{ "cells": [ { "cell_type": "markdown", "id": "f3f86015", "metadata": {}, "source": [ "This tutorial follows the work from Tikai Chang et al. 'Strong coupling of a superconducting flux qubit to single bismuth donors', Nature Communications 10.1038/s41467-025-64757-5. In this work, a spin qubit from a bismuth donor is coupled to a superconducting flux qubit. QuaCCAToo models both qubit systems within the `SiBi_flux` class." ] }, { "cell_type": "code", "execution_count": 1, "id": "41b96961", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import scipy.constants as cte\n", "from qutip import basis, fock_dm, jmat, qeye, tensor\n", "\n", "gamma_e = cte.value(\"electron gyromag. ratio in MHz/T\") * 1e-3\n", "\n", "from quaccatoo import Analysis, Ramsey, SiBiFlux, SpinLocking" ] }, { "cell_type": "markdown", "id": "bb238e3d", "metadata": {}, "source": [ "# Flux Qubit" ] }, { "cell_type": "markdown", "id": "5d3dd27a", "metadata": {}, "source": [ "We begin reproducing the results from the flux qubit characterization as shown in the Results section and in Fig 1. We assume the same experimental values for $\\Delta$, $\\Gamma^{2R}$ and $\\Omega$ as in the text. For $\\varepsilon$, we take an arbitrary value to match the experimental results. An object of the `SiBi_flux` class is instantiated considering an initial state $|0\\rangle$, observable $|0\\rangle \\langle 0|$ and collapse operator $\\sqrt{\\Gamma^{2R}} \\hat{S}_z$. The `spin` variable in this experiment is set to `False`, since the spin Hamiltonian does not need to be simulated." ] }, { "cell_type": "code", "execution_count": 4, "id": "bcbbe8d1", "metadata": {}, "outputs": [], "source": [ "Delta = 7.257e3\n", "epsilon = 400\n", "Omega = 60.5\n", "L2 = 0.627**.5*jmat(1/2, 'z')\n", "\n", "sys = SiBiFlux(\n", " rho0 = basis(2,0),\n", " observable = fock_dm(2,0),\n", " Delta = Delta,\n", " epsilon = epsilon,\n", " c_ops = L2,\n", " spin = False,\n", ")" ] }, { "cell_type": "markdown", "id": "a277a77c", "metadata": {}, "source": [ "Based on the defined system, we instantiate a Ramsey sequence from the corresponding predefined class in QuaCCAToo and run the simulation, from which we obtain a decaying Ramsey fringe as in Fig 1h of the text." ] }, { "cell_type": "code", "execution_count": 5, "id": "aeabe07f", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ramsey_sim = Ramsey(\n", " free_duration=np.linspace(.1, 1, 300),\n", " system = sys,\n", " pi_pulse_duration = 1/2/Omega,\n", " h1 = 2*Omega*jmat(1/2, 'x'),\n", " pulse_params = {'f_pulse': Delta}\n", ")\n", "\n", "ramsey_sim.run()\n", "Analysis(ramsey_sim).plot_results()" ] }, { "cell_type": "markdown", "id": "d0cd8a0f", "metadata": {}, "source": [ "# Spin-Locking" ] }, { "cell_type": "markdown", "id": "b685ea71", "metadata": {}, "source": [ "Following the Ramsey simulation of the flux qubit, we now couple both qubits in a spin-locking experiment as in Fig 2d. The bismuth electron spin must be brought into resonance with the driven flux qubit $\\omega_s = \\Delta + \\Omega = 7.3175$ GHz, which is the flip-flop condition used in the text. Here we set `N = False`, so the nuclear spin and the hyperfine term of Eq. (3) are not simulated. In the actual experiment the ∼7.3 GHz spin transition originates almost entirely from the hyperfine interaction, not from a Zeeman splitting. Without the hyperfine term, we can place the electron spin at the required frequency through the electron Zeeman energy by imposing $B_0 = (\\Delta + \\Omega)/\\gamma_e \\approx 261$ mT, even though this is not the experimental condition. " ] }, { "cell_type": "code", "execution_count": 6, "id": "f1706d97", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Delta = 7.257e3\n", "Omega = 60.5\n", "g = 4*1.8\n", "B0 = (Delta + Omega)/gamma_e\n", "L1 = 0.150**.5*tensor(jmat(1/2, '-'), qeye(2))\n", "\n", "init_state = tensor(basis(2,0), basis(2,0))\n", "obs = tensor(jmat(1/2, 'z'), qeye(2))\n", "\n", "sys = SiBiFlux(\n", " rho0 = init_state,\n", " observable = obs,\n", " Delta = Delta,\n", " B0 = B0,\n", " g = g,\n", " N = False,\n", " c_ops = L1\n", ")\n", "\n", "spin_lock_sim = SpinLocking(\n", " pulse_duration=np.linspace(0, 6, 100),\n", " system = sys,\n", " pi_pulse_duration = 1/2/Omega,\n", " h1 = 2*Omega*tensor(jmat(1/2, 'x'), qeye(2)),\n", " pulse_params = {'f_pulse': Delta},\n", " options = {'nsteps':1e6}\n", ")\n", "\n", "spin_lock_sim.run()\n", "Analysis(spin_lock_sim).plot_results()" ] } ], "metadata": { "kernelspec": { "display_name": "quaccatoo-env", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.13.9" } }, "nbformat": 4, "nbformat_minor": 5 }