{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Quickstart: The Rydberg Blockade" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following walkthrough highlights some of Pulser's core features and uses them to display a crucial physical effect for neutral atom devices: the **Rydberg blockade**. Bear in mind that it is not meant to be a comprehensive step-by-step guide on how to use Pulser, but rather a showcase of Pulser in action. \n", "\n", "For a more detailed introduction to Pulser, check the tutorials on [Pulse Sequence Creation](tutorials/creating.nblink) and [Simulation of Sequences](tutorials/simulating.nblink). To better understand neutral atom devices and how they serve as quantum computers and simulators, check the pages in [Quantum Computing with Neutral Atoms](review.rst)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Pulser's main features" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pulser\n", "from pulser_simulation import QutipEmulator" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With ``pulser``, it is easy to define a ``Register`` consisting of any arrangement of atoms in a quantum processor. For example, we can generate a register with hexagonal shape:" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "layers = 3\n", "reg = pulser.Register.hexagon(layers, prefix=\"q\")\n", "reg.draw(with_labels=False)" ] }, { "attachments": { "download%20%282%29.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "In fact, we can place the atoms in arbitrary positions by specifying the positions of each one. As an exotic example, here is a picture of the Gioconda as a register of neutral atoms made using Pulser:\n", "\n", "![download%20%282%29.png](attachment:download%20%282%29.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is also simple to create and design a ``Pulse`` that will act on the atom array:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "duration = 1000 # Typical: ~1 µsec\n", "pulse = pulser.Pulse(\n", " amplitude=pulser.BlackmanWaveform(duration, np.pi),\n", " detuning=pulser.RampWaveform(duration, -5.0, 10.0),\n", " phase=0,\n", ")\n", "pulse.draw()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Each pulse acts on a set of atoms at a certain moment of time. The entire ``Sequence`` is stored by Pulser and can then be either simulated or sent to a real device. Below is the example of a sequence sending the same $\\pi$-pulse to two atoms, sequentially, using the same channel." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "reg = pulser.Register.rectangle(1, 2, spacing=8, prefix=\"atom\")\n", "reg.draw()\n", "\n", "pi_pulse = pulser.Pulse.ConstantDetuning(\n", " pulser.BlackmanWaveform(duration, np.pi), 0.0, 0.0\n", ")\n", "\n", "seq = pulser.Sequence(reg, pulser.DigitalAnalogDevice)\n", "\n", "seq.declare_channel(\"ryd\", \"rydberg_local\", \"atom0\")\n", "\n", "seq.add(pi_pulse, \"ryd\")\n", "seq.target(\"atom1\", \"ryd\")\n", "seq.add(pi_pulse, \"ryd\")\n", "\n", "seq.draw()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Probing the Rydberg Blockade Mechanism" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Rydberg atoms are a prominent architecture for exploring condensed matter physics and quantum information processing. For example, one can use Pulser to write a sequence of succesive $\\pi$-pulses on a two atom system, each one coupling the atom to its excited Rydberg state. This will allow us to study the *Rydberg Blockade* effect, using the dedicated ``pulser_simulation`` library:\n", "\n", "The presence of the van der Waals interaction when both atoms are in the Rydberg state, prevents the collective ground state $|gg\\rangle$ to couple to $|rr\\rangle$, which is shifted out of resonance. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Hamiltonian for the two-atom system can be written as:\n", "\n", "$$H = \\frac{\\hbar \\Omega_1(t)}{2} \\sigma_1^x + \\frac{\\hbar \\Omega_2(t)}{2} \\sigma_2^x + U n_1n_2 $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We shall explore this blockade by changing the interatomic distance $R$:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "data = []\n", "distances = np.linspace(6.5, 14, 7)\n", "\n", "r = [1, 0] # |r>\n", "rr = np.kron(r, r) # |rr>\n", "occup = [np.outer(rr, np.conj(rr))] # |rr>