{ "cells": [ { "cell_type": "markdown", "id": "3bb64b95", "metadata": {}, "source": [ "This tutorials reproduces section III.C from:\n", "\n", "- L. Tsunaki, A. Singh, S. Trofimov, & B. Naydenov. (2025). Digital Twin Simulations Toolbox of the Nitrogen-Vacancy Center in Diamond. arXiv:2507.18759 quant-ph. [2507.18759](https://arxiv.org/abs/2507.18759).\n", "\n", "While Tutorial 3 focuses on basic operations with the NV component and Tutorial 4 and 5 discuss three applications related to sensing and computing, this tutorial introduces a problem relevant to quantum communication and cryptography.\n", "The process of quantum teleportation consists of transferring the state of one qubit to another spatially separated one, through non-local properties of quantum entanglement.\n", "This way, making itself a corner stone of quantum networks.\n", "Here, we simulate an adapted version of an unconditional teleportation between two NV centers, as originally demonstrated by:\n", "\n", "- W. Pfaff, B. J. Hensen, H. Bernien, S. B. van Dam, M. S. Blok, T. H. Taminiau, M. J. Tiggelman, R. N. Schouten, M. Markham, D. J. Twitchen, and R. Hanson, Unconditional quantum teleportation between distant solid-state quantum bits, Science 345, 532 (2014).\n", "\n", "Specifically, we focus on simulating a simplified version of the MW and RF pulses implementation, rather than the photonic component of the experiment, which is on itself the greatest technical challenge of the experiment and the main source of errors." ] }, { "cell_type": "code", "execution_count": 1, "id": "ad43e9b2", "metadata": {}, "outputs": [], "source": [ "from quaccatoo import NV, compose_sys, PulsedSim, Analysis, plot_histogram\n", "from qutip import tensor, basis, qeye, fock_dm, ptrace\n", "import numpy as np\n", "import copy" ] }, { "cell_type": "markdown", "id": "b9241bc0", "metadata": {}, "source": [ "# 1. System Definition" ] }, { "cell_type": "markdown", "id": "975dca8c", "metadata": {}, "source": [ "This simple form of teleportation consists of two network parties: 'Alice' and 'Bob'.\n", "Alice has a 14NV center with two qubits, the nitrogen nuclear spin and the electron spin.\n", "Bob has another distant NV, where the nuclear spin can be neglected.\n", "This system can be defined in QuaCCAToo using:" ] }, { "cell_type": "code", "execution_count": 2, "id": "5df602cb", "metadata": {}, "outputs": [], "source": [ "NVa = NV(B0=25, units_B0='mT', N=14)\n", "NVb = NV(B0=18, units_B0='mT', N=0)\n", "\n", "NVa.truncate(mS=1, mI=1)\n", "NVb.truncate(mS=1)\n", "\n", "sys = compose_sys(NVb, NVa)" ] }, { "cell_type": "markdown", "id": "5f2991cd", "metadata": {}, "source": [ "where we assume some typical values for $B_0$.\n", "To avoid performance issues of simulating a large Hilbert space with dimension $d=3^2=27$ from the three spins-1 subsystems, the `truncate` method is used to exclude the $\\ket{m_S=+1}$ and $\\ket{m_I=+1}$ levels.\n", "Which, as seen in the previous tutorials, does not compromise the modeling of the system, as long as the transition frequencies are well separated compared to the spectral width of the excitation. \n", "This way, the system is defined within the subspaces $m_{S,I}=0,-1$, with a total dimension of $d=2^3=8$ instead.\n", "Lastly, the `compose_sys` function is used to compose the two NV centers from Alice and Bob, which internally calculates the new attributes of the `sys` object.\n", "\n", "Initially, the two NVs' electron spins are in a maximally entangled Bell state $\\ket{\\Psi^-} = (\\ket{01} - \\ket{10})/\\sqrt{2}$, where $\\ket{0} \\equiv \\ket{m_S=0}$ and $\\ket{1} \\equiv \\ket{m_S=-1}$.\n", "While this is presented as a postulate for the simulation applications, the experimental generation of the Bell state poses a great technological challenge, given the poor spectral stability of NVs and high relative background counts.\n", "This is achieved through a photon emission mixing by a beam splitter and mutual photon detection, which thus heralds an entanglement event for the two NVs' electron spins.\n", "The optical properties of the NVs optical emission can be nonetheless improved by micro-engineering of the diamond surface.\n", "\n", "Apart from the initial state of the electron, the state $\\ket{\\psi} = \\alpha \\ket{0} + \\beta \\ket{1}$ to be teleported between Alice and Bob is initially stored in Alice's 14N spin.\n", "Experimentally, it can initialized into the state $\\ket{1} \\equiv \\ket{m_I = -1}$ by a projective measurement of the electron spin. \n", "Which is then rotated to the state $\\ket{\\psi}$ with the appropriate resonance pulses, as discussed in Tutorial 3.\n", "In the software component, the initial state of the three spins $\\ket{\\Psi^-}\\otimes\\ket{\\psi}$ is hence represented by:" ] }, { "cell_type": "code", "execution_count": 3, "id": "c4d586fd", "metadata": {}, "outputs": [], "source": [ "Psi_ = tensor(basis(2, 0),basis(2,1)) - tensor(basis(2,1),basis(2,0))\n", "\n", "alpha = 1\n", "beta = 0\n", "\n", "psi = alpha*basis(2,0)+beta*basis(2,1)\n", "\n", "sys.rho0 = tensor(Psi_,psi).unit()" ] }, { "cell_type": "markdown", "id": "eb65d7db", "metadata": {}, "source": [ "for given values of $\\alpha, \\beta \\in \\mathbb{C}$.\n", "By taking $\\alpha=\\beta=1/\\sqrt{2}$ we have the initial state $\\ket{+X}$, with $\\alpha=1/\\sqrt{2}$ and $\\beta=i/\\sqrt{2}$ we have $\\ket{+Y}$, and finally with $\\alpha=1$ and $\\beta=0$ we have $\\ket{+Z}$.\n", "Here, we first consider the $\\ket{+Z}$ state.\n", "\n", "To define the remaining experimental constants of the experiment we use:" ] }, { "cell_type": "code", "execution_count": null, "id": "5fb0c56f", "metadata": {}, "outputs": [], "source": [ "# Rabi frequencies of the spins in MHz\n", "w1_rf = .2\n", "w1_mwa = 16\n", "w1_mwb = 22\n", "w1_cnot = 2.14/3**.5\n", "\n", "# pi pulse times\n", "tpi_rf = 1/(2*w1_rf)\n", "tpi_mwa = 1/(2*w1_mwa)\n", "tpi_mwb = 1/(2*w1_mwb)\n", "tpi_cnot = 1/(2*w1_cnot)\n", "\n", "# Larmor frequencies of the spins\n", "w0_rf = NVa.RF_freqs[2]\n", "w0_mwa = NVa.MW_freqs[0]\n", "w0_cnot = NVa.energy_levels[2]\n", "w0_mwb = NVb.MW_freqs[0]\n", "\n", "# Hamiltonian terms for the RF and MW pulses\n", "h1_rf = w1_rf * tensor(qeye(2), NVa.RF_h1)\n", "h1_mwa = w1_mwa * tensor(qeye(2), NVa.MW_h1)\n", "h1_cnot = w1_cnot * tensor(qeye(2), NVa.MW_h1)\n", "h1_mwb = w1_mwb * tensor(NVb.MW_h1, qeye(2), qeye(2))\n", "\n", "sol_opt = {'nsteps':1e9}" ] }, { "cell_type": "markdown", "id": "21f744ce", "metadata": {}, "source": [ "# 2. Hadamard Gate Optimization" ] }, { "cell_type": "markdown", "id": "56a0f088", "metadata": {}, "source": [ "Before realizing the protocol, the phase $\\varphi^{rf}$ of the nuclear pulse during the Hadamard gate needs to be optimized to reduce phase accumulations between states. This is achieved with:" ] }, { "cell_type": "code", "execution_count": null, "id": "c8298a5d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "np.float64(2.95)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sys2 = copy.deepcopy(NVa)\n", "\n", "sys2.rho0 = tensor(\n", " basis(2, 0) - basis(2, 1), basis(2, 0) - basis(2, 1)\n", ").unit()\n", "\n", "sys2.observable = [\n", " tensor(fock_dm(2, 0), fock_dm(2, 0)),\n", " tensor(fock_dm(2, 0), fock_dm(2, 1)),\n", " tensor(fock_dm(2, 1), fock_dm(2, 0)),\n", " tensor(fock_dm(2, 1), fock_dm(2, 1))\n", "]\n", "\n", "def hadamard_phi(phi_rf, **kwargs):\n", " \"\"\"\n", " CNOT and Hadamard gates sequence for teleportation.\n", " The phase of the RF pulse is optimized to maximize the fidelity of the teleportation.\n", "\n", " Parameters\n", " ----------\n", " phi_rf : float\n", " Phase of the RF pulse in radians.\n", " kwargs : dict\n", " Dictionary containing the pulse parameters:\n", " - tpi_rf: float\n", " Duration of the RF pi pulse.\n", " - tpi_mwa: float\n", " Duration of the MW pi pulse for the first NV.\n", " - tpi_cnot: float\n", " Duration of the CNOT gate.\n", " - w0_rf: float\n", " Larmor frequency of the RF pulse.\n", " - w0_mwa: float\n", " Larmor frequency of the first NV's MW pulse.\n", " - w0_cnot: float\n", " Larmor frequency of the CNOT gate.\n", " - h1_rf: Qobj\n", " Hamiltonian term for the RF pulse.\n", " - h1_mwa: Qobj\n", " Hamiltonian term for the first NV's MW pulse.\n", " - h1_cnot: Qobj\n", " Hamiltonian term for the CNOT gate.\n", " \"\"\"\n", " seq_in = PulsedSim(sys2)\n", "\n", " seq_in.add_pulse(kwargs['tpi_cnot'], kwargs['h1_cnot'], pulse_params={'f_pulse': kwargs['w0_cnot'], 'phi_t':np.pi/2}, options=sol_opt)\n", "\n", " seq_in.add_pulse(kwargs['tpi_rf']/2, kwargs['h1_rf'], pulse_params={'f_pulse': kwargs['w0_rf'], 'phi_t':phi_rf}, options=sol_opt)\n", " seq_in.add_pulse(kwargs['tpi_mwa'], kwargs['h1_mwa'], pulse_params={'f_pulse': kwargs['w0_mwa'], 'phi_t':np.pi/2}, options=sol_opt)\n", " seq_in.add_pulse(kwargs['tpi_rf']/2, kwargs['h1_rf'], pulse_params={'f_pulse': kwargs['w0_rf'], 'phi_t':phi_rf}, options=sol_opt)\n", "\n", " return seq_in.rho\n", "\n", "phi_array = np.arange(0, 2*np.pi, 0.01)\n", "\n", "seq_phi = PulsedSim(sys2)\n", "seq_args = {\n", " 'tpi_rf': tpi_rf,\n", " 'tpi_mwa': tpi_mwa,\n", " 'tpi_cnot': tpi_cnot,\n", " 'w0_rf': w0_rf,\n", " 'w0_mwa': w0_mwa,\n", " 'w0_cnot': w0_cnot,\n", " 'h1_rf': w1_rf * NVa.RF_h1,\n", " 'h1_mwa': w1_mwa * NVa.MW_h1,\n", " 'h1_cnot': w1_cnot * NVa.MW_h1,\n", "}\n", "\n", "seq_phi.run(phi_array, hadamard_phi, sequence_kwargs=seq_args)\n", "\n", "Analysis(seq_phi).plot_results()\n", "phi_rf = phi_array[np.argmax(seq_phi.results[0]**2 + seq_phi.results[3]**2)]\n", "phi_rf" ] }, { "cell_type": "markdown", "id": "b1bca067", "metadata": {}, "source": [ "By taking the maximum value for observables 0 and 3, as done in the Ref., we obtain $\\varphi^{rf}=2.95$.\n", "Finally, we also have the freedom to choose $\\tau_2$ and the total refocus time `tau_refocus` such that the final fidelities are optimized. From previous tests, we observe that:" ] }, { "cell_type": "code", "execution_count": 7, "id": "c0de26bf", "metadata": {}, "outputs": [], "source": [ "tau_refocus = 2.26" ] }, { "cell_type": "markdown", "id": "d5864794", "metadata": {}, "source": [ "leads to high fidelities and gives a solution $\\tau_2>0$. The user can test this by changing the value." ] }, { "cell_type": "markdown", "id": "78860550", "metadata": {}, "source": [ "# 3. Teleportation Protocol" ] }, { "cell_type": "markdown", "id": "2598f48a", "metadata": {}, "source": [ "Given the initial state and the optmized values of `tau_refocus` and $\\varphi^{rf}$, the teleportation protocol can then be simulated.\n", "Since there is no standard predefined sequence in QuaCCAToo for this protocol, we can simulate it by instantiating an object from `PulsedSim` with `sys` as an argument:" ] }, { "cell_type": "code", "execution_count": null, "id": "33bce50e", "metadata": {}, "outputs": [], "source": [ "seq = PulsedSim(sys)" ] }, { "cell_type": "markdown", "id": "5cb33f7b", "metadata": {}, "source": [ "The first part of the teleportation protocol is a CNOT gate to Alice's electron spin conditioned to her nuclear spin.\n", "This is expressed by a soft selective $\\hat{R}_y(\\pi)$ pulse of the $\\ket{m_S=0} \\leftrightarrow \\ket{m_S=-1}$ electron transition for the $\\ket{m_I=-1}$ nuclear state.\n", "The intensity of this pulse needs to be small, in order to ensure a narrow bandwidth excitation.\n", "Furthermore, the $\\ket{m_I=0}$ states would ideally remain unchanged during the operation.\n", "But due to the system's evolution under the time-independent Hamiltonian $\\hat{H}_0$ during the finite pulse length, these states also accumulate a phase.\n", "This phase is minimized however by taking the Rabi frequency of the CNOT pulse as $\\omega_1^{cnot} = a_\\parallel^n/\\sqrt{3}$, where $a_\\parallel^n$ is the parallel component of the hyperfine interaction on the NV center.\n", "\n", "A pulse with the parameters as defined above can be added to the sequences with the `add_pulse` method using:" ] }, { "cell_type": "code", "execution_count": null, "id": "ac00c2e3", "metadata": {}, "outputs": [], "source": [ "# CNOT gate\n", "seq.add_pulse(\n", "\tduration = tpi_cnot,\n", "\th1 = h1_cnot,\n", "\tpulse_params = {'f_pulse':w0_cnot,\n", "\t\t'phi_t':np.pi/2},\n", "\toptions = sol_opt\n", "\t)" ] }, { "cell_type": "markdown", "id": "3bb170e5", "metadata": {}, "source": [ "By default, `add_pulse` assumes a square pulse and 100 time steps in the time array discretization, which should not be confused with the `nsteps` key for the solver options dictionary that is increased to `1e9`.\n", "In the lab frame, the $\\phi$ angle of the rotation axis is expressed in terms of the temporal phase of the excitation field `phi_t`.\n", "Within this implementation, the simulation is already executed upon calling `add_pulse`, differently from predefined methods which require the `run` command.\n", "However, if the user desires to execute a sequence in parallel in regards to some changing variable, it can be defined within a function and called with `run` as done with Hadamard optmization.\n", "\n", "One of the main challenges of the pulse implementation of the protocol is the loss of the relative phase between the qubits due to the dynamics from $\\hat{H}_0$.\n", "Specifically, all three spins precess with different Larmor frequencies $\\omega_0$ during the finite pulse lengths.\n", "Which makes it necessary to correct for this phase accumulation in Bob's qubit while Alice performs the teleportation operation on her qubits.\n", "For that, we implement a refocusing scheme similar to a Hahn echo, with a free evolution of $\\tau_1$ followed by a $\\hat{R}_y(\\pi)$ pulse and another free evolution of $\\tau_2$.\n", "The free evolution times $\\tau_1$ and $\\tau_2$ are chosen such that the $\\hat{R}_y(\\pi)$ is exactly in the middle of the whole protocol duration prior to the state reconstruction, and thus Bob's qubit ends the protocol with the same state as he initially had.\n", "This way, we have the first free evolution time given by \n", "$$\n", "\t\\tau_1 + t_\\pi^{cnot} + \\frac{t_\\pi^B}{2} = \\frac{T}{2} ,\n", "$$\n", "where $T$ is the total duration of the protocol.\n", "\n", "To implement the refocus scheme we calculate the free evolution times from the optmized value of `tau_refocus` and use the `add_free_evolution` and `add_pulse` methods:" ] }, { "cell_type": "code", "execution_count": null, "id": "f681dbcd", "metadata": {}, "outputs": [], "source": [ "# Refocus scheme\n", "T = tpi_cnot + tau_refocus + tpi_rf/2 + tpi_mwa + tpi_rf/2\n", "tau1 = T/2 - tpi_cnot - tpi_mwb/2\n", "tau2 = tau_refocus - tau1 - tpi_mwb\n", "\n", "seq.add_free_evolution(tau1)\n", "seq.add_pulse(\n", "\tduration = tpi_mwb,\n", "\th1 = h1_mwb,\n", "\tpulse_params = {'f_pulse': w0_mwb,\n", "\t\t'phi_t':np.pi/2},\n", "\toptions = sol_opt\n", "\t)\n", "seq.add_free_evolution(tau2)" ] }, { "cell_type": "markdown", "id": "83ecfde1", "metadata": {}, "source": [ "In the Ref., the phase of Bob's qubit is protected with an XY4 sequence.\n", "However, in this simulation, the implementation would become more complex than the straight experimental realization with multi-channel pulse generation, due to the intricate time placement of the $\\pi$-pulses on Bob's qubit.\n", "In the end, this difference in the refocusing scheme will require small adjustments to Bob's state reconstruction pulses, as discussed in the following analysis.\n", "\n", "The next step of the protocol is Hadamard gate to Alice's nuclear spin, which can be decomposed with two rotations, such as $\\hat{R}_{y}(\\pi/2)\\hat{R}_{z}(\\pi)$.\n", "In this case nonetheless, the first rotation on the $z$-axis responsible for correcting the phase can be omitted, hence configuring a pseudo-Hadamard gate.\n", "In addition, due to the fact that the transition frequency of the nuclear spin depends on the $m_S$ state, the gate can be composed by three pulses: a conditional rotation of $\\hat{R}_{\\varphi^{rf}}(\\pi/2)$ on the nuclear spin over some chosen axis $\\varphi^{rf}$, an unconditional rotation of $\\hat{R}_y(\\pi)$ on Alice's electron, and another rotation of $\\hat{R}_{\\varphi^{rf}}(\\pi/2)$ on the nuclei.\n", "This way, the first pulse changes the nuclear state for $m_S=-1$, then the electron spin is inverted and the same RF pulses is applied again.\n", "Assuming some typical values for the pulse parameters, where the Rabi frequency of Alice's electron for a hard pulse `w1_mwa` is now much larger than for the CNOT gate, the three pulses are simulated using:" ] }, { "cell_type": "code", "execution_count": null, "id": "5369594d", "metadata": {}, "outputs": [], "source": [ "# Hadamard gate\n", "seq.add_pulse(\n", "\tduration = tpi_rf/2,\n", "\th1 = h1_rf,\n", "\tpulse_params={'f_pulse':w0_rf,\n", "\t\t'phi_t':phi_rf},\n", "\toptions=sol_opt\n", "\t)\n", "seq.add_pulse(\n", "\tduration = tpi_mwa,\n", "\th1 = h1_mwa,\n", "\tpulse_params={'f_pulse': w0_mwa,\n", "\t\t'phi_t':np.pi/2},\n", "\toptions=sol_opt\n", "\t)\n", "seq.add_pulse(\n", "\tduration = tpi_rf/2,\n", "\th1 = h1_rf,\n", "\tpulse_params={'f_pulse':w0_rf,\n", "\t\t'phi_t':phi_rf},\n", "\toptions=sol_opt\n", "\t)" ] }, { "cell_type": "markdown", "id": "c19c8b31", "metadata": {}, "source": [ "with the pulse phase `phi_rf` as optimized above.\n", "\n", "At this point, the teleportation of the $\\ket{\\psi} = \\alpha \\ket{0} + \\beta \\ket{1}$ state to Bob's NV has already taken place, who has a superposition state composed of four different possible combinations with the coefficients $\\alpha$ and $\\beta$.\n", "Thus, with Alice measuring her qubits, Bob's qubit will be projected in one of the four combinations.\n", "Physically, the electron spin is measured by the fluorescence observable, while the nuclear spin is measured using the electron spin as an auxiliary qubit, which gives rise to an observable as\n", "$$\n", "\t\\hat{F}_{I^n} = \\hat{1} \\otimes \\hat{1} \\otimes \\ket{1}\\bra{1} .\n", "$$\n", "Given the two observables, Alice's measurements are implemented with the `measure_qsys` method:" ] }, { "cell_type": "code", "execution_count": 12, "id": "ef0819f1", "metadata": {}, "outputs": [], "source": [ "# Alice measurements\n", "obs0 = tensor(qeye(2),fock_dm(2, 0),qeye(2))\n", "c0 = 1 - seq.measure_qsys(observable=obs0)\n", "\n", "obs1 = tensor(qeye(2),qeye(2),fock_dm(2, 1))\n", "c1 = seq.measure_qsys(observable=obs1)" ] }, { "cell_type": "markdown", "id": "b71afcf7", "metadata": {}, "source": [ "Besides collapsing the system in one of the eigenstates of the observables, the two measurements performed with the `measure_qsys` method yield two classical bits $c_0$ and $c_1$.\n", "These two classical bits are then communicated to Bob via a classical channel, who now needs to reconstruct the $\\ket{\\psi}$ state on his qubit with some operation $\\hat{U}(c_0, c_1)$, which also depends on the input state $\\ket{\\psi}$ in this application." ] }, { "cell_type": "markdown", "id": "8c1641ca", "metadata": {}, "source": [ "## 3.1 Z Input" ] }, { "cell_type": "markdown", "id": "c60cf4c4", "metadata": {}, "source": [ "First, we take the $\\ket{+Z}$ input state.\n", "If Alice's electron qubit is measured in the $\\ket{1}$ state yielding $c_0, \\, c_1 = 1, \\, 0$ or $c_0, \\, c_1 = 1, \\, 1$, Bob does not need to perform any operation on his qubit, which is already in the state $\\ket{\\psi}$.\n", "However, if Alice measures her electron in the state $\\ket{0}$ with $c_0, \\, c_1 = 0, \\, 1$ or $c_0, \\, c_1 = 0, \\, 0$, then Bob needs to perform a rotation of $\\hat{R}_y(\\pi)$ so that his qubit is then in the state $\\ket{\\psi}$.\n", "Altogether then, the state reconstruction for an initial state $\\ket{+Z}$ is implemented with:" ] }, { "cell_type": "code", "execution_count": null, "id": "ff90d759", "metadata": {}, "outputs": [], "source": [ "if c0 == 0. and c1 == 0.:\n", "\tseq.add_pulse(tpi_mwb, h1_mwb, pulse_params={'f_pulse':w0_mwb, 'phi_t':np.pi/2}, options=sol_opt)\n", "elif c0 == 0. and c1 == 1.:\n", "\tseq.add_pulse(tpi_mwb, h1_mwb, pulse_params={'f_pulse':w0_mwb, 'phi_t':np.pi/2}, options=sol_opt)\n", "elif c0 == 1. and c1 == 0.:\n", "\tpass\n", "elif c0 == 1. and c1 == 1.:\n", "\tpass" ] }, { "cell_type": "markdown", "id": "0fbb4ac5", "metadata": {}, "source": [ "To compare the real part of the densitry matrix of the teleported state with the ideal state, we use the `plot_histogram` function:" ] }, { "cell_type": "code", "execution_count": 14, "id": "d413e058", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Fidelity: 0.9997832200638801\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rho_sim = ptrace(seq.rho*seq.rho.dag(), 0)\n", "rho_theo = psi * psi.dag()\n", "plot_histogram(rho_sim, rho_theo, component='real')" ] }, { "cell_type": "markdown", "id": "fb80d86d", "metadata": {}, "source": [ "Now the imaginary:" ] }, { "cell_type": "code", "execution_count": 15, "id": "b53e30ed", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Fidelity: 0.9997832200638801\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_histogram(rho_sim, rho_theo, component='imag')" ] }, { "cell_type": "markdown", "id": "5958d78c", "metadata": {}, "source": [ "## 3.2 X Input" ] }, { "cell_type": "markdown", "id": "4f9dc0a8", "metadata": {}, "source": [ "In the $\\ket{+X}$ and $\\ket{+Y}$ inputs, $\\pi/2$ pulses are also required to reconstruct the teleported state.\n", "Where in these cases, the phase accumulated by Bob's qubit alters the final state and needs to be corrected, which is not the case for the $\\pi$-pulse with a complete population inversion.\n", "This can be achieved by adding a free evolution of duration $\\tau_3$ such that the qubit will have completed an integer number of Larmor precessions and thus will have returned to the same state.\n", "Mathematically, this means that the free evolution duration to cancel the phase accumulation must be\n", "$$\n", "\t\\tau_3 = \\frac{\\lceil \\omega_0^B t_\\pi^B/2 \\rceil}{\\omega_0^B} - \\frac{t_\\pi^B}{2} ,\n", "$$\n", "where $\\omega_0^B$ is the Larmor frequency for Bob's NV and $t_\\pi^B$ the $\\pi$-pulse duration, as previously defined.\n", "In addition, $\\lceil \\cdot \\rceil$ denotes the ceiling function, which rounds the value up to the nearest integer. Finally, the $\\pi$ rotations around the $z$-axis $\\hat{R}_z(\\pi)$ present in some $\\hat{U}(c_0, c_1)$ can also be obtained simply with a free evolution of duration $1/(2\\omega_0^B)$.\n", "\n", "For $\\ket{+X}$ state we then have:" ] }, { "cell_type": "code", "execution_count": null, "id": "039743ae", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "c0 = 1.0, c1 = 0.0\n", "Fidelity: 0.9889556512700622\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Initial state\n", "alpha = 1/2**.5\n", "beta = 1/2**.5\n", "\n", "psi = alpha*basis(2,0)+beta*basis(2,1)\n", "sys.rho0 = tensor(Psi_,psi).unit()\n", "\n", "seq = PulsedSim(sys)\n", "\n", "# CNOT gate\n", "seq.add_pulse(\n", "\tduration = tpi_cnot,\n", "\th1 = h1_cnot,\n", "\tpulse_params = {'f_pulse':w0_cnot,\n", "\t\t'phi_t':np.pi/2},\n", "\toptions = sol_opt\n", "\t)\n", "\n", "# Refocus scheme\n", "seq.add_free_evolution(tau1)\n", "seq.add_pulse(\n", "\tduration = tpi_mwb,\n", "\th1 = h1_mwb,\n", "\tpulse_params = {'f_pulse': w0_mwb,\n", "\t\t'phi_t':np.pi/2},\n", "\toptions = sol_opt\n", "\t)\n", "seq.add_free_evolution(tau2)\n", "\n", "# Hadamard gate\n", "seq.add_pulse(\n", "\tduration = tpi_rf/2,\n", "\th1 = h1_rf,\n", "\tpulse_params={'f_pulse':w0_rf,\n", "\t\t'phi_t':phi_rf},\n", "\toptions=sol_opt\n", "\t)\n", "seq.add_pulse(\n", "\tduration = tpi_mwa,\n", "\th1 = h1_mwa,\n", "\tpulse_params={'f_pulse': w0_mwa,\n", "\t\t'phi_t':np.pi/2},\n", "\toptions=sol_opt\n", "\t)\n", "seq.add_pulse(\n", "\tduration = tpi_rf/2,\n", "\th1 = h1_rf,\n", "\tpulse_params={'f_pulse':w0_rf,\n", "\t\t'phi_t':phi_rf},\n", "\toptions=sol_opt\n", "\t)\n", "\n", "# Alice measurements\n", "obs0 = tensor(qeye(2),fock_dm(2, 0),qeye(2))\n", "c0 = 1 - seq.measure_qsys(observable=obs0)\n", "\n", "obs1 = tensor(qeye(2),qeye(2),fock_dm(2, 1))\n", "c1 = seq.measure_qsys(observable=obs1)\n", "\n", "print(f'c0 = {c0}, c1 = {c1}')\n", "\n", "tau3 = np.ceil(w0_mwb*tpi_mwb/2)/w0_mwb - tpi_mwb/2\n", "\n", "# Bob recounstruction of teleported state\n", "if c0 == 0. and c1 == 0.:\n", " # R-y(pi/2)\n", " seq.add_pulse(tpi_mwb/2, h1_mwb, pulse_params={'f_pulse': w0_mwb, 'phi_t': -np.pi/2}, options=sol_opt)\n", " seq.add_free_evolution(tau3)\n", "elif c0 == 0. and c1 == 1.:\n", " # Ry(pi/2)\n", " seq.add_pulse(tpi_mwb/2, h1_mwb, pulse_params={'f_pulse': w0_mwb, 'phi_t': np.pi/2}, options=sol_opt)\n", " tau3 += 1/(2*w0_mwb)\n", " seq.add_free_evolution(tau3) \n", "elif c0 == 1. and c1 == 0.:\n", " # Ry(pi/2)\n", " seq.add_pulse(tpi_mwb/2, h1_mwb, pulse_params={'f_pulse': w0_mwb, 'phi_t': np.pi/2}, options=sol_opt)\n", " tau3 += 1/(2*w0_mwb)\n", " seq.add_free_evolution(tau3)\n", "elif c0 == 1. and c1 == 1.:\n", " # R-y(pi/2)\n", " seq.add_pulse(tpi_mwb/2, h1_mwb, pulse_params={'f_pulse': w0_mwb, 'phi_t': -np.pi/2}, options=sol_opt)\n", " seq.add_free_evolution(tau3)\n", "\n", "rho = ptrace(seq.rho*seq.rho.dag(), 0)\n", "rho_theo = psi * psi.dag()\n", "plot_histogram(rho, rho_theo,component='real')" ] }, { "cell_type": "code", "execution_count": 17, "id": "4c7fc812", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Fidelity: 0.9889556512700622\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_histogram(rho, rho_theo, component='imag')" ] }, { "cell_type": "markdown", "id": "43f901d5", "metadata": {}, "source": [ "## 3.3 Y Input" ] }, { "cell_type": "markdown", "id": "abeba511", "metadata": {}, "source": [ "Finnaly, for $\\ket{+Y}$ state:" ] }, { "cell_type": "code", "execution_count": null, "id": "f2c3cc8e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "c0 = 0.0, c1 = 1.0\n", "Fidelity: 0.9713054945602968\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Initial state\n", "alpha = 1/2**.5\n", "beta = 1j/2**.5\n", "\n", "psi = alpha*basis(2,0)+beta*basis(2,1)\n", "sys.rho0 = tensor(Psi_,psi).unit()\n", "\n", "seq = PulsedSim(sys)\n", "\n", "# CNOT gate\n", "seq.add_pulse(\n", "\tduration = tpi_cnot,\n", "\th1 = h1_cnot,\n", "\tpulse_params = {'f_pulse':w0_cnot,\n", "\t\t'phi_t':np.pi/2},\n", "\toptions = sol_opt\n", "\t)\n", "\n", "# Refocus scheme\n", "seq.add_free_evolution(tau1)\n", "seq.add_pulse(\n", "\tduration = tpi_mwb,\n", "\th1 = h1_mwb,\n", "\tpulse_params = {'f_pulse': w0_mwb,\n", "\t\t'phi_t':np.pi/2},\n", "\toptions = sol_opt\n", "\t)\n", "seq.add_free_evolution(tau2)\n", "\n", "# Hadamard gate\n", "seq.add_pulse(\n", "\tduration = tpi_rf/2,\n", "\th1 = h1_rf,\n", "\tpulse_params={'f_pulse':w0_rf,\n", "\t\t'phi_t':phi_rf},\n", "\toptions=sol_opt\n", "\t)\n", "seq.add_pulse(\n", "\tduration = tpi_mwa,\n", "\th1 = h1_mwa,\n", "\tpulse_params={'f_pulse': w0_mwa,\n", "\t\t'phi_t':np.pi/2},\n", "\toptions=sol_opt\n", "\t)\n", "seq.add_pulse(\n", "\tduration = tpi_rf/2,\n", "\th1 = h1_rf,\n", "\tpulse_params={'f_pulse':w0_rf,\n", "\t\t'phi_t':phi_rf},\n", "\toptions=sol_opt\n", "\t)\n", "\n", "# Alice measurements\n", "obs0 = tensor(qeye(2),fock_dm(2, 0),qeye(2))\n", "c0 = 1 - seq.measure_qsys(observable=obs0)\n", "\n", "obs1 = tensor(qeye(2),qeye(2),fock_dm(2, 1))\n", "c1 = seq.measure_qsys(observable=obs1)\n", "\n", "print(f'c0 = {c0}, c1 = {c1}')\n", "\n", "tau3 = np.ceil(w0_mwb*tpi_mwb/2)/w0_mwb - tpi_mwb/2\n", "\n", "# Bob recounstruction of teleported state\n", "if c0 == 0. and c1 == 0.:\n", " # Rz(pi)Rx(pi/2)\n", " seq.add_pulse(tpi_mwb/2, h1_mwb, pulse_params={'f_pulse': w0_mwb, 'phi_t': 0}, options=sol_opt)\n", " tau3 += 1/(2*w0_mwb)\n", " seq.add_free_evolution(tau3)\n", "elif c0 == 0. and c1 == 1.:\n", " # R-x(pi/2)\n", " seq.add_pulse(tpi_mwb/2, h1_mwb, pulse_params={'f_pulse': w0_mwb, 'phi_t': np.pi}, options=sol_opt)\n", " seq.add_free_evolution(tau3) \n", "elif c0 == 1. and c1 == 0.:\n", " # Rz(pi)Rx(pi/2)\n", " seq.add_pulse(tpi_mwb/2, h1_mwb, pulse_params={'f_pulse': w0_mwb, 'phi_t': 0}, options=sol_opt)\n", " tau3 += 1/(2*w0_mwb)\n", " seq.add_free_evolution(tau3)\n", "elif c0 == 1. and c1 == 1.:\n", " # R-x(pi/2)\n", " seq.add_pulse(tpi_mwb/2, h1_mwb, pulse_params={'f_pulse': w0_mwb, 'phi_t': np.pi}, options=sol_opt)\n", " seq.add_free_evolution(tau3)\n", "\n", "rho = ptrace(seq.rho*seq.rho.dag(), 0)\n", "rho_theo = psi * psi.dag()\n", "plot_histogram(rho, rho_theo,component='real')" ] }, { "cell_type": "code", "execution_count": 19, "id": "49d2e858", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Fidelity: 0.9713054945602968\n" ] }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAVAAAAESCAYAAACreI2+AAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjMsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvZiW1igAAAAlwSFlzAAAPYQAAD2EBqD+naQAAUwNJREFUeJzt3XVUlOnbwPHvDB0KiAJiAAaIYmJhIBYWtqurK3bHqqjrqrvW2q6KjYHdrouua2JgBwZ2C2KAhSJIDMw87x++8lsWdWGIGfD+nMPxzMMT18BwefctkyRJQhAEQcgwuaYDEARByK1EAhUEQVCTSKCCIAhqEglUEARBTSKBCoIgqEkkUEEQBDWJBCoIgqAmkUAFQRDUJBKoIAiCmkQCFQRBUJNIoIIgCGoSCVQQBEFNIoEKgiCoSSRQQRAENYkEKgiCoCaRQAVBENQkEqggCIKaRAIVBEFQU4YS6Nq1a5HJZMhkMoKCgtJ8X5IkSpUqhUwmw8PDQ62Ali5dytq1azN0TVBQ0BdjUsen93nx4sXPft/Lywt7e/tUx+zt7enRo0eGnnPmzBkmTZrEu3fv1AtUEASNUqsEmi9fPvz9/dMcP378OA8fPiRfvnxqB6ROAq1SpQpnz56lSpUqaj83swICAvj1118zdM2ZM2eYPHmySKCCkEuplUA7derEzp07ef/+farj/v7+uLm5Ubx48SwJ7r8kJSWRnJxM/vz5qVmzJvnz58+R535O5cqVKVmypMaer45PPz9BENSjVgLt3LkzAFu2bEk5Fh0dzc6dO+nVq9dnr5k8eTI1atSgQIEC5M+fnypVquDv788/NwW1t7fn5s2bHD9+PKWp4FNV+VM1fcOGDYwcOZIiRYpgYGDAgwcP0lThX79+TbFixahVqxZJSUkp97916xYmJiZ4e3ur87a/6t9VeJVKxdSpU3FycsLIyAhzc3MqVKjAggULAJg0aRKjR48GwMHBIU3TiEqlYvbs2ZQpUwYDAwOsrKzo1q0bT58+TfVcSZKYPn06dnZ2GBoaUrVqVQIDA/Hw8EjVjPK1n9+rV68YNGgQZcuWxdTUFCsrKxo0aMDJkydTPSssLAyZTMacOXOYNWsW9vb2GBkZ4eHhwb1790hKSuLnn3/G1tYWMzMz2rZty8uXL7P8Zy0I2kJXnYvy589Phw4dWL16Nf379wc+JlO5XE6nTp3w9fVNc01YWBj9+/dPKZ2eO3eOoUOH8uzZMyZMmAB8rAZ36NABMzMzli5dCoCBgUGq+4wdOxY3Nzf8/PyQy+VYWVkRGRmZ6pyCBQuydetWPDw8GDNmDPPmzSMuLo7vvvuO4sWL4+fnl673qVQqP1tCS89O0LNnz2bSpEn88ssvuLu7k5SUxJ07d1Kq63369CEqKopFixbx559/UrhwYQDKli0LwMCBA1mxYgVDhgzBy8uLsLAwfv31V4KCgrh8+TIFCxYEYPz48cyYMYN+/frRrl07njx5Qp8+fUhKSsLR0TFNXJ/7+b169QqAiRMnYmNjQ2xsLAEBAXh4eHDkyJE07dlLliyhQoUKLFmyhHfv3jFy5EhatmxJjRo10NPTY/Xq1Tx+/JhRo0bRp08f/vrrr3T9vAUh15EyYM2aNRIgBQcHS8eOHZMA6caNG5IkSVK1atWkHj16SJIkSeXKlZPq1av3xfsolUopKSlJmjJlimRpaSmpVKqU733p2k/Pc3d3/+L3jh07lur4rFmzJEAKCAiQunfvLhkZGUnXrl1L9/v82pednV2qa+zs7KTu3bunvPby8pIqVar01efMmTNHAqTQ0NBUx2/fvi0B0qBBg1IdP3/+vARI48aNkyRJkqKioiQDAwOpU6dOqc47e/asBKT6OX7t5/dvycnJUlJSktSwYUOpbdu2KcdDQ0MlQKpYsaKkVCpTjvv6+kqA1KpVq1T3GT58uARI0dHR//lMQciN1B7GVK9ePUqWLMnq1au5fv06wcHBX6y+Axw9epRGjRphZmaGjo4Oenp6TJgwgTdv3mSomte+fft0nzt69GhatGhB586dWbduHYsWLaJ8+fLpvn79+vUEBwen+apTp85/Xlu9enWuXr3KoEGDOHjwYJr24q85duwYQJpe/erVq+Ps7MyRI0eAj6X4xMREOnbsmOq8mjVrphkl8MmXfn5+fn5UqVIFQ0NDdHV10dPT48iRI9y+fTvNuc2bN0cu/99Hx9nZGYAWLVqkOu/T8fDw8C+8U0HI3dROoDKZjJ49e7Jx40b8/PxwdHSkbt26nz33woULeHp6ArBy5UpOnz5NcHAw48ePByA+Pj7dz/1U1U1vjD169CAhIQEbG5sMt306OztTtWrVNF9mZmb/ee3YsWP5/fffOXfuHM2aNcPS0pKGDRt+cWjUP7158wb4/Hu1tbVN+f6nf62trdOc97ljX7rnvHnzGDhwIDVq1GDnzp2cO3eO4OBgmjZt+tnfTYECBVK91tfX/+rxhISEz8YiCLldpgbS9+jRg9evX+Pn50fPnj2/eN7WrVvR09Pj77//pmPHjtSqVYuqVauq9UyZTJbucyMiIhg8eDCVKlXizZs3jBo1Sq1nqkNXVxcfHx8uX75MVFQUW7Zs4cmTJzRp0oS4uLivXmtpaQl8jP/fnj9/ntL++em8Fy9epDnv3+3Cn3zu57dx40Y8PDxYtmwZLVq0oEaNGlStWpWYmJivv0lB+MZlKoEWKVKE0aNH07JlS7p37/7F82QyGbq6uujo6KQci4+PZ8OGDWnONTAwyFCJ9EuUSiWdO3dGJpOxf/9+ZsyYkdJhk9PMzc3p0KEDgwcPJioqirCwMOB/HWT/fr8NGjQAPia2fwoODub27ds0bNgQgBo1amBgYMC2bdtSnXfu3DkeP36c7vhkMlmazrpr165x9uzZdN9DEL5FavXC/9PMmTP/85wWLVowb948unTpQr9+/Xjz5g2///57mj9agPLly7N161a2bdtGiRIlMDQ0zFC75ScTJ07k5MmTHDp0CBsbG0aOHMnx48fp3bs3lStXxsHBIcP3zIiWLVvi4uJC1apVKVSoEI8fP8bX1xc7OztKly4NkPK+FixYQPfu3dHT08PJyQknJyf69evHokWLkMvlNGvWLKUXvlixYowYMQL4WGX28fFhxowZWFhY0LZtW54+fcrkyZMpXLhwqnbKr/Hy8uK3335j4sSJ1KtXj7t37zJlyhQcHBzEOFFB+IpMJ9D0aNCgAatXr2bWrFm0bNmSIkWK0LdvX6ysrOjdu3eqcydPnkxERAR9+/YlJiYGOzu7lBJbegUGBjJjxgx+/fXXlNIafJyiWblyZTp16sSpU6dS2uiyQ/369dm5cyerVq3i/fv32NjY0LhxY3799Vf09PQA8PDwYOzYsaxbt46VK1eiUqk4duxYSnW6ZMmS+Pv7s2TJEszMzGjatCkzZsxIqboDTJs2DRMTE/z8/FizZg1lypRh2bJljB8/HnNz83TFOn78eOLi4vD392f27NmULVsWPz8/AgICsmx6rCDkRTJJSsegRiFXCQ0NpUyZMkycOJFx48ZpOhxByLNEAs3lrl69ypYtW6hVqxb58+fn7t27zJ49m/fv33Pjxo0v9sYLgpB5OVKFF7KPiYkJFy9exN/fn3fv3mFmZoaHhwfTpk0TyVMQspkogQqCIKhJLKgsCIKgJpFABUEQ1CQSqCAIgppEAhUEQVCTSKCCIAhqEglUEARBTSKBCoIgqEkkUEEQBDWJBCoIgqAmkUAFQRDUJBKoIAiCmkQCFQRBUJNIoIIgCGoSCVQQBEFNIoEKgiCoSSRQQRAENYkEKgiCoCaRQAVBENQkEqggCIKaRAIVBEFQk0iggtZ7//49bdu2RU9PDwcHB2bPnk1ycrKmwxIEkUAF7aVQKBgwYAB2dnbY2tpiYWHB1q1bCQwMxMrKCg8PD06dOqXpMIVvmEiggtZRqVRMmTKFwoUL8/r1a8LDw1myZAlyuZwaNWoQGBjIy5cvadu2LT169MDGxobBgwcTFRWl6dCFb4xIoIJW8ff3p3Dhwhw5coSrV6/yxx9/YGJiwoewSygVcTw6uZP3kaHo6uoybNgwHjx4wMWLF4mJicHJyQkXFxfWr1+PSqXS9FsRvgEySZIkTQchCPv372fAgAGYmZmxadMmypcvD0DC89vE3D5GUuxrKvaYw8HFowDQN7XAwqECBUtWwcAkf8p99uzZw2+//cbDhw9xd3dn+vTpODs7a+Q9CXmfSKCCRl2+fJmuXbsSHx/PqlWraNiwIQCKN4+JuXWExKinKef+M4GmkMkxtXbAsmRlLIo7I5d/rFTFxcUxbdo01q9fj0wmo3fv3owZMwZDQ8Mce29C3icSqKARjx8/pnPnzoSGhjJnzhy6du0KQNL7l8TePkp85L0013w2gf6DjoExFsXLYVnaFRML65Tj165dY9y4cZw9exYnJycmT55M48aNs/5NCd8c0QYq5Kh3797RsmVLqlSpQqtWrYiIiKBr164o49/z7vJuXget+GzyTA9lYhyv7wdzd58ft/ev5OXdCyQrEqlQoQJ///03r169omfPnvz4449YWVnRq1cvIiMjs/gdCt8SkUCFHKFQKOjbty8ODg6UKFGCFy9e8PPPP6NSJPD+5iFeHVlM3JOrSFLWdP7ERz3n6cX93AiYy6OTO4l+/gi5XE7fvn25ffs2N27cQFdXl4oVK+Lk5MSyZctEx5OQYSKBCtlKpVIxYcIEbGxsiI6O5smTJyxYsAA5EHv/FK+OLCL2wTlUynQMjFejtUmVnMS78Bs8PLaBG7sX8vTqMRI/vMfKyooVK1bw4sULli5dyqZNmyhYsCDNmjUjJCQkw88Rvk0igQrZZsWKFdjY2HDy5Elu3rzJ9u3bMTExIS7sMq+PLuH9raMoFfE5Fo8i9i0vb5zg5m5f7h3ZyOvQ6yiVSho2bMipU6eIjIykTp06tGnThqJFizJ27Fji4uJyLD4h9xGdSEKW+/vvvxk0aBAFChRg06ZNlCtXDoCEyLvE3D5K0vtXat33vzqR1KFjYIx58XIU/FfH07179xg3bhxBQUHY29vz66+/0rp16yx99rdIkiRkMpmmw8gyupoOQMg7goOD6datGwqFgvXr1+Ph4QGAIurJxyFJb8I1G+BnKBPjeHM/mDf3gzEqYEsBh/JYOlTC0dGRP/74A0mS2LJlC7169UKpVPLu3TtNh5xrJScn4+LigomJCZMmTcLLyyvXJ1NRAhUyLTQ0lM6dOxMeHs7cuXPp3LkzAEmxr4m9eYT4yLtZ8pzsKIF+jkxHj/xFSlOwpCsXb4fSs2dPChYsSHh4OK9fv8725+dVkiRx7tw5atWqhZmZGZaWlgQFBVGsWDFNh6Y20QYqZIqHhweurq60b9+e58+f07lzZ5QJsbwL2cObY8uzLHnmJEmZxK2Lp6lZuw5dv+/AzJ+HcPbEMXR1RYUtM2QyGZUqVQLg5s2b+Pr6UqRIkUzd88SJE7Rs2RJbW1tkMhm7du36z2uOHz+Oq6srhoaGlChRAj8/P7WfLz4RQqacO3cOU1NTtmzZglPpktR3MuPDo2BUyQpNh6aW+AQFE5YHcPFWGH3auPNDMzcgnqu7F6FMTtJ0eLlebGwsAJaWlrRs2TLT9/vw4QMVK1akZ8+etG/f/j/PDw0NpXnz5vTt25eNGzdy+vRpBg0aRKFChdJ1/b+JBCpkirm5Oc+fPWPtgt8YPWwQb97F0LSmM2O9G2GRzzhrH5aNrU0qlQq/ncfYHhhMw+plCVwyCl1dHZTIiFXIiE1MytbnfytiY2PR1dXFwMAgS+7XrFkzmjVrlu7z/fz8KF68OL6+vgA4Oztz8eJFfv/9d5FABQ1QKXl9bAlNS8ppunAQL9/GMH19IO6DF2FTIB8jOnnQ3K2spqP8qoNnr/P7hgM4FCnEn3OGUMDMFAmITdbhfUIyKd0Eubu/QyvExMRgamqqsc6js2fP4unpmepYkyZN8Pf3JykpCT09vQzdTyRQIVMkVTJ6ivfI9XRJSlZhZZEP32HtAPjr1A3mbj3GmGV78KzmxLhujbA0M9VwxP9zJyyCcUs+9rQvGNWFsiU+tsfFq+S8j1eRrEpdZRcF0MyLjY3F1FRzn4HIyEisra1THbO2tiY5OZnXr19TuHDhDN1PJFAhC0jooERHR0Il00WpkkhWKmlVx4VWdVyIev+B6RsOU3/oEgqZmzKsYz1a1XHJ+GOyqNTy9v0Hxi7+g4dPX+LTtQnNalUAIEmS8y5BQiG2C8k2mk6gQJrS76cahjqlYpFAhcz554dOJkOOErkc9ORylMhJSlZRIL8Jvw9uDYNbc+D8beZtDWL8ir00dC3NuG6NsbLIlyOhJicrmbV+H4HnbvJdo6os/dkbuVxOsiQjRgFxiq8nzlw+ZFErxMTEkC9fzvy+P8fGxibNAjIvX75EV1cXS0vLDN9PJFAhm3y+VNq0hjNNazjzNiaOWRuP0Gj4MgrkN+bH9nVp51HxP++qUqlS1vzMiC0Hz7Ey4DhVytixb+EIjA0NUEnwPklObIISifTUz0UGzSxNl0Dd3NzYs2dPqmOHDh2iatWqGW7/BJFAhez2z1Kp7P9LpUoVFvmMmTmwJTMHtuRw8F1+33KMCf778ahcil+6e2JjmT/trQCVSiIj+fPCjYdMWrEbi3zGrJvch2LWH0sZcUo57+OVKKWMVNdFI2hmZXUCjY2N5cGDBymvQ0NDCQkJoUCBAhQvXpyxY8fy7Nkz1q9fD8CAAQNYvHgxPj4+9O3bl7Nnz+Lv78+WLVvUer5IoELOkX2+VNqomhONqjkRHRvPnM1HaTLSDzMTIwa3q8N39Ssil8t5+vIdMXEJrP37FD286qCrq/PVRz17+ZafFm7n7fsP/Nq3FW7lSwGQqJITnSiRpFY7pyiBZlZWV+EvXrxI/fr1U177+PgA0L17d9auXUtERATh4f+bQuzg4MC+ffsYMWIES5YswdbWloULF6o1hAnEVE4hk2wKFeD2uhHq30CSpZRK/7kWaNDl+8zZfIywyCiMDPSIjU+kQ4Oq3Hkcyc1HzynjUJhh3zeijL1tqtt9Ggh/6fbHgfBdmroBkCzJeK+QEf8f7Zxf0+uXxbx6/Ubt6wX45ZdfePXqFcuXL9d0KFlClECFTMpkqSxVqVQHpUpGsjIZ90olOXfjMQ+evcLEKB+KZCVHLt6mp1dtFo/qzIb9Zxnluw2VSqJ1vcp0b1mb1btPsj0wmEbVy3Jo8ceB8CoJYpLlxCaInnVtoOk20KwmEqigHWQy5KiQy+GPo1eZsPogpYpasdd3GAXyf/yDu3DzEQu3HcV362GqlbXH/5eeJCoU/Lz4T1YGHMfE2IBpA9tRp7ITEhIf/n8gvCpD7Zxfj1HInNjY2EzPf9cmIoEKWiP4djj9f/8TXV0d1v3ajTJ2NiiRo5RkKJOTqV6uBBunlCAuQYHfziC6T1pFfGISluambJ7alyt3wpm9/gC/+f9N/ZoV6disLgb6Ge9Z/RyVSiVG0mcBTQ9jymoigQoa9+x1NL1mbCf8xTsm9mmOZ43/Tf3UQYWODCS9jz34yUolxob6+Pzgic8PntTrP5u/5/0IgJNDMZo3rM3Dpy9ZtTOQnmN9KWZTEO829XEpbZ+pGJNVqly/dqU2EFV4QcgiCYokBs8P4Ojlh/Rp6cbA9vW+eK5MJqGLEl0dPpZKVaBUKpHJ+NjOmSQnNvFjVb2ItSUTB32PSqVi3/GLLN7wN/GJCtyrudDZywNjQ/0Mx6ru+FMhNZFABSEVWYaTi0qlYtamY6z4+zwNq5bh7MpR6Oul86Mo+/9SqQ5IcjkSMiI/SEifaeeUy+V41a+OV/3qRLx6y+qdh+n7ywIKFyrAD608qOxcMt0xJyeLBJoVRBVeEP5BriMnKVmJgX76ksvOoGuMW3kAB1tLDswfQqFMTOOUyT62SaZnJF7hQhaMH/AdKpWKw2evsnL7AWI/JFCrSlm8W9XHxNjwq9cnJycjl4sqfGaJEqgg/INcLichKfk/O2su3XtKv9k7kclkrPi5C+VLaaYnVi6X41m7Mp61K/Pq7XtW7zxM/wmLKFTAjC5eHlSr4PjZ65KVKuQyUQLNLJFABeEfdHTkJCqSweTz3494855eM7fz6HkUv/ZqRvNaaqzClE0KWeRnTJ+PS+8dPXeddbuPsHDjHmpUcKRbm4bkN/3fgtDJyUpkogqfaSKBCsI/6Mh1SExK2/6YoEhi2ILdHLp4n54tarJhUs9sakPMmqFFDWqWp0HN8ryNjmX1n0cYNHkpBcxM6dTcndpVyqIUnUiZJkkSsbGxog1UED7R0dEhUaFMea1Sqfh963GW7T6HR+XSnF4xEsMsGouZEyzMTBnZ8+P+7ycv3WLz3ydYtmUfTiWKimFMmRQXF4ckSaIEKgifyHX+VwLddeIGP6/YR3HrAuybNwjrAmlXVMpN6rqWpa5rWc6G3GH6ip3Url1L0yHlas+ePQMQCVQQPtHV0eHawwh6zNiOUqVi2ZjOVCxVNOcCyMbJQe/exzJ1xZ+8ehfL7r/+ytDmZUJqYWFhlC9fHplMRmBgIE2aNMkT20SLRh0hUxIUCoYt3E3vVrU4vGhYzibPbKJSqVi65QD9Ji+n9XddeB4RKZJnJtnb27Njxw4MDAwYMGAA5cqV+zg9NpOWLl2Kg4MDhoaGuLq6cvLkyS+eGxQUhEwmS/N1584dtZ+f+/8LEDTq6LHj/DRqFLM3H2Rn0DV+7tqQyk7Fcy6ALG6WPHr+Oiv/OEz16tV58vQZ+fPn7mYIbVKgQAGsrKx49OgRd+7cyXSn3LZt2xg+fDhLly6ldu3aLF++nGbNmnHr1i2KF//yZ/Du3bupfq+FChVSOwaRQIVMsbOzY9uOHahUKpYtW8bo2TNJiP/A940qM6D1fy98rC3Cn79i+sqd6OgbcTToOJUqVdJ0SHnOpx54HR0dypUrl+n7zZs3j969e9OnTx8AfH19OXjwIMuWLWPGjBlfvM7Kygpzc/NMPx9EFV7IInK5nMGDBxP6+AmHj53k5kuo2W8efWZs5tGzV5oO74sSEhX85reDMb6b+GXyNB48ChXJM5t82hM+KygUCi5dupRmj3dPT0/OnDnz1WsrV65M4cKFadiwIceOHctUHKIEKmS5cuXKcejwERQKBVOnTqX7dD/0daCPVw06NXLVmvGU2w6cYmfgedp36EDQ+ZV5olNDm2XlIPrXr1+jVCo/u8f7v3fd/KRw4cKsWLECV1dXEhMT2bBhAw0bNiQoKAh3d3e14hCfGCHb6OvrM2XKFKZMmcKJEycYPdKHeVvnUbdSScZ6N8rUPPjMCLkdyrz1eyhmZ8/tO3extbX974uETMuOWUif2+P9S+N1nZyccHJySnnt5ubGkydP+P3339VOoNpRFBDyPHd3d84HXyTsyVOKlK1JyzH+tBi1nMALt3MshqjoWEbOWYvv5gNs3LKNi5cui+SZg7JyJaaCBQuio6Pz2T3e/10q/ZqaNWty//59teMQCVTIUfnz52fpsmW8ehPFtN8Xsuivy9TsO5cpq/cTG5+YLc9UKlUs2rSPAVOW07FrLyIiX9C4ceNseZbwZVlZAtXX18fV1ZXAwMBUxwMDA6lVK/0THq5cuULhwoXVjkNU4QWNad++Pe3bt+f58+f4+AzHY8giSthaMuaHhriWyZqhUIFnQ1j951Fq1a7Ds+cReWoWTG6T1VV4Hx8fvL29qVq1Km5ubqxYsYLw8HAGDBgAkGZPeF9fX+zt7SlXrhwKhYKNGzeyc+dOdu7cqXYMIoEKGmdra8vWrdtRqVT4+fkxZtYMEuI+0KlhJQa0qYue3leGQn1hJlLosxdMX/knBkamnDh1BhcX7VkF6lsVExNDwYIFs+x+nTp14s2bN0yZMoWIiAhcXFzYt28fdnZ2AGn2hFcoFIwaNYpnz55hZGREuXLl2Lt3L82bN1c7BrEvvKCVbt++zYhhQzl//jwVSxVhbLfGlCqadsBz9d6z2TxnVMrruAQFs1cHcO9xJPPm+9K9e/ecDDtbJSUloVKpMDAw0HQoavnuu+9wc3PDx8dH06FkGdEGKmglZ2dnDhw6zItXb/Dw6kTPGdtpMHQxmw8Ff3EK4Oa/T9Bj/CIqVK/Lq9dv8lTy/OWXXzA2NsLUxISiRYqwY8cOTYeUYXltLVAQCVTQcvr6+kyaPJnnkS/YtP1P9oZEUqPPPEYs+JMXUe8BuHzrId4/L+BORAx3791n+fIVWjPWNLNCQkKwsDBnge88Vv/Sg4vrxtOwUnF6dvfGwECfli1bEh0drekw0yUvJlBRhRdyndjYWMaOGcPWrVuIevcOG2trNmzcRIMGDTQdWpZRKpXU9/DgzNmz/NCkOqO9m6Y551ZoBBNX7ObBk5cULGjJjJmz6NGjR84Hm06VKlXit99+o2XLlpoOJcuIBCrkasHBwVSrVk3TYWQpX19ffvppNMWtLVk/sSf5TY2+er5SqWTJH8fYcigYRbISj3oebNy0KVOLZGSHUqVKsXLlSurXr6/pULKMSKCCoCUePnxI7Vq1eB/9jtlD2+PhWibD93j09CXjlu3ibngkFhYW/PbbVPr3758N0WacjY0Ne/bsyVP/4eWNhiIBhUJBo0YN0dPTxdTEhPHjx2s6JCGdlEolrVu1wsnJiRpOtlxYO16t5AlQoqgVW6f148qGCXSsV56fRo1AX1+P+h71UlaE15S8tic8iASaJwwfPhwTExPC7t7gyGIfJvRqxoqli9DX06NB/fq8eqW9qyF96zZv3oyJiTGXzp8icNEIpg1qm2X3HtDeg9Mrf2b37EG8jQjDwd4OS8sCzJs3L8uekV5KpZK4uDjRiSRoD39/f4YOGYKhvg5LRneh/L9Wg3/6MoqfFu3kVmgEtoUL4796tZjCqCVevXpF9WrVeP78Ob/2bkGbepVz5Llr9pxm9Z7TfIhPpFq1amzctAkHB4dsf25MTAz58+fn7du3WbYWpzYQCTQXOnfuHF4tWhD3IZaxPZrT1uPrf3xKpZJpa/ay59Q1dHR0GfrjMKZOnYqOTu5Y7Div6dWrF+vXr6dOxVIs8Omkkd9DxOt3jF+2i5B7TzAxMWbkqNH88ssv2fe8iAhsbW1JSkrKU8sGigSai7x69Yq6devw8OFDunhWY7R3xvfpOXDuOrPWHyQ6Jp7atWuxfccfWtdbm1cdPHiQdu3aYqSvy9pfe2Bvm3XTGjNjy8Hz+P15gvdx8VSqWIn1Gzbg7Oycpc+4d+8eFStWJD4+Pkvvq2kigeYCSqWSFi1acPjwYaqXc2DxyM7o62fuf/Fnr6IYvXAnt0MjsLGxYZW/P02aNMmiiIV/io2NpWaNGty7d5cfOzWkh1dtTYf0Wa/exjB+WQAX7zzGyNCQH4cNZ9KkSVlSQr58+TJNmjTJc+3xIoFquZEjR7Jo4UKKWJmz+pceWb4IsVKpZMa6few+cQ0dHR0GDxnK9OnTRfU+i4wZM4Z58+ZSoVQxVo71zvR/fDnlz2OXWLTjGO9i4nBxcWHduvVUqFBB7fudOHGC7t27ExoamoVRap5IoFpq48aN9OvXFwM9HRaP/J6Kjtm/02Xg+ZvMWHeAtzEfqF2rFjv+2Cmq92q6cOECno0bISmT8fu5a5oOvtwiOjaOcUsDOHfjEfoGBvTvP4BZs2Zl6D/YS5cuMXDgQF6+fMmDBw9EG6iQfS5dukTTpk2IjYlhjHcTOjSsmuMxRLx+x6hFf3Dr4XOsbaxZsWJlppb8+pYoFArq1XPnYvBFurdwY3jnvDPqYe+pa8zfepiXUe9ZtmxZugfoR0ZGMnToUP766y8sLS0ZOXIkI0eOzOZoc4YYB6olXr16RbmyZalZowaNq5QkeO14jSRPgMIFzdk0uQ8X143HvVxR2rdri4mJMaNHj0apVGokptxg7ty5mJqYEBURzsmVY/JU8gSwtsxHzIcErKwK4eXlle7rbGxsaNq0Ke7u7qxevRobG5tMx7J06VIcHBwwNDTE1dWVkydPfvX848eP4+rqiqGhISVKlMDPzy/TMYAogWqcUqmkdevWHDhwgKrOdiwd/YNWtpP9s3pfq6Yb23bsyJI/hLzg3r171K5di7jYWHxHdMStQilNh5SllEolfadv4Mq9cCZOnKTWcKcFCxZw4sSJTK3+/sm2bdvw9vZm6dKl1K5dm+XLl7Nq1Spu3bpF8eJpm7pCQ0NxcXGhb9++9O/fn9OnTzNo0CC2bNlC+/btMxWLSKAaNHbsWOb+/juFC5mz+pduWBcw03RI/ynydTSjFv3BzYfPsLa2ZsVKUb0vUqQIkZERDO/UiJ6t6mg6nCy1/8x1fvHbhYODAxcvXVZ7JtHUqVO5f/8+69aty3RMNWrUoEqVKixbtizlmLOzM23atGHGjBlpzh8zZgx//fUXt2//bwPDAQMGcPXqVc6ePZupWEQVXgO2bduGiYkxyxYvZMW4ruydNzRXJE8Am4JmbJzc+2P13qUoHdq1xcTYmJEjR36z1ftnz56xYMFC1h68SBXv3+gzbR1vomM1HVamxMYn0uanpfyyfDcrV/lz5+69TE3DzKq1QBUKBZcuXcLT0zPVcU9PT86cOfPZa86ePZvm/CZNmnDx4kWSkpIyFY9IoDno2rVr2Fhb0b2bNz7fN+DUyjFUdc7+aXTZQUdHh3E9W3Bh7XimD2jFxrWrMDQ0oEEeWqosI4YMGcKbN1HcvnMHjC1pNGQeDQbNZe+pa5oOLcPW/HWKun1nYVXUgbi4eLp165bpe2ZVAn39+jVKpTLN1sXW1tZptjj+JDIy8rPnJycn8/r160zFIxJoDoiKiqJC+fK4VqmCe3k7Lq77hU6Nq2s6rCzTsHpZfu3VAl0dOdeuXfvilhvfgpIlS3Lu/AUSEhLp3X8QU9cdoGr3qYxauJ14hULT4X3Vi6hoGg6eh9/uUxw8dIgzZ85m2XjgrF6JSSaTpXotSVKaY/91/ueOZ5RIoNlIqVTSpk0brKysMFDFcn71OCb0yTurccPHP7pmwxcycuEfzJg5m9dv3uSZ7TQyQ0dHhxkzZhATE8uJk6cIi0rCrddMmo9YyIWb2jeYfPqavTT50Rf3+o348CEuy1f3z6oSaMGCBdHR0UlT2nz58mWaUuYnNjY2nz1fV1cXS0vLTMWjfd29eURycjJGRkaYGumx3/dHChc013RIWUqpVDLCdzsnrtzHy8uLnTt3itlLX1C9enXu3LmLQqGgb9++DPl9KzIk2tSryE/eTTX6c7v7OIJev61DV9+A69dvZPkc+E+yKoHq6+vj6upKYGAgbdv+b+m/wMBAWrdu/dlr3Nzc2LNnT6pjhw4domrVqujp6WUqHlFUyCa6urr8+OOPJCZJtPlpKSt3ndB0SFlmw/4zVO85ncdvEnj69Cm7du0SyTMd9PX1WbduHXHx8WzZtp3jN55Stfs0vhvrx8OnL3M8nmHzttJp/Ep69e3Pm6i32ZY8IWur8D4+PqxatYrVq1d/3P56xAjCw8MZMGAA8HF0yz/bbQcMGMDjx4/x8fHh9u3brF69Gn9/f0aNGvWlR6SbGMaUAzZu3MiwYT8SExNDw6plmDagrVaO9fwvtx49o/+sTSQlS2zdti1Dg6mFz4uOjqZL584cPnwYQ31dereqQ69sHgp1KuQ+I3y3U7BgIYIvXsyR8bwVKlRgxowZtGjRIkvut3TpUmbPnk1ERAQuLi7Mnz8fd3d3AHr06EFYWBhBQUEp5x8/fpwRI0Zw8+ZNbG1tGTNmTErCzQyRQHNQSEgInTp+x8NHoZSxs2H+iI65omofr1DQY/Ja7oVHMmTIUObPn6/pkPKkxYsXM2niBN6/f09lp+LMHNw+SxePUSiS6fHbGu6ERTJ7zhyGDx+eZff+LyVKlGDNmjXUq1cvx56ZE0QC1YDo6GjatW3LiZMnKGhmypR+rbR29sr0NXvZceQSrq5VOBZ0HCOjr+8QKWReaGgonTt/z6VLlzDPZ8zIzo3wqlspU/f889glpq7eh7OzM+fOn8/x36OVlRX79+/H1dU1R5+b3UQC1SClUsmwYcPwX7UKHbmM/m3qas1MlsDzNxnvtwsT03wcOXI0U0uZCepRKpVMmDCBhQsXoEhU4OHqyNSBbTDS10/3Pd7HxvP9ryt5+TaGTZs2Z3rqorqMjIy4evUqjo6OGnl+dhEJVEv4+/szetRIPnz4QOPqZZnSr7VG2kkjXr+jx5S1vIn+wHxfXwYOHJjjMQhpXbhwge7du3H//gNsC5kzsbcXNVxKfPWaJTuOsmr3KerX92D/gYMa6+hLTk5GT0+PZ8+eYWtrq5EYsotIoFrmwoULdPn+e8LCwylXwpZ5w7/LkWmeSqWSH+dt5fTVh7Rt04at27aJnnUtpFAo6NevH9u2/f9QKPdKjOmWeijU05dRdJ3gj0IJhwIDqVmzpgYj/thkZW5uTnR0NPnz59doLFlNJFAtFRUVRbu2bTh95gyFLPIxtX8bqpfLnmmfa/acZtGOo9gVL86Zs+fEIsq5xF9//cXgQYOIiIykdDErZgxqy7q9Z9lz6hpdu3Zl7dq1mg4RgKdPn1KsWDGSk5Pz3H/KIoFqOaVSyaBBg1i3bi16OnIGdaiHd7NaWXLvq/fDGTx7C0pJxh87d4o9kXKp6OhounTpwpHDh8mXPx8XLgTnyFbF6XXnzh1cXV358OGDpkPJciKB5iLLly9nzJifiI+Lo7lbeSb1a6nW/+ix8Yn0nLKGB09f4uMzklmzZmVDtILw0cWLF2nRogUvXrzQdChZTsxEykX69+/Pu3fRHD9xkqvhUVTtPg3vSf68ehuT7ntMWbWHOn1nYVHYjg8f4vJk8lQqld/s0nraKKumcWojkUBzoZo1a/IoNIwnT59iYlkUz6HzaTrMl8t3Hn/xmgNnr1O9xzSOXwsjJCSEM2fOop+B4TC5xdzff8fI0JD8+Uz5oXPnTC9XJmReVq/EpE1y33xCIYWNjQ2nTp/+uOVC3770m7ERfT0dfuzYgO89Py6X9/RlFD2nrONtbByLFi2mb9++Go46e1y7do3WrbzQk6koV7Io7hVL8OLNQxxLlaBEiRL4LlxMnTraMcb2W5OXS6CiDTSPWbRoEb/+Mp6EhASKWRcg9PlrvvvuO7Zs2aLp0LKFQqHg++87cezIEQZ18qR+dRcmLN5C3QoOdGvuhiRJ/Bl0Bf89Z0hGh+EjPu4IKZbcyxkKhYI1a9YQEBDAgQMHNB1OlhOfojxm6NChvIt+z6HAw5SrUpOXL1/m2eTp7++PtVUhYl+EsWXWcOpXdwHgnyUCmUxG+/pV2DdvCIuGteGP9cuxtDCn8/ff8/Jlzq+A9K1ZvXo148aN49mzZ6ITScg93N3d2bVrFwUKFNB0KFkuNDSUMk6OTJkwnrkjvfmpZ2t0dVN/lD+30riTXWFWj/fmoO9geBuKs2MpXCtX5MSJvLPUoLbp3bs3jRs3JioqiuLFizN37twsf8bbt2/x9vbGzMwMMzMzvL29effu3Vev6dGjBzKZLNWXOhMORAIVcg2VSkWvXj2pVLECntUc8Z88gOKFC2b4PiZGhvzSszkn/EbStro93t93oEhhG2bPnv1Nb0eSHfT09ChevDjt2rXj5s2b2bKDa5cuXQgJCeHAgQMcOHCAkJAQvL29//O6pk2bEhERkfK1b9++DD9bdCIJuUJAQAB9+/SmjJ0Nm2f+iIH+V1YSz0Czftv6VWhbvwp3H0cya8MKZkyfSpOmTVm4cDFWVlZZELkQGxuLubk5pUpl/Ypjt2/f5sCBA5w7d44aNWoAsHLlStzc3Lh79y5OTk5fvNbAwCDTa6GKEqig1SIjI6lSuRKD+vdhUv/2TBrU8evJ8//JM7hXmJOdDavHe3PIdwjyd+E4O5WmSqUKqRblFdQTExOTbb3wZ8+exczMLCV5wsdhfmZmZl/c5viToKAgrKyscHR0pG/fvmq1iYsEKmgllUrFqJEjcSpdikoOBdkwfShlShTJ9ucaGxowvkczTizzob1bSXp06YitjTUzZ84U1Xs1ZecwpsjIyM/WFKysrL64zTFAs2bN2LRpE0ePHmXu3LkEBwfToEEDEhMTM/R8kUAFrXP06FFsC9twZP9u1k0bQpfmGRu/mVXj8trUq8TeeYNZPKI9uzb7Y2lhTqeO3331D1NIS50EOmnSpDSdPP/+unjxIvD5DsP/2ua4U6dOtGjRAhcXF1q2bMn+/fu5d+8ee/fuzVCcog1U0Brv3r2jdauW3Lp5g596tKSy89fXu/yazO73/U9Odtb4j+tKXEIiC7Ydo5yz08ce5fkLsnz737xInZlIQ4YM4fvvv//qOfb29ly7du2zw6NevXr1xW2OP6dw4cLY2dlx//79DMUpEqigFaZNm8bsWTNpUqsi42cM1cqB7saGBozt3pSx3Zuy+0QIvby/R6GUMXTYcMaMGaOVMWsDdUqgBQsWpGDB/x5h4ebmRnR0NBcuXKB69Y+z786fP090dDS1aqV/1bI3b97w5MkTChcunKE4xW9c0KiLFy9SvFgRNq5ezvIJfenXoVGmE1FOTK5r7V6JvXMHs2xke/ZsXYOlhTkdv+sgqvefkZ1toM7OzjRt2pS+ffty7tw5zp07R9++ffHy8krVA1+mTBkCAgJS4hk1ahRnz55N2b2zZcuWFCxYMNVe8+khEqigEQkJCbT0aoFnowb09KrNorG9KGiedauVZ2UV/mtKFbNm5dgfOLRgKAYfnlPO2YlKFcpz5MiRHHl+bpDdi4ls2rSJ8uXL4+npiaenJxUqVGDDhg2pzrl79y7R0dEA6OjocP36dVq3bo2joyPdu3fH0dGRs2fPZjhOMRdeyHFLly5l3NifqVXRkR+7NE8ziyizxi/cROOqjnT+/wVVctqek1dZvvs08UkqBg4awsSJEzUSh7YwMDDg5s2b2TIOVNNEAhVyzN27d/Fq0ZzkhDgmDfqOIlbZM8103IJNeFbTXAIFuPHwGYPnbCY2XkFCokJjcWiaQqHAwMCAiIiITA9a10aiCi9ku+TkZLp2/YEa1arSslY5Vk7qn23J85OcqsL/W3Kykp8W/cGg2ZtYOKw1Zvnz5jJu6fVpG4+8upydSKBCttq6dSuWBQrw9O41Ns8cRnP3KpoOKducuHKPBoPnoq8DdzaMolmNMpoOSeNiYmKQyWQYGxtrOpRsIYYxCdnKb9kykpMV3H70hMPnrtLc3VXTIWW5uIREfpy7lbCIN2yd+ANVyxTTdEhaIzY2FhMTkzw7xEskUCFb5c+fj07N6uJcshgrtx/EP+Aojd0q0KtNQ/T1s+/jl1M1+J1HLzFvy2G+b1CRv2d0/0yi0ExTgrbIy6vRg0igQjbT0dVFqYqnTIlizP25D2/evWf5tgN0Gj2XCo52DP2heZYOX8opr9/FMHDWJhRJSRyZ348StpaaDkkr5eX9kEAkUCGb6erqokz83yIclub5Gde/IwpFMhv3HKP/5OXYWJozuHNTypbMmqpvdg8sWbYziI37zzH8uzoM+849W5+V24kSqCBkgq6OLsmf2WJYX1+XXu0b06t9Yw6evMS0FTuRyWR0a1kPz9qV1H6eob4uunJQIUcp00WOElkWJdRHz14xeM5mCuY35uLKYViamXz1fLF6k0iggpApevr6xCu/nsCa1HWlSV1Xbj4IZ9X2A6zYGUiTWpXo3qY++rrp+4jqyOWYGsjRkX1K1hLJyuSP39PRRQcVMkm9hKZSqZi2Zi8Hz91iZv9mdGxQKV3XJSUr0dHRUeuZeYVIoIKQCbq6uihVaUugn1OuVHHmj+vHq6holm/bT6eRc6lcxoEhXZpTwOzzf4QSYGqgi4GOClByO/Q5Nx48JfT5KyzNTKnnWgalMhklIJfroCMHeTrjAbh05zGjFu6gQgkbbqwbibGhfrqvjVck59ne5/QSbaCCkAm6uroo/6ME+m+FCpjxy8DvUSiSWbfrMH0nLsXWqgCDv2+WalFlPV05Jnoy5DIlyclKfl32JxduPmJCv9boyOUs3HqY6av/pqNndXq2/LimqEoFcpkMHbkcufTlRKpITmbUgj+49uAJK0a1x6NyxqchJiQmoytKoKIEKgjq0tPTQ5WBEt8/6evr0rdjU3p38OTAyctM8duBjo6cnm3q07peZfTkSkDi6IVbTFu9h2rlSnBw8Sh0dT8mLY+qZQh99opZa/exce8Z6lZ2ZKR3U8xMjVEplciQoSPXQS5L3U568NxNpq7eS9PqjtzZMFrtUmSiIumbrsKvWrWKLVu2ULp0aU2Hkm1EAhWy1ccqfOY6ceRyOc3rVaV5varceRDOih0H8Nt+kGa1y3PtXjiv331g8RhvnB1s01zrUKQQfuO7ExuXwPxNh2jjs4iSRQvxU/fmONrZkKz6/3ZSuS6xHz7w45yNvHwbw67p3SlfImNrQ/5bQlLyN5tAVSoVd+7c4f79+zx8+BAPDw+mT5+eoTU6c4Nvu4FGyHYfE2jme6N15HLyG+pRq7w9a6cMoHmdSmw7eIF74S+pULoo1gW+PpbU1NiQX/u24ojfaOq5luHHOZtoM3IhgeduALBx3ymaD5tP7fL2hKwZlenkCZCgSEZH99tLoGFhYTRo0ICAgABOnjzJixcvaNGiRZa3B0+bNo1atWphbGyMubl5uq6RJIlJkyZha2uLkZERHh4e3Lx5U+0YRAlUyFb6+vooleonUEkCEwM9DOVKkCkJe/aKMQs2Y2xowM65wzE1MmTpjsN0+GkpdoUtGdO9GWU+UxL9RC6X492iFt4tanH22n1mr9vPuCU7sTA1InBef+wKW5KsVCH71E6Kes0PAIlJyejqfBt/YnFxcRgZGbF27VqGDx9O586d+fvvv1PaP0ePHp3lz1QoFHz33Xe4ubnh7++frmtmz57NvHnzWLt2LY6OjkydOpXGjRtz9+5dtTq7vo3frqAxurq6qNQch6mro4Opvgw5SlQqFXPW/E3QpVsM/b4pzetWSjnPx7s5w39oyp9HLjBi3lb09XQZ1KE+TWqV/+r9L94K411MHMM7unPl3jM8Ry6nXqVSTOvXnELmpiQrlcj4uACvHBUZ3a4uQZGMbjqHYeVmiYmJ2NnZYWBgQHx8PJs3b6ZFixbZ/tzJkycDsHbt2nSdL0kSvr6+jB8/nnbt2gGwbt06rK2t2bx5M/37989wDHn/tytolK6uLio12kDzGeqhJ/vYSXThxkN+W/EnZRxsCZg/EsPP7Asvl8vp0LgmHRrXJPjmQxZvOcTvGw/QvkFV+rRxT+lYArgTGsGo+VspZmXGhZUjMDc1AiAuQcFvaw/hPngRDoUtmdavOZUdi6ZMBNDR0UEHCUhfiTrxG6nCHzhwAJVKhbGxMTExMUyYMIGGDRtiaGio6dBSCQ0NJTIyEk9Pz5RjBgYG1KtXjzNnzogEKmifjwk0/VV4Az1djHUlZCiJS0hk7MKthD17xW+Dv6OSk3267lGtXEnWTR3IsxdvmLdxP40GzaFOxdL4dG3Cgi2BnA65z++DW9GiVtlU1xkb6jNjgBfT+jVn3YFg+szcho6OnFGd69OxQSWUSuXH8aQyOTpyGbL/qN4nJiWjp5s22ecV0dHRDB8+nF27drFkyRI6d+5MXFwcQUFBWpc8gZT9qv69W6e1tTWPHz9W656iE0nIVnp6eunqRJLL5OQ31MVEV4UMiYBjwbT3mY+9bSEC5vukO3n+UxFrS+aO7MrOuSPQN9Cn+Y/ziY+P5+qaUWmSZ6pY5HJ6Nq/BpdUjWTCsDSv+Oks575lMWXMQhSIZlaQiSakkWSVDxZdLmIlJyjxbhT927BgVKlTg2bNnXL9+nS5duiCTyTAxMclU9T0j+8Gr69+Lbf/XHvJfkzd/u4LW+K8qvCSBsYEeRjpKQEXEq7f85LsZlUpi1cS+FLHO/CpHxoYGjO7ekos3HjGzf4sMLaPn5uLAYd+BPHv1jrHL91K+x2xqudgzvZ8XhQvmR/WV6n1iUjJ6enmrBBofH8/48eNZsWIFs2bNYuDAgVnau57e/eDV8WlLkcjIyFTbF798+TJDe8j/k0igQrbS19f/4jjQf3cSLdkWyL6TV+jdrj4dGtXI8lgkJORy9UoaRQqZs/6XH0hQJDFzwxEaDV+KbSEzfuvTjJrl7P9XvZfL0ZGBDBUKRTK6eagKf+nSJbp164apqSmXL1/G0dExy5+R3v3g1eHg4ICNjQ2BgYFUrlwZ+NiTf/z4cWbNmqXWPUUVPgM2bNhAhw4duHz5sqZDyTX09PRQfWYRDxNDPfLrS8hRcf1BOO1Hzufe4wh2/D48W5InfCztZnavJEN9PSb1bsrNjT/Tq0UNfpz/J1V7z2X9/mBUKhUqlYokpYpklZyEZBV6n+nwym2Sk5P57bffqFu3Lp07d+b06dPZkjwzKjw8nJCQEMLDw1EqlYSEhBASEkJsbGzKOf/cD14mkzF8+HCmT59OQEAAN27coEePHhgbG9OlSxe1YhAl0AyoX78+ly5dom7duri7uzNu3Djq1q2r6bC02r+r8Pq6upjofewkSkxKYtLSP7jx4AnjerfBrVJ2/1FKyLNwqfrOjarQuVEVLt59wq8r9jFz4xHa1ivP+G6NyWdeAKzLov/ifpY9TxPu3r1Lt27diImJ4eTJk7i6as+WLBMmTGDdunUprz+VKo8dO4aHhweQej94gJ9++on4+HgGDRrE27dvqVGjBocOHVJ7wRNRAs2AokWL4uvrS2hoKFWqVMHLywt3d3cOHDiQ7Yv45lYf58Kr/r+TSA9TvY+dRIfOXqPt8HmYGhuxy3dkDiTPjyVQdavwX1PVqRj75/YnaPFgXkTFUqX3fLrNO8jL90m5thNJpVKxePFiXF1dqVOnDpcuXdKq5Akfx39KkpTm61PyhI8dRD169Eh5LZPJmDRpEhERESQkJHD8+HFcXFzUjkEkUDVYWVkxbdo0Hj9+TNOmTfH29qZq1ars3LlTLKL7L3p6esgAc0PQlSl5Ex1D70nLWfXnMZaM68H4vm1ydL54dm53XNi2CH8E7OLF6ygqVKzEwoULc+Xn4enTpzRp0oQ5c+bw999/M3fuXIyMjDQdllYSCTQTzM3NGTduHGFhYXTr1o1hw4bh4uLC+vXrSUpK0nR4WkFPTw9jcyvsK9dn/d4z/DB2Ce6uzmyfMwyHIur1fKpLktTvRPoaGWBYvDIFPAZiYFWKI0eO4O/vzw8//MCOHTuy/HnZRZIkNm3aRPny5SlatCjXr19PVZoT0hIJNAuYmJgwbNgwHj58iI+PD1OmTMHR0ZFly5aRkJCg6fA0Sl9fn6i3b6nTujtXwt5y/ujfDOzaVmPxyLN4l0wdY3PMa3bFrKIXSUqJFi1a0Lt3b/766y/Wr1+faxZUfvPmDR07dmTEiBGsWbOGNWvWkD9/7tvsL6fljt9uLmFgYECfPn24c+cO06dPZ+nSpZQoUYK5c+em6hn8llhYWHD37l0aNWrEhQsXKFujIZXbDKFs/U6YWRfP0VgkQJZFJVAZMozsq1Kg3gD0Cznw119/UaRIEaytrXn69Clubm5Z8pycsHfvXlxcXEhKSuLGjRu0adNG0yHlGiKBZgNdXV06d+7M1atX8fPzY/v27djZ2TFlyhSioqI0HV6Oqlu3LidPnuTixYtYW1szZcoUVCoVFsXL4NK0JxWa96Zgcacs7R3/kqyqwuuYWGBey5v85ZuhSFbi6enJoEGDOHDgAKtXr841pc7Y2Fj69+9Ply5dmDFjBgEBAVhZWWk6rFwld/ymcym5XE6rVq04d+4c27dvJygoCDs7O8aMGZMyL/dbULt2ba5cucKZM2c4efIkhQoVon///nz48IF8hYriVP97KrUZjI1jFXSyefm3zFThZcgwcqhOAfcB6Fva8ccff1CkSBFKlixJeHg4VatWzcJIs9fp06epWLEi9+7d49q1a/To0SNbO9jyKpFAc4BMJqNhw4YcPXqUQ4cOcevWLUqUKMGQIUPUXsQgNypZsiSBgYHcv3+f2NhYihYtSuvWrXn+/DlG+S0p6dYS1w4jKFahDnoGxlkfQCaGMemaWmJepwf5XZqQoFDQoEEDfHx8OHLkCMuWLcs1pc7ExER+/vlnPD09GTJkCEeOHMHOzk7TYeVaueO3noe4ubmxZ88ezp49y+vXr3FycqJnz57cvXtX06HlmAIFCrBp0yZevHiBk5MTFSpUoFatWly7dg09Q2OKV26Ia4cROFRrgqGpWZY9V52pnDKZHONStbBw74++RVG2bdtGsWLFcHFxISwsjEqVKmVZfNnt2rVrVK9encDAQIKDgxkxYkSuSfzaSvz0NKRixYps3bqVa9euIZfLqVixIh07duTKlSuaDi3H6OvrM3v2bF6+fEnnzp1p3rw5zs7O7N+/Hx1dXWzL1qRy2x9xcm9HPkubTD9PImNVeN18VpjX7kk+54bExcfj7u7OmDFjOH78OAsXLsw1yUepVDJr1ixq1qxJ69atOXv2LGXLfnk1KiH9cscnIA9zdHTE39+fe/fuYWNjQ+3atWnRogWnT5/WdGg5Ri6XM3ToUJ4+fcrMmTMZNmwYxYsXZ8WKFcjlcgo6lKeCV3/KNe6KhW0J9R8kQXpynkwmx6R0HSzc+6JvYcvGjRspXrw4VatWJSwsLFMzV3Law4cPqVevHv7+/hw7dowpU6agr5/+ve2FrxMJVEsUL16chQsXEhYWRoUKFWjWrBkeHh4cOnTom5om2rp1a+7du8fOnTtZuXIlVlZWjB8/nuTkZMxtS1K2sTeVW/ankIMLcnlGZzBJ/1lq1M1vjUXdPpiWqU9sbCy1atViwoQJnD59mnnz5qn/xnKYJEmsWLGCSpUqUblyZUJCQqhRI3sWafmWiQSqZaysrJgxYwbh4eE0atSILl26UL16dQICAnLltEB1VatWjeDgYIKDg7l8+TJWVlb07NmT9+/fY1zABkf39lRpO5QiZWugq2eQzrvKvphAZXJdTB09sKjbBz0za9asWYO9vT1169bl0aNHODs7Z92by2YRERF4eXkxZcoU/vzzTxYtWoSxcTZ0ygkigWorc3NzfvnlF8LCwujSpQtDhgyhfPnybNy4keTkZE2Hl2Ps7OzYv38/YWFhwMfFdJs1a8bjx48xMDXDvlpTXNsPx75yfQyMTNV6hp65LRbuvTFxqsu7d++oXr0606ZN4/z582qvE6kpO3bswMXFBQsLC65fv07jxo01HVKeJhKoljM1NWXEiBE8evSIYcOGMXHiRBwdHVm+fDmJiYmaDi/H5M+fnzVr1vDy5UuqVKlCtWrVUkqpugaGFKngTuX2wynl5oWxWfpWsZfJdTF1boBFnV7o5bNi+fLllCxZkiZNmvDgwQNKly6dze8q67x9+5auXbsyYMAA/Pz82LhxIxYWFpoOK++ThFwlKSlJ2rhxo1S2bFnJ1tZWmjt3rhQbGytJkiTFxMRoOLqc5efnJxUrVkwqXbq0FBAQkOp7UY9vS9f2+Uun1k5K+bI0M5Ui/5oiRf41RXpzcrWkeP9KkiRJevXqlVSlShWpdOnS0qNHjzTwTjLn0KFDUpEiRaTmzZtLz58/13Q4X3Ts2DHJzs4uQ9cEBARIjx8/zp6AsoBIoLmUUqmUAgICpKpVq0rm5uaSs7Oz1KhRI02HpRF79+6VypQpI9na2koLFy6UlEplyvfevwiX7hzdIp1ZN1myNDORXuydIcU+OJvy/YULF0rm5ubS5MmTNRF6pnz48EEaMmSIZGpqKq1YsUJSqVSaDumr/p1Ajx8/Lnl5eUmFCxeWgDT/CUqSJPXo0UMaM2ZMzgWZQSKB5mIqlUqaN2+eZGRkJFlbW0smJibSmDFjpMjISE2HphFXrlyR3NzcJEtLS2nUqFFSYmJiyvfiol9LhQpYSMkfoiRJkqQXL15IFStWlMqUKaPVJZwvOXfunOTo6CjVrl1bevDggabDSZd/J9B9+/ZJ48ePl3bu3PnFBLpr1y6pTJkyORdkBok20FxMJpPx4sUL9u7dS2RkJAcPHuT69es4ODgwdOhQwsPDNR1ijqpUqRJnzpzh2rVr3Lt3D2tra3744QeioqIwym+JXE8fHWML5s2bh5OTE99//z23b9+mePGcXRUqM5KSkpgwYQL169enV69eHD9+nJIlS2o6LLU0a9aMqVOn0q5duy+e4+npSXh4OPfu3cvByDJA0xlcyHpXrlyRvvvuO8nAwEDq2bOndPfuXU2HpBExMTFS//79JQsLC6lhw4aSubm55OLiIpUrV0569uyZpsPLsJs3b0pVqlSRypcvL129elXT4WTY19pA+UIJVJIkqXXr1tLs2bOzL7BMECXQPKhSpUps376dq1evIkkSFSpUoFOnTly9elXToeUoU1NT/Pz8eP36Ne7u7gD06NGDGzduYGtrq+Ho0k+lUjF//nyqVatG48aNCQ4OpkKFCpoOK8e0bt2a3bt3azqMz9N0BheyX1hYmDR48GDJyMhI8vLyks6cOaPpkIR0CgsLkzw8PKQSJUpIJ0+e1HQ4maJuCfTVq1eSjo6O9Pr16+wLTk2iBPoNsLOzY/HixTx69IiyZcvi6elJgwYNOHz48Dc1TTQ3kSSJtWvXUqFCBRwdHbl69Sp16tTRdFga8ezZM0xNTbVyixGRQL8hNjY2zJo1i/DwcDw8POjUqRM1a9Zk9+7d39Q0UW338uVL2rVrx9ixY9myZQvLly/H1FS9WVZ5we7du2nevDl6enqaDiUNkUC/QRYWFkyYMIHHjx/TsWNHBg4cSMWKFdm8efM3NU1UG+3evRsXFxd0dXW5fv06zZs313RI2SY2NpaQkBBCQkIACA0NJSQkJM3okV27dtG6dWsNRJgOmm5DEDQvPj5eWrZsmWRvby+VLFlSWrFihZSQkKDpsL4p0dHRUs+ePSVzc3Np06ZNWj8oXh3/bgM9duyYxMdlWlN9de/ePeWc8PBwSV9fX4qOjs75gNNBlEAFDA0NGTBgAPfv32fixInMnz+fkiVL4uvry4cPHzQdXp4XFBREhQoVePLkCdevX6dLly7fxP5EHh4eSB8n86T6Wrt2bco5u3btwsPDQyvbP0FU4YV/0NXVxdvbmxs3brBw4UI2btyIvb0906ZN4927d5oOL89QKpUoFAoSEhLw8fHBy8uLUaNGcfDgQYoWLarp8LTK7t27adWqlabD+CKRQIU05HI57dq1Izg4mI0bN3Lo0CHs7OwYN24cL1++1HR4ud6+ffsoVqwYdnZ2HD9+nEuXLjFkyJBcs0VITjp8+DCDBw/WdBhfJH5jwhfJZDKaNGnC8ePH2bt3LyEhITg4ODBs2DCePHmi6fBypeTkZK5cucK7d+8wNDTk/v372jtIPIvZ29szfPhwTYeRpUQCFdKlTp067Nu3j5MnT/L8+XNKly5Nnz59ePDggaZDyzXu3btHnTp12Lp1K2fOnOHx48ccPHgwV612nxkigQrfvCpVqrBjxw6uXLlCcnIyLi4udO7cmevXr2s6NK0lSRJLliyhSpUq1KpVi0uXLuHq6gp83Oa6ZcuWGo5QUJdIoIJanJ2dWbt2LXfu3KFAgQJUr16dVq1acf78eU2HplWePn1KkyZNmD17Nnv27GHevHkYGRlpOiwhi4gEKmSKvb09S5Ys4dGjR5QpU4ZGjRrRsGFDjh49+k1PE5Ukic2bN1O+fHmKFCnCtWvXqF+/vqbDErKYTPqWP+VClouKimLRokUsWLAAR0dHxo8fj5eX1zcxrvGTN2/eMHDgQIKCglixYgVt2rTRdEhCNhElUCFLFShQgIkTJ/L48WM6dOhAv379qFixIlu3bkWpVGo6vGy3b98+XFxcUCgU3LhxQyTPPE6UQIVslZCQwJo1a5g1axZ6enr8/PPPeHt7o6+vr+nQslRsbCwjR45k69atLFiwgO7du39Tpe5vlUigQo5ISkpiy5YtzJgxg9jYWEaPHk2fPn0wNjbWdGiZdvr0abp160axYsVYu3Yt9vb2mg5JyCGiCi/kCD09Pbp168bNmzfx9fVNSTQzZswgOjpa0+GpJTExkbFjx+Lp6cmQIUM4evSoSJ7fGFECFTRCkiQOHjzItGnTuH79OkOGDGH48OEULFhQ06Gly7Vr1/D29kZHR4cNGzZQrlw5TYckaIAogQoaIZPJaNq0KSdPnmTPnj1cunQJOzs7RowYwbNnzzQd3hcplUpmz56Nm5sbrVu35ty5cyJ5fsNEAtWAoKCgDFf1du3alWe3Ka5bty779+/nxIkTPHnyhFKlStGvXz8ePnyo6dBSefToEfXq1WPVqlUcPXqUKVOm5LnOMCFjRALVEkuXLsXBwQFDQ0NcXV05efJkqu/v3r2bpUuXaii6nOHq6soff/zBpUuXSExMpFy5cvzwww/cuHFDo3FJksTKlSupWLEilSpV4sqVK9SoUUOjMQnaQSRQLbBt2zaGDx/O+PHjuXLlCnXr1qVZs2apSpxt2rT5ZlbtKVu2LOvWreP27duYmZlRrVo12rRpQ3BwcI7HEhkZScuWLZk8eTI7d+5k8eLFmJiY5HgcgpbK6SXwhbRbG1SvXl0aMGBAqnPKlCkj/fzzzymv4+LiJGNjY+nu3bs5FabWeP78uTRq1CjJxMREatSokXTs2LEc2fJix44dkqWlpdSlSxcpKioq258n5D6iBKphCoWCS5cu4enpmeq4p6cnZ86cSXltZGRE48aNv5lS6D8VLlyYOXPm8PjxY2rXrk27du2oXbs2e/fuzZb59u/evaNr167079+fpUuXsmnTJiwsLLL8OULuJxKohr1+/RqlUom1tXWq49bW1kRGRqY61rp1628ygX5iaWnJpEmTePz4MW3btqV3795UrlyZ7du3Z9k00cOHD1O+fHmioqK4ceMGHTt2zJL7CnmTSKBa4t/T/iRJSnOsZcuWnDt3jjdv3uRkaFonX758jB49mtDQUPr168fo0aMpW7Ysa9asQaFQkJiYmOHB+XFxcfz444+0bduWX3/9lb1791K4cOFsegdCXiESqIYVLFgQHR2dNKXNly9fpimVPnv2DFNTU63doTCnGRkZMWjQIB48eMDYsWOZOXMmxYsXp0SJEkydOjXd97lw4QKVK1fm0qVLhISE0K9fPzGPXUgXkUA1TF9fH1dXVwIDA1MdDwwMpFatWqmO7d69m+bNm6Onp5eTIWo9PT09unbtire3N2/fvkWpVLJu3TpmzZrF+/fvv3hdUlISEydOpH79+vTq1YsTJ05QsmTJHIxcyO1EAtUCPj4+rFq1itWrV3P79m1GjBhBeHg4AwYMSHXerl27aN26tYai1G5KpZLr169z6tQpIiIiWLt2LX/99Rd2dnZMmDCB169fpzr/1q1b1KxZk4CAAM6cOcOYMWPQ0dHRUPRCrqXpYQDfon8PY5IkSVqyZIlkZ2cn6evrS1WqVJGOHz+e6vvh4eGSvr6+FB0dnYOR5m4qlUoKCgqSPD09JRMTE8nHx0d68uSJNH/+fMnY2FgaM2aMlJCQoOkwhVxMJFAN+FwC/S8LFy6UPD09syegb8CFCxektm3bSnK5XLKyspJOnjyp6ZD+kzqfk4CAAOnx48fZE5CQhqjC5xK7d++mVatWmg4j16pWrRp//vkn27Zt4+zZs9SpU0fTIalFTPnVLiKB5hKHDx9m8ODBmg4j1+vQoQMlSpTQdBhqEVN+tY9IoBpgb2/P8OHDNR2GkMvMmzeP3r1706dPH5ydnfH19aVYsWIsW7Ys5RxPT0/Cw8O5d++eBiP9dogEqgEigQoZJab8aieRQAUhFxBTfrWTSKCCkIuIKb/aRSRQQcgFxJRf7SQSqCDkAmLKr3bS1XQAgiCkj4+PD97e3lStWhU3NzdWrFjxxSm/Y8aM0VCU3xaRQAUhl+jUqRNv3rxhypQpRERE4OLiwr59+7Czs0s558mTJ9y8eZNmzZppMNJvh0iggpCLDBo0iEGDBn3x+7t27cLDw0O0f+YQ0QYqCHmImPKbs0QJVBDykMOHD2s6hG+KKIEKgpYSM9a0n0ySsmFbQ0EQhG+AKIEKgiCoSSRQQRAENYkEKgiCoCaRQAVBENQkEqggCIKaRAIVBEFQk0iggkYFBQVhb2+foWt27dqVah8gQdAUkUAFrXLixAlatmyJra0tMpmMXbt2pTlH7DwpaAuRQAWt8uHDBypWrMjixYu/eI7YeVLQFmIuvKBVmjVr9p9LsXl6etKlSxfu3buHo6NjDkUmCGmJEqiQ64idJwVtIRKokCuJnScFbSASqJAriZ0nBW0gEqiQK4mdJwVtIBKokCuJnScFbSB64QWtEhsby4MHD1Jeh4aGEhISQoECBShevHjKcbHzpKANRAIVtMrFixepX79+ymsfHx8Aunfvztq1awGx86SgPUQCFbSKh4cH/7VJgth5UtAWog1UyHXEzpOCthAlUCHXETtPCtpClEAFjRI7Twq5mdiVUxAEQU2iBCoIgqAmkUAFQRDUJBKoIAiCmkQCFQRBUJNIoIIgCGoSCVQQBEFNIoEKgiCoSSRQQRAENYkEKgiCoKb/A8fHuHmlu6oNAAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_histogram(rho, rho_theo, component='imag')" ] }, { "cell_type": "markdown", "id": "7d8152b2", "metadata": {}, "source": [ "We observe a strong agreement overall between the simulated and predicted teleported states.\n", "Nonetheless, small deviations can be seen in the diagonal elements of the $\\ket{+X}$ and $\\ket{+Y}$ states, which can be attribute to the phase accumulations.\n", "The corresponding fidelities are larger than the experimental values provided.\n", "This can be attributed to the fact that the simulation software does not consider errors in the optical initialization of the entangled state, or the readout, neither decoherence of the spins.\n", "Nonetheless, this application complements the original work with a rigorous simulation of the MW and RF pulses component of the protocol.\n", "\n", "The non-adoption of a rotating frame introduces a new layer of complexity to the dynamics of the system related to the phase accumulations of each qubit in the laboratory frame.\n", "Where these phase accumulations are often overlooked in perturbative models, such as the RWA, which may lead to discrepancies in experimental results.\n", "Another interesting result can be observed by comparing the fidelities for each input state.\n", "The $\\ket{+Z}$ state along the quantization axis of the NVs presents higher fidelities, due to the fact that this state is less prone to the phase accumulations in the perpendicular plane of the quantization." ] } ], "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": "3.13.3" } }, "nbformat": 4, "nbformat_minor": 5 }