{ "cells": [ { "cell_type": "markdown", "id": "58c426e3", "metadata": {}, "source": [ "# Double-Bracket Algorithmic Cooling (DBAC)\n", "\n", "Code accompanying [*Double-Bracket Algorithmic Cooling*](https://arxiv.org/abs/2510.00302)\n", "(M. Alghadeer, K. U. Giang, S. Cao, S. D. Fasciati, M. Piscitelli, N. Ng, P. J. Leek,\n", "M. Gluza, M. Bakr). This page walks through the paper's main experimental result (its Fig. 4):\n", "**how much a single qubit is cooled by DBAC as we spend more qubits as resources**, compared with\n", "data taken on a superconducting-qubit device.\n", "\n", "The `dbac` package provides the DME implementations, the DB-QITE/GCI recursion, the HBAC\n", "baseline and all the plotting code used for the paper figures. See [Installation](installation.md)\n", "to set it up, the [Quick start](quickstart.md) for a first example, the\n", "[guide](guide/conventions.md) for how each part works, and the [API reference](api/index.md)\n", "for every function." ] }, { "cell_type": "markdown", "id": "e0643d94", "metadata": {}, "source": [ "## Background: cooling a qubit by removing its coherence\n", "\n", "*Algorithmic cooling* (AC) lowers the entropy of one qubit by moving entropy into other qubits\n", "using only unitary operations. DBAC solves a complementary problem. The qubits carry **no\n", "entropy**: every one of them is prepared in the same *pure* state $|\\psi\\rangle$, but we do not\n", "know which state it is, and we cannot measure it without collapsing the superposition. The goal is\n", "still to rotate one qubit to the ground state $|0\\rangle$, that is, to remove its **quantum\n", "coherence**.\n", "\n", "Learning $|\\psi\\rangle$ first (tomography) does not escape the problem: the statistical error\n", "only falls as $1/\\sqrt{n}$ in the number of copies $n$. DBAC instead uses the other copies of\n", "$|\\psi\\rangle$ directly as **quantum instructions**: they act as a temporary Hamiltonian that\n", "tells the target qubit which way to rotate, with no measurement and no feedback. The circuit\n", "itself is the same for every input state, and the state it meets decides what it does.\n", "\n", "As in Nernst's unattainability principle, perfect cooling would need infinitely many\n", "instructions. With a finite number of qubits the cooling is partial, and it improves as more\n", "qubits are added. This page shows that trade-off." ] }, { "cell_type": "markdown", "id": "4dd4d6ec", "metadata": {}, "source": [ "## How DBAC works\n", "\n", "**Imaginary-time evolution.** Evolving in imaginary time under a Hamiltonian $\\hat H$,\n", "\n", "$$\n", "|\\psi(\\tau)\\rangle = \\frac{e^{-\\tau \\hat H}|\\psi\\rangle}{\\lVert e^{-\\tau \\hat H}|\\psi\\rangle\\rVert},\n", "$$\n", "\n", "maps any pure state to another pure state that gets closer to the ground state of $\\hat H$ as\n", "$\\tau$ grows, unless the input is an exact excited eigenstate. DBAC uses $\\hat H = -Z$, so the\n", "ground state is $|0\\rangle$ with energy $-1$ and the excited state is $|1\\rangle$ with energy $+1$.\n", "The energy of the data qubit is $E = \\langle\\psi|\\hat H|\\psi\\rangle$.\n", "\n", "**One DBAC step.** Imaginary-time evolution is not unitary, but for a single qubit it can be\n", "approximated by a *double-bracket* step built from the group commutator. A reflection about the\n", "state itself, $e^{it|\\psi\\rangle\\langle\\psi|}$, is sandwiched between two rotations about $\\hat H$:\n", "\n", "$$\n", "|\\psi_\\mathrm{DBAC}\\rangle = e^{it\\hat H}\\, e^{it|\\psi\\rangle\\langle\\psi|}\\, e^{-it\\hat H}\\,|\\psi\\rangle .\n", "$$\n", "\n", "When the reflection is applied exactly, the energy after one step with duration $t$, starting\n", "from energy $E_0$, is known in closed form (Eq. 3 of the paper):\n", "\n", "$$\n", "E_\\mathrm{DBAC} = E_0 - 2\\sin^2(t)\\,(1-E_0^2)\\,\\Big[(1-\\cos t)\\,E_0 + \\cos t\\Big].\n", "$$\n", "\n", "The correction vanishes for $E_0=\\pm1$. The two poles $|0\\rangle$ and $|1\\rangle$ are therefore fixed\n", "points: $|0\\rangle$ is already cold, and $|1\\rangle$ is an excited eigenstate that the flow cannot\n", "move. Every other state is cooled.\n", "\n", "**Density-matrix exponentiation (DME).** The reflection $e^{it|\\psi\\rangle\\langle\\psi|}$ would\n", "need to know $|\\psi\\rangle$. DME avoids this by using a copy of the state as the Hamiltonian. For\n", "a small duration $t$, a partial SWAP between a data qubit $\\sigma$ and an instruction qubit $\\rho$ gives\n", "\n", "$$\n", "\\mathrm{Tr}_2\\!\\left[e^{-it\\,\\mathrm{SWAP}}(\\sigma\\otimes\\rho)\\,e^{it\\,\\mathrm{SWAP}}\\right]\n", "= \\sigma - it[\\rho,\\sigma] + O(t^2) \\approx e^{-it\\rho}\\,\\sigma\\, e^{it\\rho}.\n", "$$\n", "\n", "The partial SWAP $U_\\mathrm{DME}(\\varphi)=e^{i\\varphi\\,\\mathrm{SWAP}}$ is the same circuit for every $\\rho$, so\n", "the information in $\\rho$ decides which rotation is applied. On hardware it is compiled from the\n", "Heisenberg interaction $XX+YY+ZZ$ using the native $ZZ$ interaction of the transmons\n", "($U_\\mathrm{DME}(\\varphi) = R_{ZZ}(\\varphi)\\,R_{YY}(\\varphi)\\,R_{XX}(\\varphi)$).\n", "\n", "**Two knobs: $M$ and $k$.** Using one copy per DME call only approximates the exponential. Two\n", "independent resources then control how well DBAC cools:\n", "\n", "| symbol | meaning | what it costs |\n", "|---|---|---|\n", "| $M$ | number of **DME steps** (Trotter steps) inside one DBAC step. The duration $t$ is split into $M$ pieces $t/M$, each using a fresh copy of the instruction state, and the error of the approximation shrinks as $O(t^2/M)$. | $M$ copies of $|\\psi\\rangle$ per DBAC step |\n", "| $k$ | number of **DBAC steps**, applied recursively. Step $k+1$ uses the *cooled* output of step $k$ as its instruction, so each step starts from a colder state. | the instructions of step $k$ must be prepared first, in parallel, so the copies multiply |\n", "\n", "More of either resource means more qubits $n$ in the circuit and lower energy of the data qubit." ] }, { "cell_type": "markdown", "id": "e4123dad", "metadata": {}, "source": [ "## The experiment\n", "\n", "Every circuit is run as follows.\n", "\n", "1. **Prepare.** All $n$ qubits start in $|0\\rangle$ and receive the same rotation\n", " $R_X(\\theta)$, so each holds $|\\psi(\\theta)\\rangle = R_X(\\theta)|0\\rangle$. In the paper's\n", " convention $R_X(\\theta)=e^{-i\\theta X}$, so $\\theta=0$ is the ground state $|0\\rangle$, the\n", " energy rises as $\\theta$ grows, and $\\theta=\\pi/2$ is the excited state $|1\\rangle$.\n", " The energy of the untouched state is $E_0(\\theta) = -\\cos 2\\theta$.\n", "2. **Apply DBAC** with $k$ DBAC steps and $M$ DME steps each. On the instruction qubits,\n", " $R_Z(\\pi/4) = e^{-it\\hat H}$ with $t=\\pi/4$ prepares $e^{-it\\hat H}|\\psi\\rangle$. The data\n", " qubit then interacts with the instructions through $U_\\mathrm{DME}$. The final rotation\n", " $e^{it\\hat H}$ on the data qubit is a $Z$ rotation and does not change its energy, so it is\n", " left out of the hardware circuits.\n", "3. **Read out** the energy of the data qubit and repeat for a sweep of $\\theta$.\n", "\n", "Without DBAC the energy follows the *Initial state* curve $-\\cos 2\\theta$. After DBAC it should move\n", "toward the ground-state value $-1$.\n", "\n", "The three circuits below are the ones run on the device. Dashed lines separate the DBAC steps.\n", "\n", "| circuit | $k$ (DBAC steps) | $M$ (DME steps) | qubits $n$ | instruction copies |\n", "|---|---|---|---|---|\n", "| A | 1 | 1 | 2 | 1 |\n", "| B | 1 | 2 | 3 | 2 |\n", "| C | 2 | 1 | 4 | 3 |\n", "\n", "The code that generates the circuits' energy curves, the digitized experimental data and the\n", "plot styling is in [`scripts/figure_4.py`](https://github.com/khanhuyengiang/dbac/blob/main/scripts/figure_4.py),\n", "and the plotting code is in [`src/dbac/plotting/`](https://github.com/khanhuyengiang/dbac/tree/main/src/dbac/plotting)." ] }, { "cell_type": "code", "execution_count": 1, "id": "f1f30e23", "metadata": { "execution": { "iopub.execute_input": "2026-10-26T13:05:20.832377Z", "iopub.status.busy": "2026-10-26T13:05:20.832293Z", "iopub.status.idle": "2026-10-26T13:05:21.613139Z", "shell.execute_reply": "2026-10-26T13:05:21.612647Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[Qibo 0.3.6|INFO|2026-10-26 14:05:21]: Using numpy backend on /CPU:0\n" ] } ], "source": [ "%matplotlib inline\n", "import sys\n", "sys.path.append('..')\n", "sys.path.append('../src')\n", "sys.path.append('../notebooks') # for config.py\n", "\n", "import numpy as np\n", "\n", "from config import plot_path\n", "from dbac.plotting import use_paper_style, figure_size, plot_single_energy_curve, draw_dbac_circuit\n", "from scripts.figure_4 import (\n", " CIRCUIT_COLORS, CIRCUIT_FILENAMES, CIRCUIT_MARKERS, EXPERIMENTAL_ENERGY,\n", " OPTIMAL_S_PATH, XTICKS, XTICK_LABELS, run_dbac_circuits,\n", ")\n", "from dbac.gci import GCI\n", "from dbac.dbqite import initial_psi\n", "from dbac.utils import rx_sweep\n", "\n", "use_paper_style(font_size=10, figsize=figure_size(\"PRD\", \"onecol\"))" ] }, { "cell_type": "markdown", "id": "0c287717", "metadata": {}, "source": [ "### Simulating DBAC\n", "\n", "For each $\\theta$ we build $|\\psi(\\theta)\\rangle = R_X(\\theta)|0\\rangle$ and run DB-QITE with the\n", "step durations optimized for each $(M, k)$ (cached in `optimal_s_Mk.npy`). The result is the\n", "analytical curve of each circuit, from noiseless simulation with $M$-step Trotterized DME. The\n", "*Initial state* baseline is the energy of $|\\psi(\\theta)\\rangle$ before any cooling." ] }, { "cell_type": "code", "execution_count": 2, "id": "030b2dba", "metadata": { "execution": { "iopub.execute_input": "2026-10-26T13:05:21.614902Z", "iopub.status.busy": "2026-10-26T13:05:21.614759Z", "iopub.status.idle": "2026-10-26T13:05:21.631296Z", "shell.execute_reply": "2026-10-26T13:05:21.630983Z" } }, "outputs": [], "source": [ "optimal_s_Mk = np.load(OPTIMAL_S_PATH)\n", "thetas = np.linspace(0, 1, 100)\n", "\n", "psis_energy = rx_sweep(thetas, start=np.array([[1], [0]], dtype=complex))\n", "theta_angles = thetas * np.pi / 2\n", "res_init = [GCI(initial_psi, psi, 1, np.linspace(0.01, 1, 2)).execute_gci()[0][-1] for psi in psis_energy]\n", "energy_results = run_dbac_circuits(psis_energy, optimal_s_Mk, as_fidelity=False)\n", "\n", "def plot_circuit_energy(label):\n", " plot_single_energy_curve(\n", " theta_angles, res_init, label, energy_results[label],\n", " CIRCUIT_COLORS[label], CIRCUIT_MARKERS[label],\n", " experimental=EXPERIMENTAL_ENERGY.get(label),\n", " xticks=XTICKS, xtick_labels=XTICK_LABELS, show=True,\n", " save_path=plot_path(CIRCUIT_FILENAMES[label]))" ] }, { "cell_type": "markdown", "id": "a6a228bf", "metadata": {}, "source": [ "## Each circuit individually, overlaid with hardware experiment data\n", "\n", "In each plot below, the horizontal axis is the initialization angle $\\theta$ and the vertical\n", "axis is the energy of the data qubit after the circuit.\n", "\n", "- the **dotted** curve is the *Initial state*, the energy $-\\cos 2\\theta$ with no cooling;\n", "- the **solid** curve is the *Analytical* prediction of DBAC for that circuit;\n", "- the **open circles** are the *Experiment*, measured on the superconducting device.\n", "\n", "Cooling shows up as a curve **below** the dotted one, closer to the ground-state energy $-1$.\n", "Both ends are fixed points, as discussed above: $|0\\rangle\\langle 0|$ at $\\theta=0$ is already in the\n", "ground state, and $|1\\rangle\\langle 1|$ at $\\theta=\\pi/2$ is an exact excited eigenstate that\n", "imaginary-time evolution cannot move." ] }, { "cell_type": "markdown", "id": "218d5c87", "metadata": {}, "source": [ "### Circuit A: 1 DBAC step, 1 DME step ($n=2$)\n", "\n", "The minimal DBAC circuit. One instruction qubit is rotated by $R_Z(\\pi/4)$ and the data qubit\n", "$q_1$ is coupled to it through a single $U_\\mathrm{DME}(\\pi/4)$. The step duration\n", "$t=\\pi/4$ cools a wide range of initial states." ] }, { "cell_type": "code", "execution_count": 3, "id": "583e0571", "metadata": { "execution": { "iopub.execute_input": "2026-10-26T13:05:21.632934Z", "iopub.status.busy": "2026-10-26T13:05:21.632869Z", "iopub.status.idle": "2026-10-26T13:05:21.692776Z", "shell.execute_reply": "2026-10-26T13:05:21.691777Z" } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_dbac_circuit(\"A\");" ] }, { "cell_type": "code", "execution_count": 4, "id": "698e485f", "metadata": { "execution": { "iopub.execute_input": "2026-10-26T13:05:21.694754Z", "iopub.status.busy": "2026-10-26T13:05:21.694668Z", "iopub.status.idle": "2026-10-26T13:05:21.768158Z", "shell.execute_reply": "2026-10-26T13:05:21.766686Z" } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_circuit_energy(r'$n=2$');" ] }, { "cell_type": "markdown", "id": "b1d51630", "metadata": {}, "source": [ "A single instruction already lowers the energy of the data qubit across the sweep. The\n", "experimental points lie between the analytical curve and the uncooled baseline: the cooling is\n", "real but smaller than in the noiseless simulation, because of gate errors and decoherence. Since\n", "$M=1$, the DME step is also a single, coarse partial SWAP." ] }, { "cell_type": "markdown", "id": "27fe956a", "metadata": {}, "source": [ "### Circuit B: 1 DBAC step, 2 DME steps ($n=3$)\n", "\n", "The same total duration $t=\\pi/4$ is now split into $M=2$ DME steps of $\\pi/8$ each. Each step\n", "uses its own instruction copy ($q_1$ and $q_3$, both rotated by $R_Z(\\pi/4)$), and both act on the\n", "data qubit $q_2$. This distributes the DME over two instruction qubits, a finer Trotterization of\n", "$e^{-it\\rho}$ than circuit A, at the price of one more qubit." ] }, { "cell_type": "code", "execution_count": 5, "id": "2b58472e", "metadata": { "execution": { "iopub.execute_input": "2026-10-26T13:05:21.770252Z", "iopub.status.busy": "2026-10-26T13:05:21.770167Z", "iopub.status.idle": "2026-10-26T13:05:21.803116Z", "shell.execute_reply": "2026-10-26T13:05:21.802634Z" } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_dbac_circuit(\"B\");" ] }, { "cell_type": "code", "execution_count": 6, "id": "e3881177", "metadata": { "execution": { "iopub.execute_input": "2026-10-26T13:05:21.804828Z", "iopub.status.busy": "2026-10-26T13:05:21.804761Z", "iopub.status.idle": "2026-10-26T13:05:21.870704Z", "shell.execute_reply": "2026-10-26T13:05:21.870270Z" } }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAUoAAADOCAYAAABYf0t/AAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjExLjIsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvgI3uAAAAAAlwSFlzAAAPYQAAD2EBqD+naQAAZ7JJREFUeJztnXdYU1cbwH9J2Hu4AUHciIq4Nwrubd3VuqpVq9bVWqt11vG1am21bq11K+69ceMeuAEFRWTvDUnu90dKNAUENAjq/T1PHr33nHvuexPy5pzzLokgCAIiIiIiIjkiLWwBRERERIo6oqIUERERyQVRUYqIiIjkgqgoRURERHJBVJQiIiIiuSAqShEREZFcEBWliIiISC7oFLYARQGlUsmrV68wNTVFIpEUtjgiIiIfAEEQSEhIoEyZMkilb58ziooSePXqFXZ2doUthoiISCEQFBSEra3tW/t8FIoyMTGR8+fP0759+7f2Cw8P58iRI1haWtKmTRsMDAzyNL6pqSmgesPMzMzeW14REZGiT3x8PHZ2durv/9so8orywYMHzJo1Cz8/v7cqyoCAAHr37s2RI0d48eIFX3zxBXv27EFfXz/Xe2Qut83MzERFKSLymZGX7bYib8ypVq1arjNJgClTptC7d2+KFSuGq6srBgYGbNmy5QNIKCIi8qlT5BUl5E3jHz16lPr166uPGzRowMaNGwtSLBERkc+EIr/0zgthYWHEx8dTokQJ9bnixYvj5+dXiFKJiIgUFEqlwO49D7lyMpD46BRsrAwpU9acjHQFaakKBoyrS/HSue895pVPQlG+fPkSAGNjY/U5ExMTwsPDs+2flpZGWlqa+jg+Pj5P91EoFGRkZLyHpCLaRldXF5lMVthiiBQAyely9twKJjopnWL6ulSUS7hz+SXnD/vz6HYoaSlyjf5SmQRDI10MjXVp39dJVJT/xcbGBoCUlBT1ueTk5BxdfubPn8+sWbPyPL4gCISGhhIbG/tecooUDBYWFpQqVUr0gf0IiUvJ4EloAkHRybiUtaB8cRN1m1QJXgd8Cb0eRuzDKPQFSEuVEx+Tio6uFANTXZQy1WduKJOSliwnKSEdeYaS5CTtTmg+CUVZqlQpjI2NiYqKokKFCgBERUVRqVKlbPtPmTKFCRMmqI8z3QRyIlNJlihRAiMjI/ELWUQQBIHk5GT1yqF06dKFLJFIfnkelcTe28EAmBjoUL64Ca+ex7F3/R1O7nrMq9BElIKATCpBRyolPiYVPQMZlauXoGQFS6zszChhY0ql8paYmxtw6+IL/vzpLDfOPce1sfZ8oz8JRQnQtm1brl+/rjbo3Lhxg1atWmXbV19fP09uQ6BabmcqSWtra63JK6IdDA0NAZUPbYkSJcRleBEkODaFOy9ieRIaz4CGDhQ3ff3ds7d+vV1292YI3n/c5MKRpwhKVeEFYz0ZEokEM0sD9A11SE3JYO/94ZSxt8j2Xq5N7Ajyj2HnilsM+aEROjrasVd/FFbv6OjoLMveiIgInJ2dCQoKAmD27Nns2LGDpKQkfH19efr0KSNGjHjve2fuSRoZGb33WCIFQ+ZnI+4fF018wxK46B9JRGI6vmEJGm3mhrrUNzciY98zjv54nvOH/NVKUldPhnu3yvy2oxued77mVWAcPYa7ZqsklUole/bsISUlhd6jahP2MoErpwK09gxFfkb56NEj5HI5/fv358SJE7i5uaGnp4elpSXffvut2tLt5OTE1q1b2blzJwCnT5/WMO68L+Jyu+gifjZFg9C4VO4ExdCySkn03pjJVSttxokHYUglqj3JTBLiUtmw8Ar7N/igVAhkfoqWxY3oPtSFjgOcMbdUrRiSE9OJjUqhWp3st1fatWvHiRMnaN68OV5eXshkEoIDYrX2bEVeUVatWpWqVatmOa+jo8PIkSM1ztnZ2TF48OAPJdoHRxAEdu3apbbSm5iY0K1bN/T09HK8JiAggNTU1GzfQ4BLly7h7OyMubl5gcgs8nlw6mEYpx//u1dsbkhNOwt1W3FTfb6sX5byxU0w1JMhCAIndz9mxcwLxEW/NsBaFjei/7h6dOhXDT19TdUk+1fxpqdpWroB/vzzT06cOAGAv78/8gwlCoWAjq72FsxFXlGKvEYikdC9e3caNGhAXFwc9+/ff6uSBFi/fj3h4eGsWrVKfU4ul6Ojo/rox44dy/Tp0+nSpUuOY5w9e5YDBw7g6upK//798yzvm/fRRj+RootjcWNOP1b9/05QrIailEgkONuofohDX8az+Icz3Dj7XN2uZ6BDvzF16PmNK4ZGutmOr2+gQ6UaJTh7wI+ug2qqzx84cIBx48apj0NDQzm2ywcA53pltPR0H8kepchrZDIZ9vb2lC1bNlclCTBnzhwNJbl582auXr2qPr558+ZblSRAs2bNuHTpEsHBwXmWMzU1lUmTJuXaLyUlhe+//z7P44oUHoIg4BuWwPqLAbyKTdFoK1fMmGplzOhcsww962TNxJM5ixzmvkVDSbp1rsjGi1/x1fj6OSrJTHqPdMVrvy/PHkcCqr/dvn37kllxWyKRoFAoWDbfk1qNbalco+T7PrIaUVF+hEgkEo19uYiICHx8fIiKimL37t28evVK3Zaens7NmzcBOHbsGMOHD+fgwYOcP39efa2/v79G/9OnT3Py5EmUSiUAUqlUI+rpv6SmprJ//362bt3KvXv3SE9Pp0+fPhw+fJh169YRFxenvtfevXt58OABoHL879WrF0ePHmXdunXqLYXg4GA8PT25deuWNt4uES1x60UMf18KxC88kctPozTaJBIJ/RvY07C8NUZ6mquDpIQ05n57jPljjpOUkA5AsVLG/PJPJ6avbE+JMnlzDO84oDr2lawY1W473ufv07FjR5KTk9VugJl/o/ce3GLUrGbv+7gaiIryIycwMJAWLVowceJE1q5dy969e2nYsCEZGRkEBATQqlUrfvzxR0A1M9TT08PNzY26dety9uxZqlSpwuHDhwHV/o6bmxv16tXjwoULGkuat9G3b18aNmyIvb09mzZtQkdHh+bNm1OsWDF69OiBqakpK1euZMGCBbRs2ZKvv/4aLy8vdHV1adasGcWLF6dHjx6YmJhw/Phxtm/fjr29Pd9++y0LFiwoqLdOJJ8425hjpKdyv3oRnYziX+v023j2KJIRbbdzZp+v+lyrHlVYf3YAjVo55uv+RsZ6rDreF119HXq6TSE0NBR7u4qYGalmjunRVgA41JHTwL1cvsbODXFj6D246BfJBf8IAHrXscPxjaiC6KR0Vp1/CkC1MuZ0rqm5X7LRO5Dgf5cvU9ppGlpuPo/mxMMwADrVKKPe38kOBwcHWrRoQUxMDJMnTyYuLg5LS0v8/f2pWrUq3bp1UyvCTGd5U1NTDA0NcXNzo1atWuqxAgICcHZ2xtTUlFatWjFkyJBc3wOlUom3tzdKpZLGjRujo6ODVCrFyMgIHR0dtZHoyZMnNG/eHHNzc+rVq8eJEydo0aJFln5jx45l4sSJ3Lt3D0dHRxYsWMDkyZNFy/YHRK5QcutFLAa6UmrYWqjP6+vIaOdcCgNdGU6lzZBKX38mkaGJnN77hOjwJIxM9GjY2pHnvtEsmnSK9DQFAMZm+kz4tSUtOmcfCJIXSpc1Z/v1wWxdWYmli01IDyrLraA/AWjRrC17Tj8iJOLpO4+fE6KifA9SMxTE/xtvKv/Pr6tSENRtqemKLNcmpb2+9r+ky19fm6FQ5iqHjo6O2vHa3NwcfX19kpOTAVUs9Nt4s71Vq1Z4eHhw8OBBVqxYQWpqaq73lkqluLu7U6tWLZYtW8YXX3yRbb/ff/+dhIQEFi1axPHjx2nXrl2WPmFhYUgkEnr37g1Ajx49ANH950OSkq5g6Rk/YpIzMDfUxam0GTqy1wvPOg5WGv2jI5JY8N1JTno+AglYWBuSGJ/Owkmn0dGVYmKuj66ujArOxZm5pgNl7N/fu8LYVJ9h37fk60ktuHThCk2b/4q5uTlbDs2jf/8XODrmb6aaF8Sl93tgoCvDzFAHM0MddKSaX2apRKJuM9DLGi1irP/62v+ip/P6Wl3Zh/uIoqOj6dixI3FxcUyePDnP161fv56+ffvSu3dvfvnll2z7XLhwgR49euDu7p6tkgRISEggODgYY2NjzM3N1a/MzXqRgsdQT0aJfyNn4lIy8A1LzLFvZFgiXzXeyNXTgUz4zZ2zYeM47DeKFl0qYWZhAALERqVQu1lZlh3spRUl+SYSiQTvqxcB1baSgYEBu3bt4tdff9XqfUCcUb4XTSoWo0nFYtm2WRnrZVlSv8lXDR1ybKttb0Vte6sc299XceQUwbJ69Wrs7Ozo378/Fy9ezNN9Mo1Fixcvpm3btnTr1o2ffvopy33Gjx/PggULcHFxYcOGDdnKY2dnR0ZGBlu3buWrr74CwMvLi3LlyuHg4PAOTyqSG3Epqpnjm7RxLoVAKB5VS2JnlXNE2oyhh0lKSGOz90DsHC2JDE1kYs89PHsYib6hDobGuhiZ6nH1dAByuRK9vEUN54uzZ88C0KJFC+0P/gaiovwIiY+P1wjpjI+PVyubpKQk0tLSSEpKAlRZlN7MqlS6dGmOHz+OTCajadOmGu2xsbGcP3+eY8eOcf78eWJiYjh16hQeHh4kJiaql/NvIggCy5cvp1GjRtSrV49q1aohlUopXbo0vr6+XL16FSsrK+Li4tixYwcJCQk8fvwYqVSKj48PpUuX5vHjx1y9ehVra2tGjBjBmDFjCAgIIC0tDXNz8wL/EnyOJKRmcOJBGLeDYhjTsiIlzV7Xlyptbsjgxm83hjz3i+b8YX/m/N0RO0dLAn2j+KHvPiJDVDNQYzN9Zq/rQPEyprQv/xfHtj+k+1AXrT6DXC7nwoULQMErynyv65YtW8ajR48KQhaRPLBnzx7KlSuHi4sL27Ztw9/fH3Nzc4oVK4a/vz9Hjx5l6NCh3L59m4CAAOLj46levTrXr18HVH6UMpkMGxsbvL29cXJyIjk5meDgYL7//nv69evH8+fPmTFjBhMmTEAQBC5evEjVqlWRy+UEBGjGz8pkMpycnFi5ciXbt29n3759gCqkbMaMGdy7d4+KFSuyY8cOrK2tsbS0ZOnSpVSvXh1ra2s6duzItGnTePDgARUqVGDx4sUsWrSImJgYXF1d87UFIJJ3bgTGcON5DAolHPIJyfcq5fCW+5haGNC2txMPboYwtounWkmWLmvGX4d6UauxHbblLGjctjwHNt7T+jPcvHmThIQELC0tqVGjhtbHfxOJkM93aM2aNcTHxxMQEIC9vT09e/b86JdF8fHxmJubExcXl6W4WGpqKgEBAZQrVy7PVR1FPiziZ5R/MhRKfj/pS0qGAvcqJWlcwTpfRrOZww7z5G4YE351Z/rQQ+okupVqlGDeps5YFX+dZ2Hx5DOc2v2YI/6jtPoMCxYsYMqUKXTt2pW9e/fm+/q3fe//S76X3sOGDVP/PyQkBE9PT44ePUq7du3o2bOnmBNQRKSIkZCaQXRSukZKM12ZlC8b2GNuqIuJfv534PQMdIgMTWLqwAPIM1SeGbWa2DFnfUeMTDQjxpIT09E30P4un5eXF1Dwy254h6V3WJjKvy8oKIjly5czf/58/Pz8SE9PZ/369UyYMEFcmouIFAEEQeBGYDS/n/Rj69UXpGZouqnZWBi+k5IE0DfUITQontRk1d540/blWbC5SxYlmZGh4PSex9Rupr0kuqAyIl68qLJ4fwhFme93aenSpdy8eZNTp07RokULVq1aRceOHZFKVTo3NTWVmjVrcvjwYXW2cRERkcLhwat4UjIUpGSA1+Nw2lV//xXfmf1POLzlPlKphOTEDLoNdWLyktbZJsnd9/ddIkOT6DWy9nvf902uX79OcnIyxYoVo1q1alodOzvyPaMMCQmhQoUK3L9/nxMnTtC5c2e1kgRV9vAXL15k2fQXERH5sEgkEjrXLIO+jpRadhY0rVT8vcc8s/8Jc789DgIYm+qRlipHJpMi/89sVakUOLjpHvNGH6fr4BpUqp5zroB3IdMtyM3NTUP/FBT5nlFOnDgRJyenHNslEgkPHz6kXDntxlqKiIi8nfCEVHSkUqyMXy9/LY31GN+qUhZfyXfh/GE/5o0+rs5A3mN4LUqVNeN/353k0Ob7dPqqOmUrWBIblcKRLfcJ9I2mY39npq9s/973/i+Z+5Nubm5aHzs78q0onZycmD17NtOnT0cQBLWlTC6XM3PmTBwdHWnfXvtvjEj2XLx4kSZNmhS2GAQGBvLgwQM6dOhQ2KJ8diiVAhf9Izn5MAxbS0OGN3PUsGBrQ0l6nwpgzshjKBUqJdnhS2fGLWiJVCqhSdvy7Fx5i6PbHhAdkYyhsR6N2zgyY00Haje1K5AQ1Ew7SMuWLbU+dnbke84aGxvLnj17sLW1xcTERJ1z8OTJkwQHBzNkyBA2bdqkdUFFsiIIAoMHD+bKlStaGW/btm20b9+eY8eO5al/plM7qIq5bd68+Z3um5iYyKJFi2jQoEGea6yLvCZdoeTKsyjkSoHAqGRuPI/R6vi3LgYx8+vDKOQq63ab3k6M/19LdVKMshWsmLTQg9PB33E7fQqXYyby2/Zu1GlWtsDi9P/880/WrFmTY+Z+bZNvRblmzRpKlizJH3/8ga+vLy4uLly+fJmHDx9iZaUKu8vIyMDPz0/rwopocvr0aeLi4li+fLlWxuvbty+3bt0iLS0t176hoaEaCXd79OjBtm3b3um+JiYmdOjQgatXr4px3e+Aga6MnnXskEqgSYViuLyRXfx9eXgrhGmDDpLxb2IXt84VmbTQXSNzUGHwxRdf8PXXX3+w++VbUcpkMo4ePcoXX3yBjY0N9evX58WLFyQmJqqdNmUymTo5q0jBsXfvXlauXMnOnTuJjIzUaIuOjmbr1q2kp6fzzz//sGPHDo32Z8+esWPHDnbu3KmhnExNVUlUk5KSmD9/PrNmzeLOnTuAytL4v//9j5cvX9K5c2fOnz/PokWLSElJISEhgf3792vc4+bNm6xcuZJLly6pkwALgsCNGzfYsGEDly5dynJfkdxJTpeTLtfMKlWumDGTWlemQ43SWkuk8uxxJFP6H1C7ADVs7ciUpW2QfcBELUWFfD9xu3btaNOmDWPHjqVTp060adOGkJAQLl26hEKh+tW5cuUKZcpor17F7du38fb2Vo+fE5GRkezevZvdu3fj6emp/oJ/ioSEhGBlZUXXrl0pWbIk69evV7cpFAoWLVrEkCFD+OOPPwAYM2YM27dvB2Dfvn1MnjyZ3r17c/bsWebNm5dlfGNjY8qVK8evv/6qNt6VLFmSpKQkbG1t6dKlCxUrVmTixIkkJiYyfPhwjUS/K1as4MGDB3zzzTfMmDFDnShj7Nix3Lhxgy+//JKRI0dy+fLlgnqLPkmeRiTyx2k/jt4PydJmaZx7aZC8Evoynsl995EQq0q159LYlhmr2qGr+3nWTc+3Madq1aps3LiRdevWoaenx5w5c3ByckIul9OiRQuaNm3K8+fPNRLCviuCIDBgwAA8PDyoUaMGHTt2ZPv27TlWDFy6dClnzpwBVG5Ku3fvfm8ZcmJE221Ehyfl3lGLWJUwZuWxvoAqtdmgQYOQSqUMGzaMlStXMmnSJKRSKTKZjD59+jBv3jwmTpyIVCrl5MmTXL16lT59+pCcnEyrVq0AcHV1zTH8q0ePHkyaNIk9e/bQp08f9u7dm21xseLFizNgwAD1Xml4eDj//POP+njWrFnqchN6enrUq1cPXV1dnJycuHr1Ko0aNdL6e/UpkpQmZ+PlQNIVAleeRVOllBmVS2l/Jh4Xk8LkvvuIClP9fVeqWYJf/u6UpTLi50S+n/zEiRPcuHGDadOmaZzP3K86duwYGRkZuSaMzQuenp4EBwczaNAgQJVzbtq0aSxdujRL35SUFI1sIgVNdHgSkaEfVlFmolQq2bt3L3K5Kr42NDSUgIAAjh07pvY4yPQty/zX0tJSnYi3X79+xMXFMW/ePA4cOJDjsldHR4cRI0awYsUK+vTpQ2BgoLo+yX+RyV7PNG7evEmpUqXUx40bN6Zx48YALFq0CD8/P8aNG4e3t7dWflA/F4z1dWjrXJoDd19Rvrgxpcy1F9f+MiCWyNBEJBJYNeciQU9VBiGbchbZRty8D6tXr2b48OEa554/f86lS5fo16+f+tzatWsZNGhQjhU6Q0JCuHLlCt26dVOfO3fuHPr6+jRo0EB9LjQ0lGvXrtG5c+d3ljnfivLu3bvZptsCVVijnZ32QpV27dpF06ZN1cdNmzalU6dOLF68OIsi3rx5M6tXr8bX15cxY8bQrJl2iwv9F6sSxrl3KqB7HjlyhBEjRmj8gfj6+rJ8+fI8uWbdvn2b8ePHs2zZMkqWLKlekmfHsGHDmDNnDmfOnMHWNmt1veyIiorSKHD2Jn///TfHjh1jxYoV6nBYkbzTwNEKUwMdqpUxe2+LsiAIHN/5iC1/XufO5Zfq8xKpBANDHWzKWfDb9m5YWOeck/Jd+K+h9+7du8yePZvw8HANRWlra8vRo0fp1KlTtuNs2LBBnQ0/NTWVixcvMmDAAKZNm6ahKJOSkggJybpVkR/yrSjbtWvHokWL8PT0VFu5QVWYytDQUJ1wVRs8efJEw0+qTJkyxMbG8vLlyywO7VWrVmXo0KHs3bsXNzc3li5dyrfffqs1Wf5L5hK4MNiyZQtr1qzBxOR1jZ6BAwcyePBgdRadtzF//ny6d++Os7Mzly9ffquluWTJkvTp04evvvpKw/gikUg0SkW8OYazszM3btzg1q1buLq6ArB161Z69erFjz/+iJeXF1ZWVigUCtHKnQNyhZLjD8IobWGAa1lL9fk3a2S/D4IgMGfkUTxX3aa+uwMLd3Tj8okAzux7QlqKnNQUOQmxqWRkvN0uoA1q1qxJy5Yts/xgt27dWm0LyU7+58+fq8s+GBgY4OHhUWBh0/k25vj4+LBp0ybGjRvHoEGD1K/M3IXaJCAgQEMZZFrVs5utNGnShAULFvDo0SMmT57M999/T0RERLbjpqWlER8fr/H6WHjy5Al+fn4a7wtAo0aNUCqV/PmnqtBSdHQ0gHr2HxYWpi4bq6Ojw+bNm1mzZg03b95U57EUBIHY2Ngs78fYsWOxt7fH3t5efc7e3p7bt2+zd+9eXrx4QXx8PImJqnyELi4u9OzZk1atWvHdd9/RvXt3KlSogEQiQSqV8ttvv6lnlN7e3ty8eZOYGNVS72P6LAqKNLmCNRcCuOgfyf7bwYTH5167KL+s/9Ubz1W3mb2uA2tPfUlMZDIXjvijqyfD3NqQhTu6oW+gw6j2O0hPy762U0EjlUopWbJktrPBs2fPftCEzvlWlN27d1fvHQYFBalf0dHRWrV0g8pIkJ6erj7OnMGULJlzYXOpVMrcuXOxtbXFx8cn2z7z58/XqMmize2CgkShUHD69Gk6d+6Mt7e3RtvVq1eZOXMmFhYW3Lt3j8ePHzNz5kxOnDhBQEAA1atXx9nZmefPn7N06VKGDBlCtWrVWLx4MZMmTcLJyYmDBw8yevRo4uLiNH5kjIyM6NOnj8b9+vTpw+LFi7GyssLQ0JDIyEhGjx7NiRMnANUMcuXKlZQrV45FixZRr149ZDIZXl5e1K5dm7Zt27Ju3TratGmDo6MjV65cYebMmZw7dy7HUhWfC/o6Mor/W7dGKUBInHYVZVqqnA2/XaHv6Dp0G+LC2YO+rP7l9Wrh+8UetO5Rld/39CDwSRSn9jzR6v3zw4ABA7INYNm7dy9du3b9cIII74C/v7+wZcsWQRAEISIiQti8ebOQlpb2LkO9FXd3d2HhwoXq43v37gm6urpCRkZGrtd2795duHjxYrZtqampQlxcnPoVFBQkAEJcXFyWvikpKcLDhw+FlJSUd3+Qj5xp06YJ0dHRhS1GjnyKn1FahkLYeDlACIpO0vrYh7bcE5z5RQj0jRLu33gltLZfKrQovURoUXqJsPH3qxp9h7bcLAxqvlGr9580aVKWc8uWLROaNGmSbf+RI0dqHEdHRwtTpkzJtm+TJk2EZcuWaZzz9/cXVq5cmaVvXFxcjt/7//JOS29nZ2cWLVoEQLFixfDw8KB///5aX3q3aNFCwxfyzp07NGjQIEcr2JvExMTg7OycbZu+vj5mZmYaL5GstG7dGjc3N/T09LC0tMz9ApF3IiVdQWSiZjSUno6UAQ0dsLXUriEF4OmDCMrYm6OnL9OIumnT24n+39XV6Fvf3YGnDyKzG+aD0axZM86fP68+3rZtG19++eUHlSHfinLTpk2cOXNGwzqVuRQ+d+6c9iQDRo4cye3btwkPDwdg48aNzJo1C4C4uDh69OhBREQEqampdOnSRb3s27dvH4MGDcrR31Ikb/zwww8MGjQoiyuYiPYIiUthmZcfGy8HZkmsW5AoBYGfvjpAXJSqsFytJnZM+LVlFkt6USipnpiYqLEnb2xsrN4P/1DkW1GWKFFCbcnMJCoqCm9vb40kCdrAysqK48ePs2XLFv7880+mT5+u3sDV1dXFxsYGPT09DAwMaNeuHdu2bWPVqlU4Ojpq1fr+ueLh4cGgQYMKLLHB544gCOy/84ropAwiEtM55PN+Lix5xaGyNaEv4nn2UDVTtCtvycw17bONurl65jnlqlp/ELly4k3vCYCePXuyc+fODypDvt2D+vfvz7hx40hOTubgwYP4+Pjw119/YWJiUiC+izY2NowfPz7LeSMjI3V4HsCIESMYMWKE1u8vIlJQSCQSetWxY9kZf6xN9PCoqt3ktjnhfz8ciQRSkjIo42DOvE2dMc3Ged3/QQRXTgUwf3OXApcpJCQkWy+VBw8eUL16dY1zRkZGSKXSLDNNQRAIDQ3N0dvlfcj3jLJ06dLMnj0be3t7/vnnH3x8fBgzZgxXrlwRExuIiOQTK2M9hjUrx/BmjlgYaS/6JSf2/n2XQ5sfYGisR0pyBq16VsXGwSJLv9CX8Yzvvgv7ila07lGlQGW6f/8+dnZ2jBkzhtOnT6sjzkDlPfHmNl8mvXv31kj0IpfLOXbsGOPGjcPOzo6HDx9qVcZ3Ct4sXrw4s2fP1jinUCjw9vamYcOGWhHsUyPQN4pzh/xJjEvFzNKQll0rZfsH+jbS09NZu3Yt169fR0dHh2LFiiEIAklJSSQmJjJ58mSqVCnYP2pQfdazZs1i0qRJoiEsH4TFp3I9MJoO1UtrbGeUNjf8IPe/eeEFf01X2RGMTHRxrlualbMucO9KMD1HuOJYtRhJ8Wkc3f6QvevvYmKmx9rTXxZ4jLezs3O2htf09HRSU1OztTXUqVOHtWvXMnToUEDlG9yuXbsCkzHf70BISAjjx4/Hx8dHw98tKiqK33//XVSU/+HZo0jmjz3BlVMBGBjqYGZpQFx0Kr9NOEmzDhWYsrRNnhWmnp4eI0aM4KeffuKbb75h/vz56raFCxcSFBT0QRRleno6Pj4+Gqn1Cprw8HBKlPgwS9OC4OGreHbeCCJNrsRYT4cWVT7ss7wMiGXmsCPqDOV9vq3D8KmNObTlPtuW3mBct13qvhbWhvQY5sJXE+tTrKRJTkMWOPv27Xurr6SzszP379/P0btFm+RbUS5cuJD4+HimTp2q3h8QBIHAwMAPUuTnY+KJTxiDm2/GuqQx8zZ1pnWPqugb6JCclM7RbQ9Y/csl+jfcwMaLA7Ernzf3G6lUiomJCXp6msu0oUOHFsjeTHYYGhqyb9++D3IvAG9vbzw9PVm8ePEHu6e2kUhUmcgBHobE07RiMXQ+UF7HxPg0pn51gKR4lQtSw1bl+HpKIyQSCZ36V6dT/+o894smIiQRA0MdKlYvUSB1uDOpV69envrJZDKNXA//pX///ly/fj1XRWlhYZFjMpe8IhHy6fy4evVqqlWrps4G8yaRkZEUK1bsvQQqDOLj4zE3NycuLi7LDCk1NVUdP21gkPdsLQqFkk6VV2Jirs/a019iZpH12qjwJAY13YiRqR7brw/Js3XZzs6OQYMGMWfOHPW5Cxcu0LRpUwIDA1myZAlyuZyffvqJbdu2kZaWxnfffYcgCOzbt4/q1atz9epVfH19GThwoHqzPDY2ln/++YcXL17wxRdf0KhRI+RyOUeOHKFkyZLcvXsXc3NzOnbsyJ49e2jQoAEVK1bk1q1bnDlzhuHDh7Ns2TIEQeCHH37gzp07eHp64uLiorHP5Onpyc2bN3F0dFRnqc7Mku/h4cGqVauoWrUqgwYNIjg4mObNm1OqVCl69OihkfPyfT+jD83ZJ+GExqXS3dUWvWxKuxYECoWSn746wHWv54DK4r3sYC+tZgP6WHnb9/6/5Ptnw93dnYULF5KSkqLxxY6OjiYjIyPbjdfPkQtH/Al6GsO2a4OzVZIA1iWM+fHP1oxou5273sG4NMpbdh5QpY66e/cuSqWSW7duERoaStOmTXFwcKBZs2YMGjSIuXPn8uzZM+bNm4exsTEtW7bEy8uL7t27079/f27dukXjxo3x8/PDzMyMCRMm8McffxAWFkbNmjU5deoUKSkpDBw4kJYtW+Li4sKjR4+QyWQMGjSIM2fOULZsWby8vJgxYwYWFha0bduWwYMH4+PjQ9++fWnTpg1dunShXr16VKhQgZ9//plu3brRqVMnunbtyv3795k7dy5bt27l8OHD6Orq0qxZM7p27YqzszN16tShVatW6OjoZKskiypyhTLLjLH5v+ViP6S71eq5l9RK0szSgF82dBKV5DuQb0V57Ngx1q5dy969e7MoytWrV2tVuI+ZAxvvUdW1FM513x7/3rCVIzblLDiw0SdfijIsLIw7d+6gVCrx8fHR2L/r3r07K1eupFOnTowbN069GX7q1ClsbGwYMGAAXbt2pWvXrhw/fpxt27ZhZGREVFSU+jN0dXXlypUrjB8/nkqVKtGkSRMNN63MlYO+vj7u7u5MnTpVPTts164d/v7+6v2lypUrc/fuXUqWLMmmTZuwsLDAy8uLUqVKcf/+fUxNTWnUqBGXL19m8ODBgGr/ycfHhzp16uT5PSkqvIxJZuvVF3R3taVCidd7fB/aH/W45yM8V94CQKYjZeaaDpSxF4Mw3oV8K8ru3btTv379LH/AqampXL16VWuCfexEvEqkYh6KvkulEipUK0Z4cEK+xq9ZsyYDBw5UH2/dulWjfeHChdSqVYu///77jXup9jczc3lKJBJ1zSOlUknbtm0ZOXIkoKrf/uZ1b6bUyzyXiUQi0VACpqamGsd6enokJiby5MkTbGxsNMbOaQwTE5OPMjnGq9gUVp9/RoZCYOvVF4xqUZ5iJvofXI6Ht0JY/P1p9fHoOc3z9UMsosk7+VHa2Nhw8OBB4HWdGl1dXZo3b651AT9W9A10SE7IvZohQFJCOnrvuXner18/dWo1UNUtaty4sUalxOzQ09PD1tYWmUyWJdvSfwuWvS8ymYyHDx9q1D5KT0//pFKrlTIzoHxx1SyyhJk+BoVQYyYyLJEZQw+rY7g7DqhOl4E1PrgcnxL5VpRPnjyhSpUqTJ06FVAtwerUqcOQIUO0LtzHTO1mdlw6/oyEXFJkhQXHc/tiEHWal83z2DnZ32bOnAmoXGmeP3/Oli1bOHbsGF5eXjle/+DBA9q3b0/NmjXZsmULz549A1TxtTnV0skc4212wOzaKlSoQHp6ukYpjzVr1qCvn3XG9eb1UqlU6+GxBYVUKqF3XTtaVC7O103KYVIAPoiRoYms+uUiw1ptZWDTjUzqvYdzh/xQKJSkp8mZPuSQut5NjQY2jPlFnMC8L/lWlOvXr2f79u0MGDBAfc7e3p6kpCQuXryoVeE+Zr4YVouMNAWbl1x7a7+/f72CnoEOnQZUf2u/TGJiYoiOjubRo0c8efKEp0+f4u3tzaBBg9QRDZMmTeK7777Dzs6OUaNGMWrUKI0kAmvXruXhw4csXbqUbt26UaVKFfr06UPlypVp0KABvXv3plevXvTq1QulUklYWJi6OBiotlni4+OJiooCIDg4mIyMDLUyCwkJ4flzlQFBEATCw8OJiorC1NSU6dOn8/3339OhQwdatmxJpUqV0NfX59WrV8TGxgIqh/agoCB1MpQqVapw6tQpVq1apb5nUSE5XU5CquYWgYGujNbVSmnd/UcQBJZNP0cru6WsnXcJIxNdbMpZ8MIvmtGddtK5ykqmDznE49uqEhslbExzjOEWyR/5/rmztLTEw8NDI0QoMTGRmzdvaiz9PndKlDFl8A8NWDHrAqYWBvT5tg46b7iEZKQrWLvgMlv+vM6kRR7Zxtr+l/T0dE6ePMmKFSsA1FUOQZWSrn79+jx69Ah3d3f18rZ58+ZqdyB3d3cAevXqxePHj3F3d1eXotXT0+PChQucO3cOQRBwd3dHV1eXy5cvM2PGDEBVl6dSpUqcOXOGFStWoFAoCA0NJS4ujnXr1nHx4kWcnJyoW7cudevW5fr16ygUCqZPn46uri7R0dFMnjyZNm3a8PTpUxo1akTp0qVJSEigVKlSzJw5kytXrqCrq8vs2bORSqXExcUxZswYnJ2dqVChAtbWhZug4U0iEtLY6B2Iga6MYU0dC9zlZ/EPZ9iw8AojpjdhwPj6Gt4U96+/YvwXuzmy7QEW1kYYmerxy4ZOWq9387mSbz/K58+fs3jxYlJTU+nfvz8+Pj4sXryYjIwMfHx8sLCwKCBRC46C8KMEUCoFFk46xabfr1HKzoxOA5yxLmVCWFA8BzbeIyosiVGzmjHi5yYfzCJasWJFlixZQocOHT7I/T4EheFHKQgCS8/4q7OP1y9nRddaNgV2v8d3QulZax2TFnkwcEL9LO03L7xgUu+9xIQnIZVJWbyrO26d3s/J+lOnQP0o7e3tmThxIgsXLmTWrFnIZDJ69OjB2LFjP0olWZBIpRJ+WNyKjv2d2bniFrvX3CExPg0zSwNa9ahC75G1qVCt+AeTJyMjg8jISPWyWOTdkUgk9Kxjy6pzz7A00sOtcsF+jtuX36SEjSlfjq2bpS04MJZZw48gAYxM9EiIS8O+UtGZeX8K5HtG+SlSUDPKosaJEycICQlBV1eXhg0b5lqt8WOhMD+jF1HJH8S67VZqCV0G1WD8gpYa55MT0xndaSeBT1R7t/Va2nN6ry/fzmrGoEkNshtK5F8KdEYp8vHSunXrwhbho0WuUPIwJJ4athYa58t+oD3AxLg0ipfWTFChVArMH3tcrSTLVrTi5xXtuHHuBYnxeXNNE8kboqIUEcmFlHQFm68851lkEsnpCho4fvhlrZmlAWEvNYMSNi6+yqVjKncuYzN9ftnQCalMSlxUCqY5hM2KvBv5NtOlpKRke/7FixfvLUxRRtyhKLoU9GfzJCyBZ5Eq16dj90NJKoQ61+7dK3Nw0z21E/n5w35sXKyKhJNIJfy8oi225Sw4tv0BaalyWnYVDTnaJN+Kcvny5dme379/P35+fu8tUFEjM9wvOTm5kCURyYnMzybzs9I2LnYWNK9UDBN9GUOblMO4gBPZZkefUbWJCkti7YLLPHsUyYLvTqrbhk9tTL0WDkRHJLHql0s0aVceO0exaqY2yfMnHh4ezvfff8/NmzezOJYnJSVx/fp16tSpQ8WKFbUuZGEik8mwsLBQOz8bGRmJxbaKCIIgkJycTHh4OBYWFshkBWdQaVOtFA3LF8PcsGCUcW6UdyrOt7Ob8df08+xYfgNBAJlMiscXVegxvBbepwKYN/o4qckZ/LSsbaHI+CmTL6u3r68v/fr1o1u3bhrnZTIZlStXznJeWyQnJ5OWlpan2tJRUVEYGxvny/qZm/Urs2hRZuSISNHCwsKCUqVKae0HzPtpFPbWRpSx+DAlGvJKerqcPnXW43c/AgQwtzKgZiNbAh9H8cI/hqq1SvLbju7YV7TKfTCRfFm98+0eFBcXl2O97KSkJIyNjfMzXK7Mnz+fhIQEqlWrxrlz51i+fDk6OlknwmlpaQwZMgR3d3dCQ0MxMjLKc/7CvL5hCoXio8xo8ymjq6urtZmkIAgcuRfKRf9IzAx1GNW8AuZGhTODzI4lU7w48I8PSqWATCahSq1SABQvY0Lnr2pQq7GtuNrJB1p3D0pLSyMlJQULCwsSEhIIDAzUaBcEgaioKKKjo+nZs+c7C/5fzp49i6enJ7duqXLq+fj4MG/ePKZPn56l7/z58ylRooQ6OUeDBg1wdXXVagldmUxWoMs7kcJFrhR4Ea3a74xPkfMwJJ6G5YuG4/a+DXc58I8qu5O+gQ6/7/kCJ9fShSzV50OejDlz5sxh0KBBgCpxr4uLC/Xq1aNBgwbql4eHh9YNHn///bc6PhnAw8OD1atXo1Qqs+3r4eGhPnZ3d2flypValUfk00ZXJmVAQ3uKm+rT3dWmyCjJWxeDWPbzOfXxhN/cRSX5gcnTjHLatGlqt6BevXqho6OjVpyZxMXFce7cuWyufncePnyoUYjIwcGB4OBgXr16ha3t6ySkiYmJvHjxAgcHB42+b9b9FRHJCyb6OoxtWeGDFf7KjczwxMzqib1GutKmZ9VClurzI09/DQYGBmpDipmZGYMGDSI0NBRvb29evnwJgLm5udYTLfj7+2vsHWTujWbeM5OnT5+qZXuz73/7ZZKWlkZ8fLzGS+Tz40VUMjtvBKFUam7TFxUlmRifxk9fHSAh9t/EG+4ODPspa1E/kYIn338R6enpfPnll5QpU4ZGjRpRrlw5GjVqpC46pU1MTEw0ltmZqcNMTU2z9AOy9P1vv0zmz5+Pubm5+mVnZ6dVuUWKPg9fxbP24jNuv4hl/93g93ZaVyiUeB3wZUS7bTQw+w1X/QW0r7CclXMuEBmamPsA/0EuVzJ7xFGC/GMAVXji1L/aIisiSvxzI9/v+rJly/D29ubIkSOkpKSQnp7Oxo0bWblypdb3KB0dHYmLi1Mfx8XFIZVKKV++vEa/smXLIpPJsvTNqZbvlClTiIuLU7+CgoK0KrdI0cdAV0qmboxKTEeufHdFGR+byjCPrYzt4klcVArDpjZm4kJ36jQvy7r5l2lffjnnDuUvGGPFrPPcOPu6euLcfzphYvbha++IqMh3iEFUVBTz58+nbdvXTq0VKlRg7NixXL58WcOg8r7Ur19fI0Hww4cPcXZ2zuIjqauri6urKw8fPqRGjRrqvjlV8NPX18+2/IDI54NjcRN61LblSVgC3WvZvPNyWy5X8l1XT3x9wllzqh8N3DUzMk1c6M70IYcY130Xa09/Se2muZf82LfhLnvX3QX+rZ64tgM2DhbvJJ+Idsj3X8fAgQN5/PhxFsuzr69vttbo92HkyJF4eXmpZ6q7du3ihx9+AFT7jDNnzlSXH5g4cSKenp7qtjNnzjB69GityiPy8ZLd0rqmnQW96ti9157kmX1PuHHuBUv29siiJAHMLQ1ZuKM7VWuV4o8pXtmMoMmN8y80LNzj/9cSl4Zi9cTCJk8O51OmTGHDhg3q48TERHR0dDRmdklJSTx79kxd71lbXLt2jePHj2NmZoaRkRHDhg0DUPtsbt68mdKlVa4SGzduJC4ujujoaFq2bEnTpk3zdI/8OJ6KfHwkpsnZ5P2cphWL4Wyj3brWX7tvIT1NzsaLA9/a7+Tux0zosZtdd7+mco2S2fYJeBLF2M47SUpIB6D3qNp8M62JVuUVeY3WHc6bNWtGmTJl1Mva7ChevLjWlSRAvXr1NFyEMrGysuL06dMa57766iut31/k4yYxTc6Ks/5EJ2Ww43oQpgY62FtrJ3pMEARunn/BxIXuufZ161wRXT0ZN8+/yFZRRkck8dOA/Wol2aiNI19PaaQVOUXenzwpSg8PDzw8PHLMzhITE8OOHTvUhapERIoKxnoyyhUzITopBiN9mVYLgCkUAnK5EmNTvVz76urK0DfQIT1VkaUtNSWDnwcfUuebrFi9hGjhLmLkSVG+qSAzq+29ydOnT7l06RLdunWjZMnslxUiIoWBRCKhq0sZ9HSkNK9UXKvZf3R0pFiXNMb3XkSufV89jyMxPo0SNpouawqFknmjj/PoVigAxUqbMHdjJwyLUIy5yDtYve/du4eJiYnadxFUS5CSJUuSkJAgKkqRQkUQBFIyFBjpvf7T1pFJ6VyzTIHcr9OA6uxZd4exc93eqtw8V93CxEwft86aaQhXzr7AxaOqgAlDY13mb+pMsZIm2Q0hUojkW1F+/fXXODs7Zzk/depUDA2LVloqkc8LhVJg3+1gnkclMcKtvIayLCh6jXRl8x/XmPvtMWav64hUmjV7z53LL9m85Bq9RtbGyPj1Mn3PujvsXnMHAKlMwsw1HSjv9OGqcorknXxvgjg5OaFQKDReUVFR3L17lytXrhSEjCIieeKQzytuPI8hIjGdLVdefJDyHXaOlsz5uxMHN97jmzbbuHzymTokMiw4nuUzzzPMYwvV6pZh7Fw39XXnD/vx13RNN6C6bvYFLq/Iu5Hvn9yhQ4dquApl4uLikmd3HBGRgqBZxeLcD44jNUNJfUerD5abseOXzphZGrDkRy++ab0NU3N99A11iA5PxsBIly+G1WLcghboG6i+bj5Xg5n77XF1ZFD/cfXo0C/rKk2k6JDvxL3Lli2jUaNGGgl6jY2NNbL5fGyIfpSfDkHRySgFQWsuQPlBEARuX3rJncsvSU+TU8rODI/uVTRCD589juS7rrtI+recbJveTvyw2ENMuFsIFGiG87ygVCq5ceNGtv6PRRFRUX6cPI9KoqzVx1PDKPRlPGM67SQqTBVNVsfNnrn/dEJXV0wGXRho3eH8TXbt2sWsWbPe2icmJoa5c+d+NIpS5ONCEATO+kZw4kEYLauUoJVT0fe0iItOYXK/fWolWdmlJDPXtBeV5EdCvhWlTCajadOmNGnSRJ1WLT4+Hi8vL7p06QKgkchCRETbvIpL5eTDMADOPA6nYgkTHIp9+KV2XklKSGPyl/vUKdNsylkwf1NnDQu4SNEm34ry+fPn2db2fvToEQ0aNMDeXmW58/HxeX/pRESywcbCkPbOpTl8L4Q21Upib21U2CLlSHqanJ8HH8L3rqrcsXVJY37d1hWLIiyzSFby7R5kZmaGn59mbr2MjAwuXrzI7du31efeFhcuIvK+NK5gzeiWFXCrXKLI7lFmZCiYNfwIdy6rMu2bWhjw6/ZulC6r3cQcIgVPvmeU/fr1o3v37hQvXhxHR0ciIiI4evQoiYmJNGzYsCBkFPnMeRKagFQCFUu+Dv+TSCTYFLG622+iUCiZP+Y43icDADAw0mX+5s6Uq1w0CpaJ5I98zygNDAw4ePAgHh4eBAUFERISQp8+fbhx44YYviiiVQRB4IJfBP94B7L12gvCE1ILW6Q8oVQKLJx0mrMHVCsvPX0Zc//pJFZO/Ih5pxgvmUzGgAEDGDBggLblERHRIDAqGUGA1Awl1wKi6VijYGK2tYVSKfD75DMc36EyaOroqjKU12os1mX6mBHzOIkUWSQSCb3q2FLa3ICWVUrQoXrRnpEJgsCyn89yeMt9QBW/PfWvttlmPhf5uCj4rAGfML/++qu6NAXA9evXOX/+PPr6+nTq1EntATB//nymTJmS4zgnT57EzMyM+vXrIwgC//zzD8nJyejp6TF48GC1G9apU6ewtramVq1aBftghYggCBrGGX0dGSPdyqOrpdyMSqXAldMB7Fp9m2cPIwFwdCpGz29caeDu8M6GIUEQWDrtLPv+Vnl7SKQSflrWhuYdK+ZypcjHgNZmlNeuXfsgSQiKEhERr/MQXr9+ndGjRzNu3Di+/PJLevXqRXi4yiXEwsKCe/fu5TjOnj171IXQfvrpJ169esWoUaOwtLRUl74AVbkNbVe6LErcfhHDinNPSZNrJrfVlpKMDE2kf8MNfNN6G4FPomnYqhwNW5Uj4HEUw1ttpX/DDe9UWlapFPjjpzeUpAQmL2lFyy6VtSK3SOHzTjPKs2fP8uDBA+RyOaAKWTx06BCTJk2iXbt2WhXwY2HWrFl8+eWXyGQyLC0tqVWrFitWrGDGjBn069ePBQsWMH/+/CzXhYSEULJkSWQyGVFRUfz+++88f64qU9q9e3eGDRvGDz/8QJUqVT70I31QLvpFcvheCAC7br6kX72yWnX7SYhL5Wv3LSTEprLuzJfUdbNXjy8IAte8njOl/36GeWxl46WvMDU3yGVEFQqFkt8nn+HI1geAaib54x+tafXFp/15fW7k+6fa09OTsWPHcuzYMX7//XfOnj2rrl3j6uqqdQE/Fi5cuKCxJHZ1dWXXrl0AmJubk5qaSlpaWpbrNm7cqK71c+3aNaytrdXeAxKJBBcXF3bv3v0BnqBwqVTKBP1/yzQY6sp4jzLb2bLp92u8CoxjzekvqddCc4ktkUio39KBtae/5OWzGDb/cT1PY8rlSuaPPaGhJKf8KSrJT5F8K8qoqCh8fHw4ePAgLVu2xNPTk0OHDtGyZUuMjIpOtIEgCOqlb0ETFhZGfHw8VlZW6nOWlpYEBgaqj7t27cq+ffuyXBsQEICjoyOgKvn75hjZjfOpUsLUgF517OhcswzdatkgyyYB7ruSkaFg1+rbdPqqOo5Vci6A51i1GB36O7Nr9W3k8reXXk5PkzP7myOc2fsEUNXfnra8LR7dRSX5KZJvRVm2bFl27NjBs2fP6NevHz/88ANPnz7l6tWrnD9/XusCenp6MmnSJJYtW5bt0vVN1q1bh0QiQSKRqJeyH4Lo6GgAjfK9hoaGJCcnq7cnmjdvnuX9OXfuHG5ubhrjvDlG5jhxcXEFJHnh8SwiMcuetlMZMxqWt9Z6pI3fvXAiQhLp2D/3nI8d+1cnPDgB//s5/8gmJ6YzZcABdQkHHV0ps9Z1oEXnSlqTWaRokW9F2bx5c3bu3MnOnTvx8PDAxMSEGjVqcPv2berXr69V4Xx8fJgxYwYLFixg9OjRBAQEsGrVqhz73717l9DQUEJDQ4mMjKRq1apalScnMq3biYmvDQEJCQmULVsWHZ3X28C2trYEBwerj/fv30+3bt3Uxw4ODhpjZI5Tvnz5ghL9gyNXKNl3O5g1FwK4/PTD/JClJGUAYG6deySPZTFVn+TEjGzbY6OSmdhrD7cvBgGgb6jDvE1daNTKUUvSihRF8q0ojYyM2L17Nz/++CMAs2fPJjw8nKtXr2q9rvfKlStp2bKlWtl07NiRJUuWZNvXy8uLhw8fcvbsWUxNTbMsYQsSIyMjbG1tCQ0NVZ8LDQ2lcmVNq2dkZCSWlpbqYysrK41Zb6VKlQgLC9OYaWU3zsdMYFQyVwNUM/Aj90KITMy6b6ttLIuptoRePo3JtW/Qv30si2fdRnr1PI7RnXby5I4qc5GJuT4Ld3anTrOyWpRWpCiSb0W5ePHiLOeMjY3Zt2+f1vfS7t69S6VKr5czlStX5vHjx4SFhWXp++jRIwIDA+nTpw/Ozs7cunVLq7LkRs+ePTXK+F66dIkePXqoj5OSkpDJZBr7uAMGDGDjxo3q4wYNGmBiYqJOU5ecnMzjx4/p2LHjB3iCD0OFEiY0r1QcXZmE7q62FDPRz/2i96RcFWsqVi/B7rV3cu27e80dqriUxKGS5g/tE58wRnfayatA1TaIdUljluztQbXaRdsJXkQ75Nk9KDw8nJkzZ3L9+nXu37+v0ZaUlMT58+dxdnbGwcFBa8L5+vpibv4600rm/4OCgrLElY8aNYpRo0Zx584dhg0bRq9evXjw4AH6+lm/iGlpaRoW6Pj4+PeWddq0afTp04erV68SGhqKUqlk8ODB6vYdO3bQp08fjWvs7e158eKF2slaJpPx999/M2fOHObOncsff/zB77//rvWZ+ofkvw7kAK2dSuJqb0EJ07y54LwvEomEvqNr88vIY5w75JejE7jXAV/OHfJjxur2GjJfOv6UX0YdIy1Ftd9sX8mKBVu6UNJGzIb/uZDnGWWJEiUYNmwYSUlJFCtWTOPl6OjI/PnzadasmXaFk0qzuHFkns8JFxcXTpw4oa4MmR3z58/H3Nxc/bKze/84XCsrKw4fPowgCNjY2LBnzx51RA3AzZs3s3WfatGiBV5eXupjd3d3/vrrLwIDA/n+++8ZMmTIe8tWWMQlZ7D2QgBPIzT3XaVSyQdTkpl0H+pCiy6VGNd9F6vnXiQ6IkndFh2RxKpfLjLhi924d6tM18E1AZWS91x9i+lDDqmVZPX6ZfhjX09RSX5m5MvhvFatWpw9e5YSJUpkacuMzMmLxXLx4sWEhITk2N61a1caN26Mo6Ojxmwv0/r75nI8OywtLWncuDExMdnvSU2ZMoUJEyaoj+Pj47WiLHV1dWnQoEGW8w8fPqRatWrZXtOlSxcmTZpEy5Yt1eesra1xd3d/b3kKk8jENFacfUpyuoKI60GMaVkBUwPdQpNHJpPy245uLJp0mlVzLrJy9kUq1yyBIICvTzgSCfQZXYcJv7ZEJpOSka7g9x/PcGz762z9LbtVZvLvrdDVE8s3fG7kOzKnRIkS7x2Z86aSehsuLi48ffpUffz06VMcHR0xMTHJ9dqMjIwco1n09fWzXZIXFFu3bmXSpEnZtunp6WFiYkJ0dPQHNUAVNNbGethYGOIXnohMKiExTV6oihJAV1fGj3+05pufm3Bg4z0CHqlivdv3q0bnr6qrs45HhScxa/gR7l97pb52wPh6DJrUoMgmCRYpWPKtKD09PZkzZw729vbcu3ePWrVqkZGhcqXQdmTO8OHDGTBgAAqFAplMxtGjRxk1ahSgUs47d+7kiy++QCaTsWXLFrp06YKZmRkvXrzA0dFR7bZTULRq1SpP/dzc3LCwsMixfcSIEURGRuaqKCtVqoSpqelb+xQVJBIJPevYcuJBGO2ql8JIr+jkX7EsZsTACdm7sj24GcLMrw+ri4Dp6cv4QYzb/uzJd7nalStXMmLECACGDBnC6tWr0dHRYe7cuYwdO1brX+QdO3bg4+NDiRIlePXqFfPnz0cqlRIWFoarqyuXLl2iTJkytG/fnuDgYMaNG4e+vj79+/fX8GF8G2K52vdDEASuB8ZQoYQJVh9pwSxBENi3wYcVM88jz1BF5RQrZcycvztRuaaYkPpTpEDreh85coSEhATq1q3Ls2fPOHLkCN9++y3jx4/nm2++oUOHDu8lfGEgKsp3Jzldzq6bL3kUkkBZKyO+aeaIVIvhhx+CpIQ0Fk46zbmDr2tB1Wxow88r22FVvOhWdxR5P/LzvS/SkTkiRR+ZVEJ4vMrV6kV0Mk/CEgpZovzx6HYo37TZpqEke35Ti1+3dxOVpIiafM8osyMpKQlDQ8O3uu0UZcQZ5fvxIiqZLdee09XFhqqltfP+RYQkcHDTfV74R6OjI6Wqayna9a2mtVrYCoWSHStu8vevV1D8mwDD2EyfyUta0aTtpxMyKpIzBbb0jomJYcmSJdy8eZOwsDCcnJxwc3Nj4MCBH62ShIJTlD/99BOHDh3i9OnTFC9eXGvjFib+4QnYWhphoKvpIpOhUGolwW5KcgbzRh/j0Kb76OrJcHQqhjxDgd+9CIxM9Bg6pRFDJzd8L+vzq+dxLPjuhIZVu6prKab+1ZYy9mIp2c+FAlGUt2/fplWrVkRHR1OhQgUcHR3x8/MjICCA+vXrc+DAgY9WGRSEogwICKBChQoolUqePXtGuXIfd92UlHQFR+6FcON5DHUdLOnuaqv1e6SlyhneeiuPboUyek5zug6uiZmFyjH91fM4Nv1+lc1/XKf/uHpM/j1vHgdvolQKHNx0j9W/XFQnypBIoO+YugycWB9dXdE/8nNC63uUcrmcoUOH4uHhQXR0NL6+vhw7doynT5+qEz389NNPWhH+U+GPP/5AqVTSunXrj15JAqTJFdwLVjn8Xw+M4UWU9ktSrFtwmfvXXrH6RD++Gl9frSQBytibM3lJa6b+1YbNS65x6fjTt4yUleDAWCb23M0fU7zUSrJ0WTMW7+7B1z82EpWkyFvJk6I8fvw4derUYfv27Vn8Aa2srDh48CBBQUEfLP9jUScmJoa1a9cC5Oho/rFhYaRHW+dS6OtI6epSBjur3FOW5YeMDAWeq27RbUhNXBrlPFvtPbI2VVxKsv2vm3kbN13Bxt+vMsRtM3e9X6e46/ClM2tOfUnNBjbvLbvIp0+eHA0fP37M1KlTc2yXyWR88803+Pr60rBhQ60J97GyatUqkpKSqFGjBh4eHoUtTr5RKgXuvIzFxdZCw9WnfjkrnMqYYVYAETY3z78gMjSJL4a9vcKkRCKhx/BazBt9nKSENIxNc46wun7uOcumnVOnTgMoZWfGpEUeuDYR62yL5J08KcqQkJBco1zKly/PvXv3PntFmZaWxp9//gmoZpMfW8jbq9gUdt98yau4VFLSFTSu8DpzkUQiKRAlCRAdrlrKl61gmUtPsKtgiVIpEBedmq2iDA6MZcWsC1w+/kx9TipTKdivJtTXmuVc5PMhT4oyOTkZLy+vt9bEuXXrVpGqmVNYbNu2jZCQEMqUKUPv3r0LW5x8o1AKvIpLBeDUozBq21tmsXAXBEYmKgUcG5Xy1lkiQFxUCgCGxppKOy4mhc1LrrF/g486ugbAqXYpxv+vJeWdPk5jo0jhkydFmZKSopHdJic2bNjwvvJ81AiCwKJFiwD47rvv0NP7+GYudlZG1LG3JDg2hS4uZT6IkgSo1cQOA0MdDm+5z/CpTd7a99Dm+1R1LYWFdWbZhnR2rbmN58pbJCWkq/tZlTBi+LQmtPqiykc3sxcpWuRJUTo6OnLp0iWMjbOPVBAEgRcvXmglAe7HzIkTJ7h//z4mJiYMHz68sMV5K4IgcD84nhfRyXSooZmlu0ON0ujJpB80FNHc0pB2fauxbdkNug91oVip7DNE3fF+yYUj/sxY3Z6UpAz2bbiL58rbxEWnqPvoGejQe6QrvUfWxsjk4/uxEil65ElRDhw4kLJl314XxMXFhaCgIK0I9bGycOFCAIYNG/bWbEFFga3XXnA/WPXDVrW0KY7FXyumDzWL/C+jZjXj4tGnDG25hV+3ddVIRqFUCpw75MfUgQepUd+GmMgU+tb7m4TYVHUfqUxCuz7V+GpCPYqX/jiyLIl8HGglhPFjRxsO53fu3KFWrVrIZDKePn1a4Cne3pcbgdHsvqVyl2ngaEUXl6LhJhPoG8Xojjt57hdNrca21Gxoi1yu5MJhf577RWNTzgKlUkCerlBfI5FKaNGlEoMmNcC2nEXhCS/yUZGf733RSRL4kZO5N9mzZ88ipyRD4lKwMNTD8I3M3K5lLfELT6RWWQsqlyw6sy+HStbsfTCcswf82L32Nmf2PyE9TYFEIsHC2pC0lIzXJUFkEty7Vab/d/WwK5+7tVxE5F0RFeU7kpSUxLFjx2jTpg2xsbFs374dKFoO5lGJaRy5H8rDV/G4VymBh9PrpaxUKqFvvfyXWc3IUHD2gB8PboSgkCuxdbSgbR8nzC2154CuqyvDqXYpgp46EB2eTMq/tc4zSzAYGOnSvl81egyvRSlbMYmJSMEjKsp35K+//mLy5MnMnz+f6Oho5HI5LVq0oHbt2oUtmhqZVMKTUNU+5EX/SBpVsH6vTOOeq2+xYuYFIkISKWNvjq6ejODAWBZOPEW3oS5MWuiOnv67jx8XncK5Q36c2vNEI2FFJqXszOg6pCbt+1bDxOzDlfIQEREV5TuS+O8s59mzZ+zYsQNQzSaTkpJy9A4oSDIUSuJSMjTqZFsY6eFa1pInYQk0q1j8vbL7rJxzgb+mn6fzwBoMnFifStVVBeYiwxLZveYOa+ZeIuBxFMsP985X8a3oiCS8TwZw7qAfty4GoVRobplLpBIauDvQeWAN6jQvi0wLGYpERPKLqCjfkUzn+rt37xIfH0+VKlU4evQoHTt2ZOXKlR/MPUipFDj5KIwbgdGYGegyumUFDZ/Bts6l6FyzDDrvoWBuXwrir+nn+XZ2M0b83FSjrVhJE76Z1oRajW0Z0XY76/53OUufNxEEAf8HEVzzes6VkwE8vBlCdubEshWtaNu7Kh5fVKFYydyLyYmIFCSionxHDA1Ve3L3798HVApg2bJlAB803ZxUKuFZRBKJaQoS0xQERiVTrtjrGa02inptXXoDh0pWb3UEr9fCgW5DarJzxS2GvpGNRxAEQoPiuesdzM0LL7h1IYiYiOwzD5W0NaV5p4p4dK9CeadiopO4SJFBVJTvSOaMMjk5GalUypMnTzAxMWHz5s106dJF6/cTBIEX0ckERafQpGIxjbb6jlYExybjXMYco2yWvQlxqVw6/oz46BSMzfRp2KpcnsscpKXKObX7MeMWtMjVAb3nN7XYufIWe9ffRVdPxoPrr7h37RURrxJzvMahsjWN2jjSpK0jlWuWFJWjSJFEVJR5JCNDwZl9vhzb/oDo8GSC4u6o25RKJeXLl2f//v1Uq1ZNa/dMTkrn6LYHXDkViG9QLBmGOtg2s8F5YhMs3kjsUN3GnIolTLLUzY6LTuHPqWc5uOkeKUkZSCQgCCrrceueVRk3vwWl7N5uNY6LTkEuV1KuinWWttSUDAKfRPH0YSR+9yLwvRsKwJLJZzAwyj55hoGRLi6NbKnbwp76LR3EjOIiHwVFXlGmp6ezd+9eLl26pM7KkxPbtm0jODgYpVJJmzZtqFmzplZkuH0piEm99xIenEDNhjaUrWDF0xuvZ0lVK7hy8erJXOty54WUdAWv4lK4s9+PRZNOkxifhksjWwz1ZIQ9iiLo9At6bX7MX3t6UNFZZVDRlUmzGGqiwpMY3HwTUWFJDP6+Ad2GulDSxpSYyGQObrzHxsVX+bLB3/x9bgBlK+Qst76Baob66HYYyYkZBD2NIdA3mue+UYQ8j9PYX1QqVIko3pwV6hvq4FS7NDUb2lCrsS1VapUSk+SKfHQU+cgcPz8/tmzZwv79+7l9+3aO/fbv38+qVas4cuQISUlJNG7cmIMHD2Jnl3vewbd56PtcDWZoi81Uq1uGn5a1UVt7/f39qVunLiUsKqD7vBPfL2rDwAnvV4Vy5/Ug7ryMJfBoAPfW3KPbkJp883MTbBwsiEhI49DdYHRfJrNn3mVCgxLYdOmrHDPifNNmG0/uhrHh/AAcKmWdDUaGJjLYbTMyHQmrT/YjOiyJiJBEwoMTCHuZQGhQPCEv4gl5HktwQBxSmQTzXJL1Jielk5yQTueBNXBtYke1uqVxrFpMVIwiRZJPKjKnYsWKeSqlMG/ePL799lsAjI2NadCgAStXrmTu3LnvfG9BEJjx9WEq1SjBquN90Td4/XZVqFCBmFhVQthF35/m9x9O06ZX1VwdoJ9FJBISl0pqhgL3qiU12gz1ZCRHpHB/3X3aDq3JrDUd1LOz4qb6DG7iCECXdhUY0OgfZg0/wsaLAzXGyMhQcO9qMJdPPOO7+W68eh7H4zthxEWlEPvvKyYimZiIZJRKJYEPYujuvPqt/o8GxrokxqWRka5Qu/7oG+pgX9GKclWLUd6pGKXtzZk17DDN2lfgl7875fEdFhH5OCjyijIvyOVybt++TfXq1dXnqlevzqpVq95LUd66GIT//QhWndBUkv/lm5+bsHPlLXavuc3w6U3xD08kIVWOqYEOVUqZolQKKBUCcrmSnRcDiYhLRQZUMdRHqRDISFeQniZHCE7kuacvOnpSXBvZcNzzEWkpctJSMkhJlpOanKH6f1IGxUoZc/XMcwY22whAckI6ifFppKXISYxPQyqVsOWP6281jgiCgExHSmqyPFtFKZVJKGljSkk7M+5ceklSQjpDJjdU/SDYmauNOy8DYvm+9x6SEtIZNavZO7/fIiJFlU9CUQYGBpKRkaGRscfCwiLHbEZpaWmkpaWpj3NKD3f2gB8lbExp4P56Rjt10EFueb8kPjUDQQBTfR30daRIpBLW/c+bQ1seEJ2QhqAU0JFKMPjP3mFKhoKMf/fyrupfRPYfRRYdkYSurow1086/9ZkFQUAigce3Q7MkulUolMh0pW9VkhKpBOvixkhlUtLT5HQeWINipYwpYWNKiTKmlLIzo1hpE3R0VPLHRiXzXdddLP7hDEe2PqB5p4ro6sm4dzWY84f9sS5pzOqT/bJd5ouIfOx8EooyOVnll6er+9rSqqenp6EM32T+/PnMmjUr13ET4lIpVspYwy0mKT6NxNhU0jJU2WuS0hRkyKQoFUoUciVpyRko/m1TKCXwH0WpK5Mik0qQSSRIs1FkghKkeXAOl0gkSGVSlEpVpm9jUz2MzfQxMdfH1ycceYZCVe7V0hAzSwMsrA2xsDbE3NoQq+JGmFkaIpVKmDJgP68C4xg3v8Vb72dhbcTf5wZw+cQzdiy/yd51d5DLBWwdLZixuj3t+lYTSyyIfLIUiqLct28fcXFxObbXrVsXJyenPI+XuYeZkJCgPhcfH0/FihWz7T9lyhQmTJig0Tc7o4+ZpSERrxJVM7R/lZd1SWOK25oRm5IOEgnmBjqYGOjy3C8aAPtKViSkyZHJpOjrSTEx1EUqlaCjK0OmI0WmI0VX999/9WRvvKToGeiwdekN7Cta0emr6ugb6KBvqIOBoQ4GRroYGOpiYKSDkYkeegYyermu54uvXfhunqaS27TkGot/OE2/MXWxLpGzv2RaqpyLR5/SeWCNPL3PUqmEJm3L06Rt+Tz1FxH5VCgURVmjRg1SUlJybC9Tpky+xjM1NcXOzo6goCCqVq0KwMuXL9X//y/6+vro6+eeVMGje2X+/tWbS8ef0ax9BQB+XtEuS7/42FTcy/zBsKmNcy1jkBtJ8ensWXeHzl9Vx8Aw50Je5w/7ERORTMuulbK0df6qOn9M8WLzkmtZlOib7Pv7LrFRKfQa4fpeMouIfOoUSoYBR0dHqlWrluPrv9nBc/JgygwfBBgwYABeXl7qYy8vL7766qv3krN6vTJUdS3F0qlnSU5Mz7aPIAj8OfUscrmS7kNd3ut+AL1GuJIQm8r6/3nn2CclOYO/ZpzHqXYpnOtm/VExtzJkyOSGrJ1/me3Lb2T7/p3c/Zj/jTtJtyE1sa/4/v6fIiKfMkV+jzI5ORlvb28CAwMJDg6mTJkySCQSQkJCqF69On5+flSoUIGffvqJr7/+mh07dhAYGEjDhg1p3779e91bIpEwZ31HBjbdyJAWm/nxj9bUbGijNpK8DFCVRT3wjw8/r2yXY52X/GBX3pJRs5rx1/TzpKbIGfJDAyysX1e39L0XztxRxwh4FMXf5/rnaLAZMb0pcdEpzP32ONuW3aT70JqUtjcnKiyJ/Rt8eHAjhNY9q2Y7QxYREdGkyDucv3jxQmPvsVKlSmqjTXR0dJZomPDwcPT19TE3z3toXG6Opw9vhfBDn30894umQrXilK1oSWxUCrcvBmFips/3v7ei22DtRAGBapa6/ldv/pp+HokEGrctj5mlAYFPorjrHUwJG1MWeXbHpaFtruPcOPeCbX/dwGufL3K5EokEGrVxpM+o2jTrUPGDFhATESlK5MfhvMgryg9BXFyc2p0opzdMqRS4fuYFJ3f7EhuZgqGRLnVblqVVj0pZ6ktri5jIFA5tfMCNs0GkpsixKmFE656VadqhHDr5jHaRy5UkJ6RjaKybr3yRIiKfKplG3NjY2FwnVqKiRGX4yUuoo4iIyKdHUFAQtrZvX52JihJV9p9Xr15hamqapzRfmb9Eb5uBfux8Ds8I4nN+auTnOQVBICEhgTJlyiCVvt2uXeSNOR8CqVSa6y9KdpiZmX3Sf3TweTwjiM/5qZHX58yrLUMsQCIiIiKSC6KiFBEREckFUVG+A/r6+syYMSNP0T0fK5/DM4L4nJ8aBfWcojFHREREJBfEGaWIiIhILoiKUkRERCQXRPegfJCYmMicOXMoW7YswcHBjBkzhtKlSxe2WAVCaGgoSUlJ6uMSJUpgampaiBJpH0EQCAoKIiMjQ32ubNmyGnlNP1aSk5Px8vLC1dX1k/0b/S/JycmEhISojw0MDLCxsdHO4IJInhkwYICwevVqQRAE4dGjR0L16tUFuVxeyFJpn//973+Co6Oj4OLiIlhbWwsNGjQQLl26VNhiaRW5XC4MHTpUsLGxERo0aKB+zujo6MIW7b1JSUkRfvnlF2HTpk1CpUqVhJCQkMIWqcC5e/eu0KJFC8HGxkaoUKGCUKlSJWHSpElaG1805uSR0NBQbG1tCQkJoXhxVeVDJycnfvvtNzp06FDI0mkPhUJBeHg4y5cvZ9q0afTv3x9PT8/CFkvrREVFYWRkxMyZMxk5ciTLli1j4cKFhS2WVoiJicHMzAyZTMbw4cMZN24cTk5OCILAiRMniIyMVPetXr06NWrkLXFzUSYoKIjk5GQuX77M06dP6d+/P1WqVNHa+OIeZR7x8fHB0tJSrSRBpShPnDhRiFJpH5lMRunSpUlOTubJkyc4OjoWtkgFgrW1NcnJyZibm3PmzBnq13+/UsNFCUtLS2QyGceOHSM9PZ1KlVTJnVesWMHKlSvZs2cP8+bNw9vbm9jY2MIVVkvY2dlx6NAh2rRpw61bt6hcubJWxxcVZR7x9fXNEu5kbm7Oy5cvC0miguO3336jWrVqBAUFERER8UnOKOVyOWPHjqVjx44EBQXx/PlzDh8+XNhiaY20tDSsra0JCgpi06ZNAAwePJiGDRuyatUqKlWqxLJly2jW7NOomvnkyRMuXLhAmTJlePXqFYcPH+bp06daG19UlHlEoVAgk2mmJ5PJZCgUikKSqGBITEzk2LFj9O7dGycnJ54+fYqDg0Nhi6V17ty5g46ODjVq1KBJkyYcO3aM2rVrF7ZYWkNfX5+6deuyZMkSrl+/DoChoSHBwcFIpVIMDAxQKpWFLKX22LBhA0OGDAGgUaNGXLt2jfLltVfbSdyjzCMHDx5k+PDhGla13r17Y29vz6+//lqIkomIaJKWlkZYWBhly5Zl69atlClTBjc3N6ZPn46xsTG9evWiY8eO9OrVixkzZhS2uB8FontQHqlevTqRkZEkJSVhbKyqbBgYGPje5SaKGm9LM/cp/abm9JyfwjPGx8ezaNEi6tevj7Ozs9pYo1QqGTVqFAYGBnTv3p0ePXoUsqTao6A/T3FGmQ/c3d0ZN24cnTp1IioqCmdnZ3x9fT85/0IRERFNxBllPti4cSNTp04lJiaG8+fPs3379k9SScbHx7Nz506KFy9OaGgo33zzTWGLVKAcPHiQly9fMnLkyMIWRSvkJfn0m3wqc6U///yTTZs2YWtry/r167G0tNTa2KIxJx/Y2NiwYcMGevfuzdq1a2nevHlhi1QgbNiwASMjI7p06cK9e/c09mU/NV6+fImnpyfJycmFLYrWEAQhyystLY2UlJRs2z4Fbt++jYuLC5cuXcLQ0JClS5dqdXxxRvkOfOqpqlxdXRkzZgxVqlRBV1f3kw2BUygUHD16lA4dOnySbl6ZLF26lIoVKxIeHo5MJuPLL78sbJG0TsWKFTExUZWLbt++PREREVodX5xRimShSZMmtG/fnhYtWnxSUUf/ZcuWLfTt27ewxShwNm3ahJubG3379uXAgQOFLU6BkKkkAe7du0efPn20Or44oxTJwrVr17CwsODChQt07dqVM2fOfHK+lL6+vuzcuZN79+7x+PFjEhIScHFxwd3dvbBF0zqdO3ema9eutG3blilTphS2OAWKt7c3rVu31voqSJxRimThyJEjVKlShRo1avDtt99y6dKlwhZJ65QrV45169YxadIkOnbsSPPmzWnQoEFhi1UgjBw5EgMDA5YtW4aOzqc7N3r27Bmpqam4u7sTHx+PXC7X2tif7rsm8s706dOHNWvWYGBgQGxsLAMHDixskbSOrq4uJUuWBMDCwoLExES1f+ynxogRI9i+fTvnz59n6NChXL16tbBF0jrBwcH069cPOzs7li9fjomJCX///bfWxhf9KEVyJC0t7ZM3XAGkpqaiVCoxMjIqbFEKBBcXF27cuIGOjg7169f/JBVlcnIyCQkJ6mMjIyOtuu6JilJE5BPHy8sLf39/bG1tkUgktG3btrBF+ugQFaWIiIhILojGHBEREZFcEBWliIiISC6IilJEREQkF0RFKSIiIpILoqL8zHny5AlLlizhzJkz73S9IAj07NlTqzLFxsZy7NgxrY/522+/MX78eDp37qzRlpaWhoODA48ePcp1nOvXr1OpUqUcs4PPnj2bMWPG5DpOeHg4p0+fVh9/+eWXLFu2LNfr8sKff/7JgAEDtDKWyL9orZ6jyEfHmjVrhM6dOwvBwcFCu3bthE2bNuV7jJMnTwqAcPnyZa3I9OrVK6F///6Cra2tVsbLZMyYMcK2bdsEQRCECxcuZGnfv3+/kJqamus4iYmJwuHDh9XHCoVCOH78uPr4yZMnwp07d946xtOnT4V27doJDRo0UJ+7evWqEBgYmOv9c+LIkSPq/wcEBAjXrl1757FEsiIqys+Uu3fvCiYmJkJwcLAgCIKwfv16oXbt2vkeZ9SoUUKrVq2E/v37a022I0eOaF1RNmjQQNi3b59WxxQEQZgwYcI71Y9evXq1hqJ8H2bPni18/fXXWhlLJHvEpfdnysqVK2nTpg1lypQBVBUl7927l68xQkJCsLa2ZuzYsXh6emqktoqNjWXChAl07dqVdevWUatWLdzc3EhLS1P3+euvv1i4cCF16tTRqIAolWr+Wd68eZM5c+bw9ddf06VLF4261G+yY8cOlixZwv/+9z/69OmjzqO5ZMkSAgMD2bNnD4sWLcqSg3HXrl20bt2akydPkpqayowZM2jcuDF79uyhUaNGuLq6EhkZSUpKCn/++Sc1a9YkKSmJ58+fc/78ea5fv86yZcsICAhg4sSJGmnM1q1bx+bNm5k2bRo//vhjts949+5dhgwZwk8//QSoKkT+8MMPrF+/nrZt2+Ll5QWoHMf//PNPli9fTu/evUlJSSE0NJSTJ0/i4+PDokWLCA4OZsqUKRrbC/7+/vz888+sWLGCXr16cfLkSQDOnz9Ps2bNWL16NSNHjqR48eL8888/b/vIP18KW1OLfHiUSqVgY2MjLFu2TH1uxYoVgrm5eb7G+eWXX4SnT58KCoVCKFu2rLBgwQKN9pUrVwqlS5cWAgIChPT0dMHS0lLYv3+/IAiC4O3tLbRr104QBEGYMWOGYGlpKUybNk0QBEE4duyYekYZFxcndOvWTT2mh4eHMHr06CyyXLx4UahXr576eMGCBULDhg0FpVIpCIIgODs7C7t27cr2OTIyMgRLS0vh2LFjgiAIwqFDhwRjY2Ph7t27gkKhEKpWrSr89ddfgiAIwp07dwRASExMFARBEAYNGqQxo5w5c6bg4eEhCIIgJCQkCFKpVEhMTBTS09MFAwMD9Qx+7dq1GjPKPn36qJ/r+PHjwsiRIwVBEITAwEC1XNWrVxdOnTolCIIgNGrUSNi9e7cgCIIwbtw4jRnlkiVLhDp16giCIAhpaWlC+fLlhadPnwqCoFr2GxoaCk+ePBEEQRAqVKggjBkzRhAE1d9AxYoVs32PPnfEGeVnyOPHjwkODmb16tU0bNiQhg0bMn36dKysrPI8hlKpJCAgAEdHR6RSKcOGDWPlypUaRg4TExNKliyJg4MDurq6VKlSRT3LO3DgADY2NgB07NiRpKSkbCsCent7ExERwaJFi1i0aBFt27alcePGWfqtWbNGo0b1V199hbe3d54MNDo6Oho1201MTDA0NKRGjRpIpVKcnZ3VchcrVuytY73ZbmJiws2bNzE2NlaXjM1pNvzmdRUrVuTvv/9m7dq12Nvb4+HhAcC2bdto1qwZ/v7+xMTE5GmsM2fOkJaWhqOjIwCOjo7UrVuXzZs3q2WsX78+ADVq1Piks9m/D2L2oM+Q+Ph4QJVOLVNZNWvWjJo1a+Z5jCNHjhAbG6u28Mrlcp4/f67OGJ4db9ZFL1WqlHq57eDggKWlZbYpwAIDAylbtiwTJ058qzxBQUGUKFFCfVy6dGkMDQ159eoVTk5OeX6u3OTOL1KplL59++Lm5oaurm6eSi+UK1eORYsW8e2337Jr1y48PT0xNTWlePHijBo1Cjs7O8zMzPI0VlBQUJYaOo6Ojrx69SpL3/d5zk8dUVF+hmR+wczMzADVfuLVq1eZN29ensfYtm0bmzdvxsDAQH3u8ePHLF++PE9Z0b/++mtOnTrF9OnTEQSBjRs3ZtuvePHinD9/nvT0dPT09ACVi07t2rU19vkcHBx4/PixxjPK5XIqVaqU52d6V3JSWHFxcbRp04Z79+5RrFgxjT3Kt/Hy5UtGjRqFm5sbvXv3ZurUqfz555+0b9+eRYsW0bx5c7y9vfMkg4ODAyEhIcTFxalnzXK5nKpVq+bjCUXEpfdnSN26dXFwcOD+/fsAzJ07l9GjR9OkSRN1n8DAQC5evJjt9UFBQQiCoKEkAbp168axY8d49uwZQJbEqenp6eqleXBwMK1bt2b27NnMmTOH1q1bq/splUr1F9/NzY2YmBjGjx9PfHw8ly9f5vLly1kMPsOHD+fUqVNqg9K1a9do164dZcuWVcuiUChyfE8UCoVatrfJnTlG5rGhoSGhoaEoFAqSkpI0xrlw4QJpaWmYmpoSFhZGcnIyaWlpCIKg8Yz/vf/Vq1d58uQJTk5OzJs3j/DwcCIjI7l58yaWlpakpaXx6tUr9ViZMgiCQEJCgsZYbm5ulC9fnp07dwIqhXr//n0GDRqU5VnffE6R/1AYG6MihY+Xl5fQvn17YdSoUcLUqVMFhUKh0b5ixQrB0dFRbQzJJDo6WujUqZNQv359wdfXV30+Li5O+O677wRAaNOmjeDv7y90795dMDMzEy5fvixcvXpVMDU1FTp27CjExsYK27dvFwwNDQUHBwehevXqQo8ePYTbt28L4eHhwoABAwSpVCocOHBAEARB2Ldvn+Do6ChYWloKI0aMENLT07N9Jk9PT2HAgAHC+vXrhVmzZgmxsbGCIAjCgQMHBAMDA6FPnz6Cn59flusOHDgg6OrqCiNGjBBCQ0OFb775RpBKpcKRI0eEBw8eCLa2tkLDhg2Fp0+fCvPnzxcAYcWKFYJcLhe8vLwEBwcHYebMmYKfn5/QoUMHoVSpUsK1a9eE+Ph4oWHDhkLt2rWFtWvXCp07dxY8PDyEmzdvCu3btxfMzc2Fc+fOCffv3xdq1qwp1KpVS3jy5Ilw6NAhoXPnzsLmzZuF8ePHCw8fPhQEQRAGDhwoODo6CjNnzhR+/vlnoVq1asLNmzeFa9euCY6OjsKPP/4o+Pv7C7179xbMzc3V/qLPnj0TevToISxdulT43//+p/axvHz5smBoaCj07dtXiIiIEIYPHy4ABeJG9bEjplkTyZG9e/fStWvXfNeJzgvr1q2jUaNGGBoaEh8fT0xMDCdOnGDu3Llav5eIyPsi7lGK5IhcLi8QJRkVFcX06dPx8fHB2toaUO3Lubi4aP1eIiLaQFSUItny4sULtUVc21hbWzN48GDc3NwwNDTEycmJNm3aaL3EqIiIthCX3iIiIiK5IFq9RURERHJBVJQiIiIiuSAqShEREZFcEBWliIiISC6IilJEREQkF0RFKSIiIpILoqIUERERyQVRUYqIiIjkgqgoRURERHLh/37oE8bneXDkAAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_circuit_energy(r'$n=3$');" ] }, { "cell_type": "markdown", "id": "3b1e5d49", "metadata": {}, "source": [ "Cooling is stronger than in circuit A: the curve is flatter and sits lower, and the experimental\n", "data confirm this. Of the three circuits, this one agrees best with the analytical prediction.\n", "The extra instruction qubit improves the DME approximation, which shows that distributing DME\n", "improves cooling." ] }, { "cell_type": "markdown", "id": "2091afde", "metadata": {}, "source": [ "### Circuit C: 2 DBAC steps, 1 DME step ($n=4$)\n", "\n", "Here the DBAC recursion is applied twice ($k=2$) with a single DME step in each. The first step is\n", "circuit A, run twice in parallel: once to cool the data qubit $q_2$ (instruction $q_1$) and once to\n", "prepare a cooled copy on $q_3$ (instruction $q_4$). The second step, after the second dashed line,\n", "uses that cooled copy on $q_3$ as the instruction for $q_2$, so it starts from a colder state than\n", "a single step could provide." ] }, { "cell_type": "code", "execution_count": 7, "id": "0d7f7063", "metadata": { "execution": { "iopub.execute_input": "2026-10-26T13:05:21.872432Z", "iopub.status.busy": "2026-10-26T13:05:21.872345Z", "iopub.status.idle": "2026-10-26T13:05:21.915627Z", "shell.execute_reply": "2026-10-26T13:05:21.914992Z" } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_dbac_circuit(\"C\");" ] }, { "cell_type": "code", "execution_count": 8, "id": "f17e743c", "metadata": { "execution": { "iopub.execute_input": "2026-10-26T13:05:21.917425Z", "iopub.status.busy": "2026-10-26T13:05:21.917355Z", "iopub.status.idle": "2026-10-26T13:05:21.983381Z", "shell.execute_reply": "2026-10-26T13:05:21.982924Z" } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_circuit_energy(r'$n=4$');" ] }, { "cell_type": "markdown", "id": "0553f798", "metadata": {}, "source": [ "In the noiseless simulation, the two recursion steps cool even more than circuit B. On the device,\n", "however, this circuit is the deepest and has the most entangling gates, and the siZZle pulses that\n", "implement them are relatively long. Decoherence accumulates, so the experimental points lie well above the analytical curve and\n", "only modestly below the uncooled state. Circuit C is at the verge of **break-even** for this device,\n", "even though the analytical curve predicts further cooling with more steps." ] }, { "cell_type": "markdown", "id": "a6e87bbf", "metadata": {}, "source": [ "## Summary\n", "\n", "| circuit | $k$ | $M$ | $n$ | what it demonstrates |\n", "|---|---|---|---|---|\n", "| A | 1 | 1 | 2 | the minimal DBAC step: coherence is removed with one instruction and no measurement |\n", "| B | 1 | 2 | 3 | distributing DME over more instruction qubits improves cooling |\n", "| C | 2 | 1 | 4 | recursion cools further in theory, but decoherence limits it on today's device |\n", "\n", "Starting from $|\\psi(\\theta)\\rangle = R_X(\\theta)|0\\rangle$, DBAC with $k$ DBAC steps and $M$ DME\n", "steps moves the data qubit toward the ground state. Spending more qubits ($M$ and $k$) gives lower\n", "energy in theory. Reaching $|0\\rangle$ exactly would take infinitely many instructions, which is\n", "the analogue of Nernst's principle. In practice, hardware noise sets how far the recursion pays off.\n", "\n", "To regenerate all figures of the paper, see [Reproducing the figures](figures.md)." ] }, { "cell_type": "markdown", "id": "06fdb924", "metadata": {}, "source": [ "```{toctree}\n", ":hidden:\n", ":caption: Getting started\n", "\n", "installation\n", "quickstart\n", "```\n", "\n", "```{toctree}\n", ":hidden:\n", ":caption: Guide\n", "\n", "guide/conventions\n", "guide/dme\n", "guide/dbac-step\n", "guide/recursion\n", "guide/hbac\n", "guide/plotting\n", "```\n", "\n", "```{toctree}\n", ":hidden:\n", ":caption: Reproducing the paper\n", "\n", "figures\n", "```\n", "\n", "```{toctree}\n", ":hidden:\n", ":caption: API reference\n", "\n", "api/index\n", "api/utils\n", "api/dme\n", "api/dbqite\n", "api/gci\n", "api/hbac\n", "api/plotting\n", "```" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.12.3" } }, "nbformat": 4, "nbformat_minor": 5 }