{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Simulating Gate Noise\n", "$$\n", "\\newcommand{ket}[1]{\\left|{#1}\\right\\rangle}\n", "\\newcommand{bra}[1]{\\left\\langle {#1}\\right|}\n", "\\newcommand{tr}{\\mathrm{Tr}}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Pure states vs. mixed states\n", "\n", "Errors in quantum computing can introduce classical uncertainty in what the underlying state is.\n", "When this happens we sometimes need to consider not only wavefunctions but also probabilistic sums of\n", "wavefunctions when we are uncertain as to which one we have. For example, if we think that an X gate\n", "was accidentally applied to a qubit with a 50-50 chance then we would say that there is a 50% chance\n", "we have the $\\ket{0}$ state and a 50% chance that we have a $\\ket{1}$ state.\n", "This is called an \"impure\" or\n", "\"mixed\"state in that it isn't just a wavefunction (which is pure) but instead a distribution over\n", "wavefunctions. We describe this with something called a density matrix, which is generally an\n", "operator. Pure states have very simple density matrices that we can write as an outer product of a\n", "ket vector $\\ket{\\psi}$ with its own bra version $\\bra{\\psi}=\\ket{\\psi}^\\dagger$.\n", "For a pure state the density matrix is simply\n", "\n", "\n", "$$\n", " \\rho_\\psi = \\ket{\\psi}\\bra{\\psi}.\n", "$$\n", "The expectation value of an operator for a mixed state is given by\n", "\n", "$$\n", " \\langle X \\rangle_\\rho = \\tr{X \\rho}\n", "$$\n", "where $\\tr{A}$ is the trace of an operator, which is the sum of its diagonal elements\n", "which is independent of choice of basis.\n", "Pure state density matrices satisfy\n", "\n", "$$\n", " \\rho \\text{ is pure } \\Leftrightarrow \\rho^2 = \\rho\n", "$$\n", "which you can easily verify for $\\rho_\\psi$ assuming that the state is normalized.\n", "If we want to describe a situation with classical uncertainty between states $\\rho_1$ and\n", "$\\rho_2$, then we can take their weighted sum\n", "$$\n", " \\rho = p \\rho_1 + (1-p) \\rho_2\n", "$$\n", "where $p\\in [0,1]$ gives the classical probability that the state is $\\rho_1$.\n", "\n", "Note that classical uncertainty in the wavefunction is markedly different from superpositions.\n", "We can represent superpositions using wavefunctions, but use density matrices to describe\n", "distributions over wavefunctions. You can read more about density matrices [here](https://en.wikipedia.org/wiki/Density_matrix)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Quantum gate errors\n", "## What are they?\n", "For a quantum gate given by its unitary operator $U$, a \"quantum gate error\" describes the scenario in which the actually induces transformation deviates from $\\ket{\\psi} \\mapsto U\\ket{\\psi}$. \n", "There are two basic types of quantum gate errors:\n", "\n", "1. **coherent errors** are those that preserve the purity of the input state, i.e., instead of the above mapping we carry out a perturbed, but unitary operation $\\ket{\\psi} \\mapsto \\tilde{U}\\ket{\\psi}$, where $\\tilde{U} \\neq U$. \n", "2. **incoherent errors** are those that do not preserve the purity of the input state, \n", " in this case we must actually represent the evolution in terms of density matrices. \n", " The state $\\rho := \\ket{\\psi}\\bra{\\psi}$ is then mapped as \n", " $$\n", " \\rho \\mapsto \\sum_{j=1}^n K_j\\rho K_j^\\dagger, \n", " $$ \n", " where the operators $\\{K_1, K_2, \\dots, K_m\\}$ are called Kraus operators and must obey \n", " $\\sum_{j=1}^m K_j^\\dagger K_j = I$ to conserve the trace of $\\rho$. \n", " Maps expressed in the above form are called Kraus maps. It can be shown that every physical map on a finite\n", " dimensional quantum system can be represented as a Kraus map, though this representation is not generally unique.\n", " [You can find more information about quantum operations here](https://en.wikipedia.org/wiki/Quantum_operation#Kraus_operators)\n", " \n", "In a way, coherent errors are *in principle* amendable by more precisely calibrated control. Incoherent errors are more tricky." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Why do incoherent errors happen?\n", "When a quantum system (e.g., the qubits on a quantum processor) is not perfectly isolated from its environment it generally co-evolves with the degrees of freedom it couples to. The implication is that while the total time evolution of system and environment can be assumed to be unitary, restriction to the system state generally is not.\n", "\n", "**Let's throw some math at this for clarity:**\n", "Let our total Hilbert space be given by the tensor product of system and environment Hilbert spaces:\n", "$\\mathcal{H} = \\mathcal{H}_S \\otimes \\mathcal{H}_E$.\n", "Our system \"not being perfectly isolated\" must be translated to the statement that the global Hamiltonian contains a contribution that couples the system and environment:\n", "$$\n", "H = H_S \\otimes I + I \\otimes H_E + V\n", "$$\n", "where $V$ non-trivally acts on both the system and the environment.\n", "Consequently, even if we started in an initial state that factorized over system and environment $\\ket{\\psi}_{S,0}\\otimes \\ket{\\psi}_{E,0}$\n", "if everything evolves by the Schrödinger equation\n", "$$\n", "\\ket{\\psi_t} = e^{-i \\frac{Ht}{\\hbar}} \\left(\\ket{\\psi}_{S,0}\\otimes \\ket{\\psi}_{E,0}\\right)\n", "$$\n", "the final state will generally not admit such a factorization." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A toy model\n", "**In this (somewhat technical) section we show how environment interaction can corrupt an identity gate and derive its Kraus map.**\n", "For simplicity, let us assume that we are in a reference frame in which both the system and environment Hamiltonian's vanish $H_S = 0, H_E = 0$ and where the cross-coupling is small even when multiplied by the duration of the time evolution $\\|\\frac{tV}{\\hbar}\\|^2 \\sim \\epsilon \\ll 1$ (any operator norm $\\|\\cdot\\|$ will do here).\n", "Let us further assume that $V = \\sqrt{\\epsilon} V_S \\otimes V_E$ (the more general case is given by a sum of such terms) and that \n", "the initial environment state satisfies $\\bra{\\psi}_{E,0} V_E\\ket{\\psi}_{E,0} = 0$. This turns out to be a very reasonable assumption in practice but a more thorough discussion exceeds our scope.\n", "\n", "Then the joint system + environment state $\\rho = \\rho_{S,0} \\otimes \\rho_{E,0}$ (now written as a density matrix) evolves as\n", "$$\n", "\\rho \\mapsto \\rho' := e^{-i \\frac{Vt}{\\hbar}} \\rho e^{+i \\frac{Vt}{\\hbar}}\n", "$$\n", "Using the Baker-Campbell-Hausdorff theorem we can expand this to second order in $\\epsilon$\n", "$$\n", "\\rho' = \\rho - \\frac{it}{\\hbar} [V, \\rho] - \\frac{t^2}{2\\hbar^2} [V, [V, \\rho]] + O(\\epsilon^{3/2})\n", "$$\n", "We can insert the initially factorizable state $\\rho = \\rho_{S,0} \\otimes \\rho_{E,0}$ and trace over the environmental degrees of freedom to obtain\n", "\\begin{align}\n", "\\rho_S' := \\tr_E \\rho' & = \\rho_{S,0} \\underbrace{\\tr \\rho_{E,0}}_{1} - \\frac{i\\sqrt{\\epsilon} t}{\\hbar} \\underbrace{\\left[ V_S \\rho_{S,0} \\underbrace{\\tr V_E\\rho_{E,0}}_{\\bra{\\psi}_{E,0} V_E\\ket{\\psi}_{E,0} = 0} - \\rho_{S,0}V_S \\underbrace{\\tr \\rho_{E,0}V_E}_{\\bra{\\psi}_{E,0} V_E\\ket{\\psi}_{E,0} = 0} \\right]}_0 \\\\\n", "& \\qquad - \\frac{\\epsilon t^2}{2\\hbar^2} \\left[ V_S^2\\rho_{S,0}\\tr V_E^2 \\rho_{E,0} + \\rho_{S,0} V_S^2 \\tr \\rho_{E,0}V_E^2 - 2 V_S\\rho_{S,0}V_S\\tr V_E \\rho_{E,0}V_E\\right] \\\\\n", "& = \\rho_{S,0} - \\frac{\\gamma}{2} \\left[ V_S^2\\rho_{S,0} + \\rho_{S,0} V_S^2 - 2 V_S\\rho_{S,0}V_S\\right]\n", "\\end{align}\n", "where the coefficient in front of the second part is by our initial assumption very small $\\gamma := \\frac{\\epsilon t^2}{2\\hbar^2}\\tr V_E^2 \\rho_{E,0} \\ll 1$.\n", "This evolution happens to be approximately equal to a Kraus map with operators $K_1 := I - \\frac{\\gamma}{2} V_S^2, K_2:= \\sqrt{\\gamma} V_S$:\n", "\\begin{align}\n", "\\rho_S \\to \\rho_S' &= K_1\\rho K_1^\\dagger + K_2\\rho K_2^\\dagger\n", " = \\rho - \\frac{\\gamma}{2}\\left[ V_S^2 \\rho + \\rho V_S^2\\right] + \\gamma V_S\\rho_S V_S + O(\\gamma^2)\n", "\\end{align}\n", "This agrees to $O(\\epsilon^{3/2})$ with the result of our derivation above. This type of derivation can be extended to many other cases with little complication and a very similar argument is used to derive the [Lindblad master equation](https://en.wikipedia.org/wiki/Lindblad_equation)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Support for noisy gates on the Rigetti QVM\n", "\n", "As of today, users of our Forest API can annotate their QUIL programs by certain pragma statements that inform the QVM that a particular gate on specific target qubits should be replaced by an imperfect realization given by a Kraus map.\n", "\n", "## But the QVM propagates *pure states*: How does it simulate noisy gates?\n", "It does so by yielding the correct outcomes **in the average over many executions of the QUIL program**:\n", "When the noisy version of a gate should be applied the QVM makes a random choice which Kraus operator is applied to the current state with a probability that ensures that the average over many executions is equivalent to the Kraus map.\n", "In particular, a particular Kraus operator $K_j$ is applied to $\\ket{\\psi}_S$\n", "$$\n", "\\ket{\\psi'}_S = \\frac{1}{\\sqrt{p_j}} K_j \\ket{\\psi}_S\n", "$$\n", "with probability $p_j:= \\bra{\\psi}_S K_j^\\dagger K_j \\ket{\\psi}_S$.\n", "In the average over many execution $N \\gg 1$ we therefore find that\n", "\\begin{align}\n", "\\overline{\\rho_S'} & = \\frac{1}{N} \\sum_{n=1}^N \\ket{\\psi'_n}_S\\bra{\\psi'_n}_S \\\\\n", "& = \\frac{1}{N} \\sum_{n=1}^N p_{j_n}^{-1}K_{j_n}\\ket{\\psi'}_S \\bra{\\psi'}_SK_{j_n}^\\dagger\n", "\\end{align}\n", "where $j_n$ is the chosen Kraus operator label in the $n$-th trial.\n", "This is clearly a Kraus map itself! And we can group identical terms and rewrite it as\n", "\\begin{align}\n", "\\overline{\\rho_S'} & = \n", " \\sum_{\\ell=1}^n \\frac{N_\\ell}{N} p_{\\ell}^{-1}K_{\\ell}\\ket{\\psi'}_S \\bra{\\psi'}_SK_{\\ell}^\\dagger\n", "\\end{align}\n", "where $N_{\\ell}$ is the number of times that Kraus operator label $\\ell$ was selected.\n", "For large enough $N$ we know that $N_{\\ell} \\approx N p_\\ell$ and therefore\n", "\\begin{align}\n", "\\overline{\\rho_S'} \\approx \\sum_{\\ell=1}^n K_{\\ell}\\ket{\\psi'}_S \\bra{\\psi'}_SK_{\\ell}^\\dagger\n", "\\end{align}\n", "which proves our claim.\n", "**The consequence is that noisy gate simulations must generally be repeated many times to obtain representative results**." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## How do I get started?\n", "\n", "1. Come up with a good model for your noise. We will provide some examples below and may add more such \n", " examples to our public repositories over time. Alternatively, you can characterize the gate under \n", " consideration using [Quantum Process Tomography](https://arxiv.org/abs/1202.5344) or \n", " [Gate Set Tomography](http://www.pygsti.info/) and use the resulting process matrices to obtain a \n", " very accurate noise model for a particular QPU.\n", "2. Define your Kraus operators as a list of numpy arrays `kraus_ops = [K1, K2, ..., Km]`.\n", "3. For your QUIL program `p`, call:\n", " ```\n", " p.define_noisy_gate(\"MY_NOISY_GATE\", [q1, q2], kraus_ops)\n", " ```\n", " where you should replace `MY_NOISY_GATE` with the gate of interest and `q1, q2` the indices of the qubits.\n", " \n", "**Scroll down for some examples!**" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.stats import binom\n", "import matplotlib.colors as colors\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "from pyquil import Program, get_qc\n", "from pyquil.gates import CZ, H, I, X, MEASURE\n", "from scipy.linalg import expm" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# We could ask for \"2q-noisy-qvm\" but we will be specifying\n", "# our noise model as PRAGMAs on the Program itself.\n", "qc = get_qc('2q-qvm')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Example 1: Amplitude damping\n", "\n", "Amplitude damping channels are imperfect identity maps with Kraus operators\n", "$$\n", "K_1 = \\begin{pmatrix} \n", "1 & 0 \\\\\n", "0 & \\sqrt{1-p}\n", "\\end{pmatrix} \\\\\n", "K_2 = \\begin{pmatrix} \n", "0 & \\sqrt{p} \\\\\n", "0 & 0\n", "\\end{pmatrix}\n", "$$\n", "where $p$ is the probability that a qubit in the $\\ket{1}$ state decays to the $\\ket{0}$ state.\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "def damping_channel(damp_prob=.1):\n", " \"\"\"\n", " Generate the Kraus operators corresponding to an amplitude damping \n", " noise channel.\n", " \n", " :params float damp_prob: The one-step damping probability.\n", " :return: A list [k1, k2] of the Kraus operators that parametrize the map.\n", " :rtype: list\n", " \"\"\"\n", " damping_op = np.sqrt(damp_prob) * np.array([[0, 1],\n", " [0, 0]])\n", " \n", " residual_kraus = np.diag([1, np.sqrt(1-damp_prob)])\n", " return [residual_kraus, damping_op]\n", "\n", "def append_kraus_to_gate(kraus_ops, g):\n", " \"\"\"\n", " Follow a gate `g` by a Kraus map described by `kraus_ops`.\n", " \n", " :param list kraus_ops: The Kraus operators.\n", " :param numpy.ndarray g: The unitary gate.\n", " :return: A list of transformed Kraus operators.\n", " \"\"\"\n", " return [kj.dot(g) for kj in kraus_ops]\n", "\n", "\n", "def append_damping_to_gate(gate, damp_prob=.1):\n", " \"\"\"\n", " Generate the Kraus operators corresponding to a given unitary \n", " single qubit gate followed by an amplitude damping noise channel.\n", " \n", " :params np.ndarray|list gate: The 2x2 unitary gate matrix.\n", " :params float damp_prob: The one-step damping probability.\n", " :return: A list [k1, k2] of the Kraus operators that parametrize the map.\n", " :rtype: list\n", " \"\"\"\n", " return append_kraus_to_gate(damping_channel(damp_prob), gate)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "20/21, CPU times: user 74.2 ms, sys: 6.16 ms, total: 80.3 ms\n", "Wall time: 744 ms\n" ] } ], "source": [ "%%time\n", "\n", "# single step damping probability\n", "damping_per_I = 0.02\n", "\n", "# number of program executions\n", "trials = 200\n", "\n", "results_damping = []\n", "lengths = np.arange(0, 201, 10, dtype=int)\n", "for jj, num_I in enumerate(lengths):\n", " \n", " print(\"\\r{}/{}, \".format(jj, len(lengths)), end=\"\")\n", "\n", " p = Program(X(0))\n", " ro = p.declare(\"ro\")\n", " # want increasing number of I-gates\n", " p.inst([I(0) for _ in range(num_I)])\n", " p.inst(MEASURE(0, ro[0]))\n", " \n", " # overload identity I on qc 0\n", " p.define_noisy_gate(\"I\", [0], append_damping_to_gate(np.eye(2), damping_per_I))\n", " p.wrap_in_numshots_loop(trials)\n", " qc.qam.random_seed = int(num_I)\n", " res = qc.run(p)\n", " results_damping.append([np.mean(res), np.std(res) / np.sqrt(trials)])\n", " \n", "results_damping = np.array(results_damping)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "dense_lengths = np.arange(0, lengths.max()+1, .2)\n", "survival_probs = (1-damping_per_I)**dense_lengths\n", "logpmf = binom.logpmf(np.arange(trials+1)[np.newaxis, :], trials, survival_probs[:, np.newaxis])/np.log(10)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "DARK_TEAL = '#48737F'\n", "FUSCHIA = \"#D6619E\"\n", "BEIGE = '#EAE8C6'\n", "cm = colors.LinearSegmentedColormap.from_list('anglemap', [\"white\", FUSCHIA, BEIGE], N=256, gamma=1.5)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0, 1)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(14, 6))\n", "plt.pcolor(dense_lengths, np.arange(trials+1)/trials, logpmf.T, cmap=cm, vmin=-4, vmax=logpmf.max())\n", "plt.plot(dense_lengths, survival_probs, c=BEIGE, label=\"Expected mean\")\n", "plt.errorbar(lengths, results_damping[:,0], yerr=2*results_damping[:,1], c=DARK_TEAL, \n", " label=r\"noisy qvm, errorbars $ = \\pm 2\\hat{\\sigma}$\", marker=\"o\")\n", "cb = plt.colorbar()\n", "cb.set_label(r\"$\\log_{10} \\mathrm{Pr}(n_1; n_{\\rm trials}, p_{\\rm survival}(t))$\", size=20)\n", "\n", "plt.title(\"Amplitude damping model of a single qubit\", size=20)\n", "plt.xlabel(r\"Time $t$ [arb. units]\", size=14)\n", "plt.ylabel(r\"$n_1/n_{\\rm trials}$\", size=14)\n", "plt.legend(loc=\"best\", fontsize=18)\n", "plt.xlim(*lengths[[0, -1]])\n", "plt.ylim(0, 1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Example 2: dephased CZ-gate\n", "\n", "Dephasing is usually characterized through a qubit's $T_2$ time. \n", "For a single qubit the dephasing Kraus operators are\n", "$$\n", "K_1(p) = \\sqrt{1-p} I_2 \\\\\n", "K_2(p) = \\sqrt{p} \\sigma_Z\n", "$$\n", "where $p = 1 - \\exp(-T_2/T_{\\rm gate})$ is the probability that the qubit is dephased over the time interval of interest, $I_2$ is the $2\\times 2$-identity matrix and $\\sigma_Z$ is the Pauli-Z operator.\n", "\n", "For two qubits, we must construct a Kraus map that has *four* different outcomes:\n", "\n", "1. No dephasing\n", "2. Qubit 1 dephases\n", "3. Qubit 2 dephases\n", "4. Both dephase" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Kraus operators for this are given by\n", "\\begin{align}\n", "K'_1(p,q) = K_1(p)\\otimes K_1(q) \\\\\n", "K'_2(p,q) = K_2(p)\\otimes K_1(q) \\\\\n", "K'_3(p,q) = K_1(p)\\otimes K_2(q) \\\\\n", "K'_4(p,q) = K_2(p)\\otimes K_2(q) \n", "\\end{align}\n", "where we assumed a dephasing probability $p$ for the first qubit and $q$ for the second.\n", "\n", "Dephasing is a *diagonal* error channel and the CZ gate is also diagonal, therefore we can get the combined map of dephasing and the CZ gate simply by composing $U_{\\rm CZ}$ the unitary representation of CZ with each Kraus operator\n", "\\begin{align}\n", "K^{\\rm CZ}_1(p,q) = K_1(p)\\otimes K_1(q)U_{\\rm CZ} \\\\\n", "K^{\\rm CZ}_2(p,q) = K_2(p)\\otimes K_1(q)U_{\\rm CZ} \\\\\n", "K^{\\rm CZ}_3(p,q) = K_1(p)\\otimes K_2(q)U_{\\rm CZ} \\\\\n", "K^{\\rm CZ}_4(p,q) = K_2(p)\\otimes K_2(q)U_{\\rm CZ} \n", "\\end{align}\n", "\n", "**Note that this is not always accurate, because a CZ gate is often achieved through non-diagonal interaction Hamiltonians! However, for sufficiently small dephasing probabilities it should always provide a good starting point.**" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "def dephasing_kraus_map(p=.1):\n", " \"\"\"\n", " Generate the Kraus operators corresponding to a dephasing channel.\n", "\n", " :params float p: The one-step dephasing probability.\n", " :return: A list [k1, k2] of the Kraus operators that parametrize the map.\n", " :rtype: list\n", " \"\"\"\n", " return [np.sqrt(1-p)*np.eye(2), np.sqrt(p)*np.diag([1, -1])]\n", "\n", "def tensor_kraus_maps(k1, k2):\n", " \"\"\"\n", " Generate the Kraus map corresponding to the composition\n", " of two maps on different qubits.\n", " \n", " :param list k1: The Kraus operators for the first qubit.\n", " :param list k2: The Kraus operators for the second qubit.\n", " :return: A list of tensored Kraus operators.\n", " \"\"\"\n", " return [np.kron(k1j, k2l) for k1j in k1 for k2l in k2]\n" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "199/200, CPU times: user 568 ms, sys: 43.2 ms, total: 611 ms\n", "Wall time: 1.89 s\n" ] } ], "source": [ "%%time\n", "# single step damping probabilities\n", "ps = np.linspace(.001, .5, 200)\n", "\n", "# number of program executions\n", "trials = 500\n", "\n", "results = []\n", "\n", "for jj, p in enumerate(ps):\n", "\n", " corrupted_CZ = append_kraus_to_gate(\n", " tensor_kraus_maps(\n", " dephasing_kraus_map(p),\n", " dephasing_kraus_map(p)\n", " ), \n", " np.diag([1, 1, 1, -1]))\n", "\n", " \n", " print(\"\\r{}/{}, \".format(jj, len(ps)), end=\"\")\n", " \n", " # make Bell-state\n", " p = Program(H(0), H(1), CZ(0,1), H(1))\n", " ro = p.declare(\"ro\", memory_size=2)\n", " p.inst(MEASURE(0, ro[0]))\n", " p.inst(MEASURE(1, ro[1]))\n", " \n", " # overload identity I on qc 0\n", " p.define_noisy_gate(\"CZ\", [0, 1], corrupted_CZ)\n", " p.wrap_in_numshots_loop(trials)\n", " qc.qam.random_seed = jj\n", " res = qc.run(p)\n", " results.append(res)\n", " \n", "results = np.array(results)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "Z1s = (2*results[:,:,0]-1.)\n", "Z2s = (2*results[:,:,1]-1.)\n", "Z1Z2s = Z1s * Z2s\n", "\n", "Z1m = np.mean(Z1s, axis=1)\n", "Z2m = np.mean(Z2s, axis=1)\n", "Z1Z2m = np.mean(Z1Z2s, axis=1)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(14, 6))\n", "plt.axhline(y=1.0, color=FUSCHIA, alpha=.5, label=\"Bell state\")\n", "\n", "plt.plot(ps, Z1Z2m, \"x\", c=FUSCHIA, label=r\"$\\overline{Z_1 Z_2}$\")\n", "plt.plot(ps, 1-2*ps, \"--\", c=FUSCHIA, label=r\"$\\langle Z_1 Z_2\\rangle_{\\rm theory}$\")\n", "\n", "plt.plot(ps, Z1m, \"o\", c=DARK_TEAL, label=r\"$\\overline{Z}_1$\")\n", "plt.plot(ps, 0*ps, \"--\", c=DARK_TEAL, label=r\"$\\langle Z_1\\rangle_{\\rm theory}$\")\n", "\n", "plt.plot(ps, Z2m, \"d\", c=\"k\", label=r\"$\\overline{Z}_2$\")\n", "plt.plot(ps, 0*ps, \"--\", c=\"k\", label=r\"$\\langle Z_2\\rangle_{\\rm theory}$\")\n", "\n", "plt.xlabel(r\"Dephasing probability $p$\", size=18)\n", "plt.ylabel(r\"$Z$-moment\", size=18)\n", "plt.title(r\"$Z$-moments for a Bell-state prepared with dephased CZ\", size=18)\n", "plt.xlim(0, .5)\n", "plt.legend(fontsize=18)" ] } ], "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": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }