_state, 0) # Apply initialisation operation to the 0th qubit\n", "qc.draw(output='mpl') # Let's view our circuit" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A continuación, podemos utilizar uno de los simuladores de Qiskit para ver el estado resultante de nuestro qubit." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "tags": [ "thebelab-init" ] }, "outputs": [], "source": [ "sim = Aer.get_backend('aer_simulator') # le dice a Qiskit cómo debe simular el circuito" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Para obtener los resultados de nuestro circuito, usamos `run` para ejecutar nuestro circuito, dando el circuito y el backend como argumentos. Luego usamos `.result()` para obtener el resultado de esto:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "qc = QuantumCircuit(1) # Create a quantum circuit with one qubit\n", "initial_state = [0,1] # Define initial_state as |1>\n", "qc.initialize(initial_state, 0) # Apply initialisation operation to the 0th qubit\n", "qc.save_statevector() # Tell simulator to save statevector\n", "#qobj = assemble(qc) # Create a Qobj from the circuit for the simulator to run\n", "#result = sim.run(qobj).result() # Do the simulation and return the result\n", "result = sim.run(qc).result() # Do the simulation and return the result" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "del `resultado`, podemos obtener el vector de estado final usando `.get_statevector()`:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Statevector([0.+0.j, 1.+0.j],\n", " dims=(2,))\n" ] } ], "source": [ "out_state = result.get_statevector()\n", "print(out_state) # Display the output state vector" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Nota:** Python usa `j` para representar $i$ en el caso de los números complejos. En la salida anterior vemos un vector con dos números complejos: `0.+0.j` = 0, and `1.+0.j` = 1.\n", "\n", "Midamos ahora nuestro qubit como lo haríamos en un ordenador cuántico real y veamos el resultado:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc.measure_all()\n", "qc.draw(output='mpl')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Esta vez, en lugar del vector estado obtendremos los recuentos de los resultados 0 y 1 utilizando `.get_counts()`:" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#qobj = assemble(qc)\n", "#result = sim.run(qobj).result()\n", "result = sim.run(qc).result()\n", "counts = result.get_counts()\n", "plot_histogram(counts)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Podemos ver que (como era de esperar) tenemos un 100% de posibilidades de medir $|1\\rangle$. Esta vez, pongamos nuestro qubit en superposición y veamos qué ocurre. Usaremos el estado $|q_0\\rangle$ de antes en esta sección:\n", "\n", "$$ |q_0\\rangle = \\tfrac{1}{\\sqrt{2}}|0\\rangle + \\tfrac{i}{\\sqrt{2}}|1\\rangle $$\n", "\n", "Necesitamos añadir estas amplitudes a una lista de Python. Para añadir una amplitud compleja, Python utiliza `j` para la unidad imaginaria (normalmente la llamamos \"$i$\" en términos matemáticos):" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "initial_state = [1/sqrt(2), 1j/sqrt(2)] # Definimos el estado |q_0>" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Y entonces repetimos los pasos para inicializar el qubit como antes:" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Statevector([0.70710678+0.j , 0. +0.70710678j],\n", " dims=(2,))\n" ] } ], "source": [ "qc = QuantumCircuit(1) # Must redefine qc\n", "qc.initialize(initial_state, 0) # Initialize the 0th qubit in the state `initial_state`\n", "qc.save_statevector() # Save statevector\n", "#qobj = assemble(qc)\n", "#state = sim.run(qobj).result().get_statevector() # Execute the circuit\n", "state = sim.run(qc).result().get_statevector() # Execute the circuit\n", "print(state) # Print the result" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#qobj = assemble(qc)\n", "results = sim.run(qc).result().get_counts()\n", "plot_histogram(results)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Podemos ver que tenemos la misma probabilidad de medir $|0\\rangle$ o $|1\\rangle$. Para explicar esto, tenemos que hablar de la medición en programación cuántica.\n", "\n", "## Reglas de la medición \n", "\n", "A continuación se comentan una serie de reglas que hay que tener en cuenta en programación cuántica para hacer las mediciones de los estados de los qubits\n", "\n", "### Una regla muy importante \n", "\n", "Existe una regla simple para la medición de los estados cuánticos. Para encontrar la probabilidad de medir un estado $|\\psi \\rangle$ en el estado $|x\\rangle$ hacemos lo siguiente:\n", "\n", "$$p(|x\\rangle) = | \\langle x| \\psi \\rangle|^2$$\n", "\n", "Los símbolos $\\langle$ y $|$ nos dicen que $\\langle x |$ es un vector fila y los símbolos $|$ y $\\rangle$ nos dicen que $|\\psi\\rangle$ es un vector columna. En mecánica cuántica llamamos a los vectores columna _kets_ y a los vectores fila _bra._ Juntos forman la notación _bra-ket_. Cualquier ket $|a\\rangle$ tiene su correspondiente bra $\\langle a|$, y los unos se convierten en los otros utilizando la transpuesta conjugada.\n", "\n", "\n", ":::{note}\n", "Sabemos que un ket (vector columna) se representa de la siguiente manera:\n", "\n", "$$\\quad|a\\rangle = \\begin{bmatrix}a_0 \\\\ a_1 \\\\ \\vdots \\\\ a_n \\end{bmatrix}$$\n", "\n", "En el método de transpuesta conjugada, la matriz se transpone y los elementos se convierten en números complejos conjugados (representado por la operación \"$*$\"), donde el conjugado complejo (\"$*$\") de un número complejo es un número con una parte real igual y una parte imaginaria igual en magnitud pero de signo opuesto. De este modo se obtiene el correspondiente *bra* (vector fila) de la siguiente manera:\n", "\n", "$$\\langle a| = \\begin{bmatrix}a_0^*, & a_1^*, & \\dots & a_n^* \\end{bmatrix}$$\n", "\n", ":::\n", "\n", ":::{note}\n", "

Producto interno

\n", "Hay distintas formas de multiplicar vectores, aquí vamos a explicar en qué consiste el producto interno de dos vectores. En esta guía, utilizamos el producto interior entre un *bra* (vector fila) y un *ket* (vector columna), y sigue esta regla:\n", "\n", "$$\\langle a| = \\begin{bmatrix}a_0^*, & a_1^*, & \\dots & a_n^* \\end{bmatrix}, \\quad |b\\rangle = \\begin{bmatrix}b_0 \\\\ b_1 \\\\ \\vdots \\\\ b_n \\end{bmatrix}$$\n", "\n", "y entonces se tiene:\n", "\n", "$$ \\langle a|b\\rangle =a_0^* b_0 + a_1^* b_1 \\dots a_n^* b_n$$\n", "\n", " \n", "Vemos que el producto interno de dos vectores *siempre nos da un escalar*. Una cosa útil para recordar es que el producto interno de dos vectores ortogonales es 0, por ejemplo si tenemos los vectores ortogonales $|0\\rangle$ y $|1\\rangle$:\n", "\n", "$$\\langle1|0\\rangle = \\begin{bmatrix} 0 & 1\\end{bmatrix}\\begin{bmatrix}1 \\\\ 0\\end{bmatrix} = 0$$\n", "\n", "Además, recuerde que los vectores $|0\\rangle$ y $|1\\rangle$ también están normalizados (las magnitudes son iguales a 1):\n", "\n", "$$\n", " \\begin{aligned} \n", " \\langle0|0\\rangle & = \\begin{bmatrix} 1 & 0\\end{bmatrix}\\begin{bmatrix}1 \\\\ 0\\end{bmatrix} = 1 \\\\\n", " \\langle1|1\\rangle & = \\begin{bmatrix} 0 & 1\\end{bmatrix}\\begin{bmatrix}0 \\\\ 1\\end{bmatrix} = 1\n", " \\end{aligned}\n", "$$\n", "\n", ":::\n", "\n", "En la ecuación anterior, $|x\\rangle$ puede ser cualquier estado qubit. Para hallar la probabilidad de medir $|x\\rangle$, tomamos el producto interno de $|x\\rangle$ y el estado que estamos midiendo (en este caso $|\\psi\\rangle$), y elevamos la magnitud al cuadrado. Esto puede parecer un poco enrevesado, pero pronto se convertirá en algo natural.\n", "\n", "Si nos fijamos en el estado $|q_0\\rangle$ de antes, podemos ver que la probabilidad de medir $|0\\rangle$ es efectivamente 0,5$: \n", "\n", "$$\n", "\\begin{aligned}\n", "|q_0\\rangle & = \\tfrac{1}{\\sqrt{2}}|0\\rangle + \\tfrac{i}{\\sqrt{2}}|1\\rangle \\\\\n", "\\langle 0| q_0 \\rangle & = \\tfrac{1}{\\sqrt{2}}\\langle 0|0\\rangle + \\tfrac{i}{\\sqrt{2}}\\langle 0|1\\rangle \\\\\n", "& = \\tfrac{1}{\\sqrt{2}}\\cdot 1 + \\tfrac{i}{\\sqrt{2}} \\cdot 0\\\\\n", "& = \\tfrac{1}{\\sqrt{2}}\\\\\n", "|\\langle 0| q_0 \\rangle|^2 & = \\tfrac{1}{2}\n", "\\end{aligned}\n", "$$\n", "\n", "Debes verificar la probabilidad de medir $|1\\rangle$ como ejercicio.\n", "\n", "Esta regla establece cómo obtenemos información de los estados cuánticos. Por tanto, es muy importante para todos los que hacemos en computación cuántica. También implica de inmediato varios hechos importantes, que vemos en el siguiente apartado.\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Implicaciones de esta norma \n", "\n", "A continuación pasamos a ver cuales son las implicaciones a las que se hace mención en el párrafo anterior. \n", "\n", "### Normalización.\n", "\n", "La regla nos muestra que las amplitudes están relacionadas con las probabilidades. Si queremos que las probabilidades sumen 1 (¡y así debe ser!), tenemos que asegurarnos de que el vector de estado está correctamente normalizado. En concreto, necesitamos que la magnitud del vector de estado sea 1.\n", "\n", "\n", "\n", "$$ \\langle\\psi|\\psi\\rangle = 1 \\\\ $$\n", "\n", "Entonces si:\n", "\n", "$$ |\\psi\\rangle = \\alpha|0\\rangle + \\beta|1\\rangle $$\n", "\n", "Se tiene que:\n", "\n", "$$ |\\alpha|^2 + |\\beta|^2 = 1 $$\n", "\n", "Esto explica los factores de $\\sqrt{2}$ que has visto a lo largo de este capítulo. De hecho, si intentamos dar a `initialize()` un vector que no esté normalizado, nos dará un error, como se puede ver en el código siguiente:\n" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "tags": [ "raises-exception" ] }, "outputs": [ { "ename": "QiskitError", "evalue": "'Sum of amplitudes-squared is not 1, but 1.4142135623730951.'", "output_type": "error", "traceback": [ "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[1;31mQiskitError\u001b[0m Traceback (most recent call last)", "Cell \u001b[1;32mIn[28], line 2\u001b[0m\n\u001b[0;32m 1\u001b[0m vector \u001b[38;5;241m=\u001b[39m [\u001b[38;5;241m1\u001b[39m,\u001b[38;5;241m1\u001b[39m]\n\u001b[1;32m----> 2\u001b[0m \u001b[43mqc\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43minitialize\u001b[49m\u001b[43m(\u001b[49m\u001b[43mvector\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m)\u001b[49m\n", "File \u001b[1;32mD:\\MisTrabajos\\Iberdrola_Miguel\\ProgramacionCuantica\\venv\\Lib\\site-packages\\qiskit\\extensions\\quantum_initializer\\initializer.py:194\u001b[0m, in \u001b[0;36minitialize\u001b[1;34m(self, params, qubits, normalize)\u001b[0m\n\u001b[0;32m 191\u001b[0m qubits \u001b[38;5;241m=\u001b[39m [qubits]\n\u001b[0;32m 192\u001b[0m num_qubits \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mlen\u001b[39m(qubits) \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28misinstance\u001b[39m(params, \u001b[38;5;28mint\u001b[39m) \u001b[38;5;28;01melse\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m\n\u001b[1;32m--> 194\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mappend(\u001b[43mInitialize\u001b[49m\u001b[43m(\u001b[49m\u001b[43mparams\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mnum_qubits\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mnormalize\u001b[49m\u001b[43m)\u001b[49m, qubits)\n", "File \u001b[1;32mD:\\MisTrabajos\\Iberdrola_Miguel\\ProgramacionCuantica\\venv\\Lib\\site-packages\\qiskit\\extensions\\quantum_initializer\\initializer.py:58\u001b[0m, in \u001b[0;36mInitialize.__init__\u001b[1;34m(self, params, num_qubits, normalize)\u001b[0m\n\u001b[0;32m 36\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21m__init__\u001b[39m(\u001b[38;5;28mself\u001b[39m, params, num_qubits\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m, normalize\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mFalse\u001b[39;00m):\n\u001b[0;32m 37\u001b[0m \u001b[38;5;250m \u001b[39m\u001b[38;5;124mr\u001b[39m\u001b[38;5;124;03m\"\"\"Create new initialize composite.\u001b[39;00m\n\u001b[0;32m 38\u001b[0m \n\u001b[0;32m 39\u001b[0m \u001b[38;5;124;03m Args:\u001b[39;00m\n\u001b[1;32m (...)\u001b[0m\n\u001b[0;32m 56\u001b[0m \u001b[38;5;124;03m normalize (bool): Whether to normalize an input array to a unit vector.\u001b[39;00m\n\u001b[0;32m 57\u001b[0m \u001b[38;5;124;03m \"\"\"\u001b[39;00m\n\u001b[1;32m---> 58\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_stateprep \u001b[38;5;241m=\u001b[39m \u001b[43mStatePreparation\u001b[49m\u001b[43m(\u001b[49m\u001b[43mparams\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mnum_qubits\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mnormalize\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mnormalize\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m 60\u001b[0m \u001b[38;5;28msuper\u001b[39m()\u001b[38;5;241m.\u001b[39m\u001b[38;5;21m__init__\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124minitialize\u001b[39m\u001b[38;5;124m\"\u001b[39m, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_stateprep\u001b[38;5;241m.\u001b[39mnum_qubits, \u001b[38;5;241m0\u001b[39m, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_stateprep\u001b[38;5;241m.\u001b[39mparams)\n", "File \u001b[1;32mD:\\MisTrabajos\\Iberdrola_Miguel\\ProgramacionCuantica\\venv\\Lib\\site-packages\\qiskit\\circuit\\library\\data_preparation\\state_preparation.py:107\u001b[0m, in \u001b[0;36mStatePreparation.__init__\u001b[1;34m(self, params, num_qubits, inverse, label, normalize)\u001b[0m\n\u001b[0;32m 105\u001b[0m params \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39marray(params, dtype\u001b[38;5;241m=\u001b[39mnp\u001b[38;5;241m.\u001b[39mcomplex128) \u001b[38;5;241m/\u001b[39m norm\n\u001b[0;32m 106\u001b[0m \u001b[38;5;28;01melif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m math\u001b[38;5;241m.\u001b[39misclose(norm, \u001b[38;5;241m1.0\u001b[39m, abs_tol\u001b[38;5;241m=\u001b[39m_EPS):\n\u001b[1;32m--> 107\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m QiskitError(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mSum of amplitudes-squared is not 1, but \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mnorm\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m.\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[0;32m 109\u001b[0m num_qubits \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_get_num_qubits(num_qubits, params)\n\u001b[0;32m 110\u001b[0m params \u001b[38;5;241m=\u001b[39m [params] \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28misinstance\u001b[39m(params, \u001b[38;5;28mint\u001b[39m) \u001b[38;5;28;01melse\u001b[39;00m params\n", "\u001b[1;31mQiskitError\u001b[0m: 'Sum of amplitudes-squared is not 1, but 1.4142135623730951.'" ] } ], "source": [ "vector = [1,1]\n", "qc.initialize(vector, 0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Quick Ejercicios\n", "\n", "1. Crear un vector de estado que dará una probabilidad de $1/3$ de medir $|0\\rangle$.\n", "\n", "\n", "2. Crear un vector de estado diferente que dará las mismas probabilidades de medición.\n", "\n", "\n", "3. Verificar que la probabilidad de medir $|1\\rangle$ para estos dos estados es de $2/3$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Puedes comprobar tu respuesta en el widget de abajo (acepta respuestas con ±1% de precisión, puedes usar términos numpy como `pi` y `sqrt()` en el vector):" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "37ba36e00fac49508c9a9a9121de46e9", "version_major": 2, "version_minor": 0 }, "text/plain": [ "VBox(children=(Label(value='State Vector:'), HBox(children=(Text(value='[1, 0]', placeholder='Type something')…" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "82ca78e3d1a849bf87254f836473c59a", "version_major": 2, "version_minor": 0 }, "text/plain": [ "HTML(value='
')"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Run the code in this cell to interact with the widget\n",
    "from qiskit_textbook.widgets import state_vector_exercise\n",
    "state_vector_exercise(target=1/3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Medición alternativa​.\n",
    "\n",
    "La regla de medida nos da la probabilidad $p(|x\\rangle)$ de que un estado $|\\psi\\rangle$ se mida como $|x\\rangle$. En ninguna parte nos dice que $|x\\rangle$ sólo puede ser $|0\\rangle$ o $|1\\rangle$.\n",
    "\n",
    "Las medidas que hemos considerado hasta ahora son, de hecho, sólo una de las infinitas formas posibles de medir un qubit. Para cualquier par ortogonal de estados, podemos definir una medida que haga que un qubit elija entre los dos.\n",
    "\n",
    "Esta posibilidad se estudiará más a fondo en la siguiente sección. Por ahora, sólo hay que tener en cuenta que $|x\\rangle$ no se limita a ser simplemente $|0\\rangle$ o $|1\\rangle$.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fase global.\n",
    "\n",
    "Sabemos que medir el estado $|1\\rangle$ nos dará la salida `1` con certeza. Pero también somos capaces de escribir estados como​ el siguiente: \n",
    "\n",
    "$$\\begin{bmatrix}0 \\\\ i\\end{bmatrix} = i|1\\rangle.$$\n",
    "\n",
    "Para ver cómo se comporta, aplicamos la regla de la medida vista anteriormente.\n",
    "\n",
    "$$ |\\langle x| (i|1\\rangle) |^2 = | i \\langle x|1\\rangle|^2 = |\\langle x|1\\rangle|^2 $$\n",
    "\n",
    "Aquí encontramos que el factor de $i$ desaparece una vez que tomamos la magnitud del número complejo. Este efecto es completamente independiente del estado medido $|x\\rangle$. No importa qué medida estemos considerando, las probabilidades para el estado $i|1\\rangle$ son idénticas a las de $|1\\rangle$. Dado que las mediciones son la única forma de extraer información de un qubit, esto implica que estos dos estados son equivalentes en todos los aspectos físicamente relevantes.\n",
    "\n",
    "De forma más general, nos referimos a cualquier factor global $\\gamma$ sobre un estado para el que $|\\gamma|=1$ como una \"fase global\". *Los estados que difieren sólo por una fase global son físicamente indistinguibles*.\n",
    "\n",
    "\n",
    "$$ |\\langle x| ( \\gamma |a\\rangle) |^2 = | \\gamma \\langle x|a\\rangle|^2 = |\\langle x|a\\rangle|^2 $$\n",
    "\n",
    "Nótese que esto es distinto de la diferencia de fase _entre_ los términos de una superposición, que se conoce como \"fase relativa\". Esto adquiere relevancia cuando consideramos distintos tipos de medición y múltiples qubits.\n",
    "\n",
    "\n",
    "### El efecto observado.\n",
    "\n",
    "Sabemos que las amplitudes contienen información sobre la probabilidad de que encontremos el qubit en un estado específico, pero una vez que hemos medido el qubit, sabemos con certeza cuál es el estado del qubit. Por ejemplo, si medimos un qubit en el estado\n",
    "\n",
    "$$ |q\\rangle = \\alpha|0\\rangle + \\beta|1\\rangle$$\n",
    "\n",
    "Y encontrarlo en el estado $|0\\rangle$, si volvemos a medir, hay un 100% de posibilidades de encontrar el qubit en el estado $|0\\rangle$. Esto significa que el acto de medir _cambia_ el estado de nuestros qubits.\n",
    "\n",
    "\n",
    "$$ |q\\rangle = \\begin{bmatrix} \\alpha \\\\ \\beta \\end{bmatrix} \\xrightarrow{\\text{Measure }|0\\rangle} |q\\rangle = |0\\rangle = \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix}$$\n",
    "\n",
    "A este efecto se le suele llamar \"colapsar\" el estado del qubit. Se trata de un efecto muy potente que debe utilizarse con prudencia. Por ejemplo, si midiéramos constantemente cada uno de nuestros qubits para controlar su valor en cada punto de un cálculo, siempre estarían en un estado bien definido de $|0\\rangle$ o $|1\\rangle$. Como tales, no se diferenciarían de los bits clásicos y nuestra computación podría sustituirse fácilmente por una computación clásica. Para lograr una computación verdaderamente cuántica debemos permitir que los qubits exploren estados más complejos. Por tanto, las mediciones sólo se utilizan cuando necesitamos extraer un resultado. Esto significa que solemos colocar todas las mediciones *al final de nuestro circuito cuántico*.\n",
    "\n",
    "Podemos demostrarlo utilizando el simulador de vectores de estado de Qiskit. Inicialicemos un qubit en superposición:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOMAAABuCAYAAADVoKRKAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy81sbWrAAAACXBIWXMAAA9hAAAPYQGoP6dpAAAJfElEQVR4nO3deVCU9x3H8c9yZblWRNQFQVGQQUhZVNTAJI0k0ojUY5JeU6NxPFLHGs2UwEz7R9KxMzVEquORUZg6PZKJocZRmyFR0yEaolYhFEREV0AJy+4qyxFuZNmnf9huJFkOl+P5Pcvn9d/DPr+HLzu8fZ49WFWSJEkgItm5yT0AET3EGIkEwRiJBMEYiQTBGIkEwRiJBMEYiQTBGIkEwRiJBMEYiQTBGIkEwRiJBMEYiQTBGIkEwRiJBMEYiQTBGIkEwRiJBMEYiQTBGIkEwRiJBMEYiQTBGIkEwRiJBMEYiQTBGIkEwRiJBMEYiQTBGIkEwRiJBMEYiQTBGIkEwRiJBMEYiQTBGIkEwRiJBMEYiQThIfcAE50kAbZeuaeYONw8AZVK7ikcY4wys/UCnx+Qe4qJI3kH4O4l9xSO8TKVSBCMkUgQjJFIEIyRSBCMkUgQjJFIEIyRvif98FKkH17q9PqPLx/BjzLd0NhqGr2hJgDGSKMuMWYVAODfNz6WeRJlYYw06oImhSAqNAEXK07JPYqiMEYaE0mxa1BaVYCunna5R1EMxkjDtm1/AjbumWff3vX3n+DFNwPt2wdPbkdKhgrtXS1Iil2NXmsPim6dkWNURWKMNCx9fVbUmisQERJv/1pV/X8wJ0Rn3642lkI7ORx+3gEI18YiJCgSl66fGv9hFYox0rDUNdzCA2u3PcaO7laYm+/YtyVJwh3TNUTMmG9fkxSzGldvfoK+PqsMEyuPy8VosViQmZmJyMhIqNVqhIWFYefOnejo6MCmTZugUqlw6NAhucdUnGpjKQDY46sxlkGSJPu2qbEGnT1t/c6cSbGr0dbVjGt3vhjfYRXKpf6EqrS0FKmpqTCbzfD19UVMTAyMRiMOHDiA6upqNDU1AQDi4+PlHVSBaoxlAIDI/8X2/zgjQ+b32340Rjc3dwCAzdY3LjMqncucGS0WC1auXAmz2Yz09HSYTCaUlJTAbDYjKysL+fn5KCoqgkqlQlxcnNzjKk61qQyB/lpM9p/+cNtYCk+PJzBz+jz77QAQ+chl6qXrp+CrngRdxNJxn1eJXCbGHTt2wGAwYPv27cjOzoa/v7/9tszMTOh0OlitVoSHh0Oj0cg4qTLVN+gxRRNi3642lmLW9Bh4uHsCAIpufoqpAWGYFhBm3+fSjdNYHL3Cvg8NziVirKysRF5eHoKCgrB7926H+yxcuBAAoNPpHN5Og+uzWdHa2QhJktDXZ8Xde98+s1p86xz0hmI8P3+tff/ae5UwNOiRFLtapomVxyViPHbsGGw2G9auXQs/Pz+H+3h7ewNgjM7SRSTjXnMt9p/Yii+vn0SvtQd+6gB8dGEv/vD+TxE6NQq/eO639v0vV5yGp7sXFkWnyji1srjEEzgFBQUAgOTk5AH3MRgMABijs7au2ovm9nvIv5KL/Cu5AIAThfvg5aFG6pLNWJ/ye/iqv738v1RxGrqI5H5fo8G5RIy1tbUAgFmzZjm83Wq14uLFiwBGFmNCQgLMZrPT6x3x8vBG7vbbo3rMsTDJNwhvbzkLo6UaB0/+Gl/dPoe3N5/Dk7Ofhpenut++Ta1m3Ky7gtfWvCvTtAObGzUXD6xdY3Z8rVaL4uJip9a6RIwdHR0AgK4ux3dyXl4eLBYL/P39MXv2bKe/j9lsRn19vdPrHVF7+ozq8cZaSFAErH0PEBw4Bwuiljnc5/KNfwIAEgV8vGgyGtHd2yn3GA65RIxarRbNzc0oKSlBYmJiv9tMJhMyMjIAAHFxcVCN4EMztVrtiOZ0xMvDe9SPOdaqTWWIjxj4IcHyRRuRkvAKvDyeGMephic4JGTMz4zOcokYly1bhsrKSmRlZSElJQVRUVEAgKKiIqxbtw4WiwXAyF/sd/byYzB9D5T1uakNLQa0dTb1e3H/u9zdPeAu6K/Wbf1tYT83VSVJkiT3ECNlMBgQHx+PxsZGeHh4IDo6Gt3d3aiqqkJqaipsNhvOnj2L3NxcbNmyRe5x+1FajErHDzEeY6GhoSgsLERaWhrUajXu3r2LwMBA5OTkID8/H3q9HgCfSSWxucSZcTDt7e3QaDRQqVRoa2uDj49YT5jwzDi+eGaUUUVFBSRJwty5c4ULkehRLh9jeXk5AF6ikvjEfMprFCk9xpQMFcK1T2LziiwsmbcChobb2JP3Cr7psMBXPQkZP/8rwrWx/da0djQiI+d5+3ZPbydMTTU4/tZ9aHwCBzzGUOu6H3Tid39ejuyt5+Hm5vjf8aHmc3a24ax940gyaoxleDnlTbz4zOsjut/lwBgVYN+2Qvh5BwAA9p/4FVYseRUvLNqAL659hD15G/DuzqJ++2t8pyDnN6X27ePns3Gt5gI0PoGDHmOodWovH+zdNvgfCg81n7OzDWdt9tbP8c6HG4a8P0Xl8pepBQUFkCQJaWlpco8yYs3t96E3FGPZgpcBAM/84CU0tNSh3lI16LpPi45i+eJNj32MR9cBwHuf7cLfzr41qvM5O5uj+ZTO5WN0JQ0tdQjUBMPd/eEFjUqlwrTJM3G/5esB11TcvYT2zmY8Ne/Hj3WM764DAH1dEaLCEkZtPmdnG2g+pWOMLu7M1aNIWbje/gs+knX6+q8QFTpwjOM120jXiooxKsjUgDA0tZrsn7YmSRLuN3+NaQEzHe7f1dOOC9f+gRcWb3ysYzhaZ/mmHiqoMEUTPCrzOTvbQGtdAWNUkMl+0xA5YwH+VfI+AKCw/ASCAkIxIyjS4f7ny/IwJ1iHmdOiH+sYjtbp64r7nRWzjq3Hl+UnnZ7P2dkGWusKXOccP0G8/lIO9uRtwLGCP8JHrUHGz/5iv+1PxzcjMWYVkmIf/sczZ64eReqS778Xd7BjDLROb+gfo95QjDVP73B6PmdnG+znUjqXfzuc6IZ6O1xKhgondzXbX9qQy2sHn8LmFVnQRTyLlvYG7P7gl8h69TNZZ3LknQ83IHJG/ICvM/LtcOS0yX7TkX74WVyp/ESW72+0VGPrvvmICNYhbs4PAQABflOFDPGNI8kor7kAtZev3KM4hWdGmfGN4uOLZ0YiGhJjJBIEYyQSBB8zykySAFuv3FNMHG6ewAg+k2xMMUYiQfAylUgQjJFIEIyRSBCMkUgQjJFIEIyRSBCMkUgQjJFIEIyRSBCMkUgQjJFIEIyRSBCMkUgQjJFIEIyRSBCMkUgQjJFIEIyRSBCMkUgQjJFIEIyRSBCMkUgQjJFIEIyRSBCMkUgQ/wXpFOwsgKRq1QAAAABJRU5ErkJggg==",
      "text/plain": [
       "
"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(1) # We are redefining qc\n",
    "initial_state = [0.+1.j/sqrt(2),1/sqrt(2)+0.j]\n",
    "qc.initialize(initial_state, 0)\n",
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Esto debería inicializar nuestro qubit en el estado:\n",
    "\n",
    "$$ |q\\rangle = \\tfrac{i}{\\sqrt{2}}|0\\rangle + \\tfrac{1}{\\sqrt{2}}|1\\rangle $$\n",
    "\n",
    "Podemos comprobarlo con el simulador:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Qubit State = Statevector([0.        +0.70710678j, 0.70710678+0.j        ],\n",
      "            dims=(2,))\n"
     ]
    }
   ],
   "source": [
    "qc.save_statevector()\n",
    "#result = sim.run(assemble(qc)).result()\n",
    "result = sim.run(qc).result()\n",
    "state = result.get_statevector()\n",
    "print(\"Qubit State = \" + str(state))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podemos ver aquí que el qubit se inicializa en el estado `[0.+0.70710678j 0.70710678+0.j]`, como esperábamos.\n",
    "\n",
    "Creemos ahora un circuito en el que midamos este qubit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "
"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(1) # We are redefining qc\n",
    "initial_state = [0.+1.j/sqrt(2),1/sqrt(2)+0.j]\n",
    "qc.initialize(initial_state, 0)\n",
    "qc.measure_all()\n",
    "qc.save_statevector()\n",
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cuando simulamos este circuito completo, podemos ver que una de las amplitudes es siempre 0:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "State of Measured Qubit = Statevector([0.+1.j, 0.+0.j],\n",
      "            dims=(2,))\n"
     ]
    }
   ],
   "source": [
    "#qobj = assemble(qc)\n",
    "#state = sim.run(qobj).result().get_statevector()\n",
    "state = sim.run(qc).result().get_statevector()\n",
    "print(\"State of Measured Qubit = \" + str(state))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Puedes volver a ejecutar esta celda unas cuantas veces para reinicializar el qubit y medirlo de nuevo. Observarás que cualquiera de los dos resultados es igualmente probable, pero que el estado del qubit nunca es una superposición de $|0\\rangle$ y $|1\\rangle$. Curiosamente, la fase global en el estado $|0\\rangle$ sobrevive, pero como se trata de una fase global, nunca podremos medirla en un ordenador cuántico real.\n",
    "\n",
    "###  Una nota sobre los simuladores cuánticos.\n",
    "\n",
    "Podemos ver que escribir el estado de un qubit requiere llevar la cuenta de dos números complejos, pero al utilizar un ordenador cuántico real sólo recibiremos una respuesta de sí o no (`0` o `1`) para cada qubit. La salida de un ordenador cuántico de 10 qubits tendrá este aspecto:\n",
    "\n",
    "`0110111110`\n",
    "\n",
    "Sólo 10 bits, sin superposición ni amplitudes complejas. Cuando utilizamos un ordenador cuántico real, no podemos ver los estados de nuestros qubits a mitad del cálculo, ¡ya que los destruiríamos!. Este comportamiento no es ideal para el aprendizaje, por lo que Qiskit proporciona diferentes simuladores cuánticos: Por defecto, el `aer_simulator` imita la ejecución de un ordenador cuántico real, pero también te permitirá echar un vistazo a los estados cuánticos antes de la medición si incluimos ciertas instrucciones en nuestro circuito. Por ejemplo, aquí hemos incluido la instrucción `.save_statevector()`, lo que significa que podemos usar `.get_statevector()` sobre el resultado de la simulación. \n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## La esfera de  Bloch  \n",
    "\n",
    "Un elemento muy importante para representar qubit es la denominada esfera de Bloch que a continuación se pasa a presentar.\n",
    "\n",
    "### Describiendo los estados de un qubit. \n",
    "\n",
    "Hemos visto anteriormente en este capítulo que el estado general de un qubit ($|q\\rangle$) es:\n",
    "\n",
    "$$\n",
    "|q\\rangle = \\alpha|0\\rangle + \\beta|1\\rangle\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\alpha, \\beta \\in \\mathbb{C}\n",
    "$$\n",
    "\n",
    "(La segunda línea nos dice que $\\alpha$ y $\\beta$ son números complejos). Las dos primeras implicaciones de la sección 2 nos dicen que no podemos diferenciar entre algunos de estos estados. Esto significa que podemos ser más específicos en nuestra descripción del qubit.\n",
    "\n",
    "En primer lugar, como no podemos medir la fase global, sólo podemos medir la diferencia de fase entre los estados $|0\\rangle$ y $|1\\rangle$. En lugar de que $\\alpha$ y $\\beta$ sean complejos, podemos limitarlos a los números reales y añadir un término que nos diga la fase relativa entre ellos:\n",
    "\n",
    "\n",
    "$$\n",
    "|q\\rangle = \\alpha|0\\rangle + e^{i\\phi}\\beta|1\\rangle\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\alpha, \\beta, \\phi \\in \\mathbb{R}\n",
    "$$\n",
    "\n",
    "Por último, dado que el estado del qubit debe estar normalizado, i.e.\n",
    "\n",
    "$$\n",
    "\\sqrt{\\alpha^2 + \\beta^2} = 1\n",
    "$$\n",
    "\n",
    "Podemos usar la identidad trigonométrica:\n",
    "\n",
    "$$\n",
    "\\sqrt{\\sin^2{x} + \\cos^2{x}} = 1\n",
    "$$\n",
    "\n",
    "para describir los reales $\\alpha$ y $\\beta$ en términos de una variable, $\\theta$:\n",
    "\n",
    "$$\n",
    "\\alpha = \\cos{\\tfrac{\\theta}{2}}, \\quad \\beta=\\sin{\\tfrac{\\theta}{2}}\n",
    "$$\n",
    "\n",
    "A partir de aquí podemos describir el estado de cualquier qubit utilizando las dos variables $\\phi$ y $\\theta$:\n",
    "\n",
    "$$\n",
    "|q\\rangle = \\cos{\\tfrac{\\theta}{2}}|0\\rangle + e^{i\\phi}\\sin{\\tfrac{\\theta}{2}}|1\\rangle\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\theta, \\phi \\in \\mathbb{R}\n",
    "$$\n",
    "\n",
    "### Representación visual del estado de un qubit. \n",
    "\n",
    "Queremos trazar el estado general de nuestro qubit:\n",
    "\n",
    "$$\n",
    "|q\\rangle = \\cos{\\tfrac{\\theta}{2}}|0\\rangle + e^{i\\phi}\\sin{\\tfrac{\\theta}{2}}|1\\rangle\n",
    "$$\n",
    "\n",
    "Si interpretamos $\\theta$ y $\\phi$ como coordenadas esféricas ($r = 1$, ya que la magnitud del estado qubit es $1$), podemos representar cualquier estado qubit individual en la superficie de una esfera, conocida como la esfera _Bloch_.\n",
    "\n",
    "A continuación hemos representado un qubit en el estado $|{+}\\rangle$. En este caso, $\\theta = \\pi/2$ y $\\phi = 0$.\n",
    "\n",
    "Qiskit tiene una función para trazar una esfera Bloch, `plot_bloch_vector()`. Esta función acepta coordenadas cartesianas por defecto, pero también puede aceptar coordenadas esféricas pasando el argumento `coord_type='spherical'.`\n",
    "\n",
    "\n",
    "También se puede consultar  esta interactiva esfera de Bloch .\n",
    "\n",
    "Desde qiskit podemos hacer esta representación de la siguiente manera."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.visualization import plot_bloch_vector\n",
    "coords = [1,pi/2,0]  # [Radius, Theta, Phi]\n",
    "plot_bloch_vector(coords, coord_type='spherical')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Nota aclaratoria.\n",
    "\n",
    "Cuando se aprende por primera vez sobre los estados de los qubits, es fácil confundir el _vector de estado_ de los qubits con su _vector Bloch_. Recuerda que el vector de estado es el vector del que hablamos al principio de este apartado, que contiene las amplitudes de los dos estados en los que puede estar nuestro qubit. El vector de Bloch es una herramienta de visualización que mapea el vector de estado complejo 2D en un espacio real 3D.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Quick Ejercicios\n",
    "Utilizar `plot_bloch_vector()` para dibujar un qubit en los siguientes estados:\n",
    "1. $|0\\rangle$\n",
    "\n",
    "2. $|1\\rangle$\n",
    "\n",
    "3. $\\tfrac{1}{\\sqrt{2}}(|0\\rangle + |1\\rangle)$\n",
    "\n",
    "4. $\\tfrac{1}{\\sqrt{2}}(|0\\rangle - i|1\\rangle)$\n",
    "\n",
    "5. $\\tfrac{1}{\\sqrt{2}}\\begin{bmatrix}i\\\\1\\end{bmatrix}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
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Version Information
SoftwareVersion
qiskit0.44.2
qiskit-terra0.25.2
qiskit_aer0.12.2
System information
Python version3.11.4
Python compilerMSC v.1916 64 bit (AMD64)
Python buildmain, Jul  5 2023 13:38:37
OSWindows
CPUs4
Memory (Gb)11.799663543701172
Mon Jan 15 12:04:21 2024 Hora estándar romance
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   ],
   "source": [
    "import qiskit.tools.jupyter\n",
    "%qiskit_version_table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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