{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Gate Configuration - A Full Use Case" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "An example for a real use case of qupulse is the search for and evaluation of parameters for pulses that represent quantum gate operations on a toy example. To see an example closer to reality but less verbose in explanations, please see [Free Induction Decay - A Real Use Case](03FreeInductionDecayExample.ipynb).\n", "\n", "## Description of the Experiment\n", "The experiment will typically involve a set of gate pulses $G_j, 0 \\leq j \\lt N_{Gates}$.\n", "\n", "The template for a gate pulse $G_j$ is a sequence of $\\epsilon_i, 0 \\leq i \\lt N_{G_j}$ voltage levels held for time $\\Delta t = 1$ ns as illustrated in the figure below (with $N_{G_j} = 7$).\n", "\n", "![Template of a gate pulse](img/gate_pulse_scheme.png)\n", "\n", "The experiment defines a number of sequences $S_k, 0 \\leq k \\lt N_{Sequences}$ of the $G_j$ as $$S_k = (G_{m_k(1)}, G_{m_k(2)}, \\dots, G_{m_k(N_{S_k})})$$ where $N_{S_k}$ is the length of sequence $k$ and $m_k(i): \\{0, \\dots, N_{S_k} - 1\\} \\rightarrow \\{0, \\dots, N_{Gates} - 1\\}$ is a function that maps an index $i$ to the $m_k(i)$-th gate of sequence $S_k$ and thus fully describes the sequence. (These sequences express the sequential application of the gates to the qubit. In terms of quantum mathematics they may rather be expressed as multiplication of the matrices describing the unitary transformations applied by the gates: $S_k = \\prod_{i=N_{S_k} - 1}^{0} G_{m_k(i)} = G_{(N_{S_k} - 1)} \\cdot \\dots \\cdot G_{1} \\cdot G_{0}$.)\n", "\n", "Measuring and analysing the effects of these sequences on the qubit's state to derive parameters $\\epsilon_i$ for gate pulses that achieve certain state transformations is the goal of the experiment.\n", "\n", "To this end, every sequence must be extended by some preceeding initialization pulse and a succeeding measurement pulse. Furthermore, due to hardware constraints in measuring, all sequences must be of equal length (which is typically 4 µs). Thus, some sequences require some wait time before initialization to increase their playback duration. These requirements give raise to extended sequences $S_k'$ of the form:\n", "$$S_k' = I_{p(k)} | W_k | S_k | M_{q(k)}$$\n", "where the functions $p(k)$ and $q(k)$ respectively select some initialization pulse $I_{p(k)} \\in \\{I_1, I_2, \\dots\\}$ and measurement pulse $M_{q(k)} \\in \\{M_1, M_2, \\dots\\}$ for sequence $k$ and $W_k$ is the aforementioned wait pulse. The '|' denote concatenation of pulses, i.e., sequential execution.\n", "\n", "Since measurement of quantum state is a probabilistic process, many measurements of the effect of a single sequence must be made to reconstruct the resulting state of the qubit. Thus, the experiment at last defines scanlines (typically of duration 1 second), which are sequences of the $S_k'$. (These simply represent batches of sequences to configure playback and measurement systems and have no meaning to the experiment beyond these practical considerations.)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Implementation Using qupulse\n", "\n", "We now want to illustrate how to setup the experiment described above using qupulse. Let us assume the experiment considers only two different gates pulses ($N_{Gates} = 2$). We further assume that $N_{G_1} = 20$ and $N_{G_2} = 18$. We define them using instances of `TablePulseTemplate`:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from qupulse.pulses import TablePT\n", "\n", "delta_t = 1 # assuming that delta_t is 1 elementary time unit long in pulse defintions, i.e. 1 time unit = 1 ns\n", "\n", "gate_0 = TablePT({0: [(i*delta_t, 'gate_0_eps_' + str(i))\n", " for i in range(19)]})\n", " \n", "gate_1 = TablePT({0: [(i*delta_t, 'gate_2_eps_' + str(i))\n", " for i in range(17)]})\n", " \n", "gates = [gate_0, gate_1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We thus obtain two `TablePulseTemplate` of the desired form with parameters 'gate_1_eps_1' to 'gate_1_eps_20' and 'gate_2_eps_1' to 'gate_2_eps_18'.\n", "\n", "Next, we will define sequences as `SequncePulseTemplate` objects. We assume that the mapping functions $m_k$ are given as a 2 dimensional array (which impilicitly also defines $N_{Sequences}$ and $N_{S_k}$), e.g.:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "m = [\n", " [0, 1, 0, 0, 0, 1, 1, 0, 1], # m_0(i)\n", " [1, 1, 0, 0, 1, 0], # m_1(i)\n", " [1, 0, 0, 1, 1, 0, 0, 1] #m_2(i)\n", " ]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `SequencePulseTemplate` objects can now easily be constructed:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "from qupulse.pulses import SequencePT\n", "\n", "# SequencePulseTemplate requires a definition of parameter mappings from parameters passed into the\n", "# SequencePulseTemplate object to its subtemplates. In this case, we want parameters to map 1 to 1\n", "# and thus create an identity mapping of parameter names for both gates using python list/set/dict comprehension\n", "epsilon_mappings = [\n", " {param_name: param_name for param_name in gates[0].parameter_names},\n", " {param_name: param_name for param_name in gates[1].parameter_names}\n", "]\n", "all_epsilons = gates[0].parameter_names | gates[1].parameter_names\n", "\n", "sequences = []\n", "for m_k in m:\n", " subtemplates = []\n", " \n", " sequences.append(SequencePT(*(gates[g_ki] for g_ki in m_k)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We end up with a list `sequences` which contains the sequences described by our $m$ as qupulse pulse templates.\n", "\n", "To visualize our progress, let us plot our two gates and the second sequence with some random values between $-5$ and $5$ for the $\\epsilon_i$:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "scrolled": false }, "outputs": [ { "data": { "application/javascript": [ "/* Put everything inside the global mpl namespace */\n", "window.mpl = {};\n", "\n", "\n", "mpl.get_websocket_type = function() {\n", " if (typeof(WebSocket) !== 'undefined') {\n", " return WebSocket;\n", " } else if (typeof(MozWebSocket) !== 'undefined') {\n", " return MozWebSocket;\n", " } else {\n", " alert('Your browser does not have WebSocket support.' +\n", " 'Please try Chrome, Safari or Firefox ≥ 6. 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But how to set the MIME type? It doesn't seem\n", " * to be part of the websocket stream */\n", " evt.data.type = \"image/png\";\n", "\n", " /* Free the memory for the previous frames */\n", " if (fig.imageObj.src) {\n", " (window.URL || window.webkitURL).revokeObjectURL(\n", " fig.imageObj.src);\n", " }\n", "\n", " fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n", " evt.data);\n", " fig.updated_canvas_event();\n", " fig.waiting = false;\n", " return;\n", " }\n", " else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n", " fig.imageObj.src = evt.data;\n", " fig.updated_canvas_event();\n", " fig.waiting = false;\n", " return;\n", " }\n", "\n", " var msg = JSON.parse(evt.data);\n", " var msg_type = msg['type'];\n", "\n", " // Call the \"handle_{type}\" callback, which takes\n", " // the figure and JSON message as its only arguments.\n", " try {\n", " var callback = fig[\"handle_\" + msg_type];\n", " } catch (e) {\n", " console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n", " return;\n", " }\n", "\n", " if (callback) {\n", " try {\n", " // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n", " callback(fig, msg);\n", " } catch (e) {\n", " console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n", " }\n", " }\n", " };\n", "}\n", "\n", "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n", "mpl.findpos = function(e) {\n", " //this section is from http://www.quirksmode.org/js/events_properties.html\n", " var targ;\n", " if (!e)\n", " e = window.event;\n", " if (e.target)\n", " targ = e.target;\n", " else if (e.srcElement)\n", " targ = e.srcElement;\n", " if (targ.nodeType == 3) // defeat Safari bug\n", " targ = targ.parentNode;\n", "\n", " // jQuery normalizes the pageX and pageY\n", " // pageX,Y are the mouse positions relative to the document\n", " // offset() returns the position of the element relative to the document\n", " var x = e.pageX - $(targ).offset().left;\n", " var y = e.pageY - $(targ).offset().top;\n", "\n", " return {\"x\": x, \"y\": y};\n", "};\n", "\n", "/*\n", " * return a copy of an object with only non-object keys\n", " * we need this to avoid circular references\n", " * http://stackoverflow.com/a/24161582/3208463\n", " */\n", "function simpleKeys (original) {\n", " return Object.keys(original).reduce(function (obj, key) {\n", " if (typeof original[key] !== 'object')\n", " obj[key] = original[key]\n", " return obj;\n", " }, {});\n", "}\n", "\n", "mpl.figure.prototype.mouse_event = function(event, name) {\n", " var canvas_pos = mpl.findpos(event)\n", "\n", " if (name === 'button_press')\n", " {\n", " this.canvas.focus();\n", " this.canvas_div.focus();\n", " }\n", "\n", " var x = canvas_pos.x * mpl.ratio;\n", " var y = canvas_pos.y * mpl.ratio;\n", "\n", " this.send_message(name, {x: x, y: y, button: event.button,\n", " step: event.step,\n", " guiEvent: simpleKeys(event)});\n", "\n", " /* This prevents the web browser from automatically changing to\n", " * the text insertion cursor when the button is pressed. We want\n", " * to control all of the cursor setting manually through the\n", " * 'cursor' event from matplotlib */\n", " event.preventDefault();\n", " return false;\n", "}\n", "\n", "mpl.figure.prototype._key_event_extra = function(event, name) {\n", " // Handle any extra behaviour associated with a key event\n", "}\n", "\n", "mpl.figure.prototype.key_event = function(event, name) {\n", "\n", " // Prevent repeat events\n", " if (name == 'key_press')\n", " {\n", " if (event.which === this._key)\n", " return;\n", " else\n", " this._key = event.which;\n", " }\n", " if (name == 'key_release')\n", " this._key = null;\n", "\n", " var value = '';\n", " if (event.ctrlKey && event.which != 17)\n", " value += \"ctrl+\";\n", " if (event.altKey && event.which != 18)\n", " value += \"alt+\";\n", " if (event.shiftKey && event.which != 16)\n", " value += \"shift+\";\n", "\n", " value += 'k';\n", " value += event.which.toString();\n", "\n", " this._key_event_extra(event, name);\n", "\n", " this.send_message(name, {key: value,\n", " guiEvent: simpleKeys(event)});\n", " return false;\n", "}\n", "\n", "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n", " if (name == 'download') {\n", " this.handle_save(this, null);\n", " } else {\n", " this.send_message(\"toolbar_button\", {name: name});\n", " }\n", "};\n", "\n", "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n", " this.message.textContent = tooltip;\n", "};\n", "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n", "\n", "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n", "\n", "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n", " // Create a \"websocket\"-like object which calls the given IPython comm\n", " // object with the appropriate methods. Currently this is a non binary\n", " // socket, so there is still some room for performance tuning.\n", " var ws = {};\n", "\n", " ws.close = function() {\n", " comm.close()\n", " };\n", " ws.send = function(m) {\n", " //console.log('sending', m);\n", " comm.send(m);\n", " };\n", " // Register the callback with on_msg.\n", " comm.on_msg(function(msg) {\n", " //console.log('receiving', msg['content']['data'], msg);\n", " // Pass the mpl event to the overridden (by mpl) onmessage function.\n", " ws.onmessage(msg['content']['data'])\n", " });\n", " return ws;\n", "}\n", "\n", "mpl.mpl_figure_comm = function(comm, msg) {\n", " // This is the function which gets called when the mpl process\n", " // starts-up an IPython Comm through the \"matplotlib\" channel.\n", "\n", " var id = msg.content.data.id;\n", " // Get hold of the div created by the display call when the Comm\n", " // socket was opened in Python.\n", " var element = $(\"#\" + id);\n", " var ws_proxy = comm_websocket_adapter(comm)\n", "\n", " function ondownload(figure, format) {\n", " window.open(figure.imageObj.src);\n", " }\n", "\n", " var fig = new mpl.figure(id, ws_proxy,\n", " ondownload,\n", " element.get(0));\n", "\n", " // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n", " // web socket which is closed, not our websocket->open comm proxy.\n", " ws_proxy.onopen();\n", "\n", " fig.parent_element = element.get(0);\n", " fig.cell_info = mpl.find_output_cell(\"\");\n", " if (!fig.cell_info) {\n", " console.error(\"Failed to find cell for figure\", id, fig);\n", " return;\n", " }\n", "\n", " var output_index = fig.cell_info[2]\n", " var cell = fig.cell_info[0];\n", "\n", "};\n", "\n", "mpl.figure.prototype.handle_close = function(fig, msg) {\n", " var width = fig.canvas.width/mpl.ratio\n", " fig.root.unbind('remove')\n", "\n", " // Update the output cell to use the data from the current canvas.\n", " fig.push_to_output();\n", " var dataURL = fig.canvas.toDataURL();\n", " // Re-enable the keyboard manager in IPython - without this line, in FF,\n", " // the notebook keyboard shortcuts fail.\n", " IPython.keyboard_manager.enable()\n", " $(fig.parent_element).html('');\n", " fig.close_ws(fig, msg);\n", "}\n", "\n", "mpl.figure.prototype.close_ws = function(fig, msg){\n", " fig.send_message('closing', msg);\n", " // fig.ws.close()\n", "}\n", "\n", "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n", " // Turn the data on the canvas into data in the output cell.\n", " var width = this.canvas.width/mpl.ratio\n", " var dataURL = this.canvas.toDataURL();\n", " this.cell_info[1]['text/html'] = '';\n", "}\n", "\n", "mpl.figure.prototype.updated_canvas_event = function() {\n", " // Tell IPython that the notebook contents must change.\n", " IPython.notebook.set_dirty(true);\n", " this.send_message(\"ack\", {});\n", " var fig = this;\n", " // Wait a second, then push the new image to the DOM so\n", " // that it is saved nicely (might be nice to debounce this).\n", " setTimeout(function () { fig.push_to_output() }, 1000);\n", "}\n", "\n", "mpl.figure.prototype._init_toolbar = function() {\n", " var fig = this;\n", "\n", " var nav_element = $('')\n", " nav_element.attr('style', 'width: 100%');\n", " this.root.append(nav_element);\n", "\n", " // Define a callback function for later on.\n", " function toolbar_event(event) {\n", " return fig.toolbar_button_onclick(event['data']);\n", " }\n", " function toolbar_mouse_event(event) {\n", " return fig.toolbar_button_onmouseover(event['data']);\n", " }\n", "\n", " for(var toolbar_ind in mpl.toolbar_items){\n", " var name = mpl.toolbar_items[toolbar_ind][0];\n", " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", " var image = mpl.toolbar_items[toolbar_ind][2];\n", " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", "\n", " if (!name) { continue; };\n", "\n", " var button = $('');\n", " button.click(method_name, toolbar_event);\n", " button.mouseover(tooltip, toolbar_mouse_event);\n", " nav_element.append(button);\n", " }\n", "\n", " // Add the status bar.\n", " var status_bar = $('');\n", " nav_element.append(status_bar);\n", " this.message = status_bar[0];\n", "\n", " // Add the close button to the window.\n", " var buttongrp = $('');\n", " var button = $('');\n", " button.click(function (evt) { fig.handle_close(fig, {}); } );\n", " button.mouseover('Stop Interaction', toolbar_mouse_event);\n", " buttongrp.append(button);\n", " var titlebar = this.root.find($('.ui-dialog-titlebar'));\n", " titlebar.prepend(buttongrp);\n", "}\n", "\n", "mpl.figure.prototype._root_extra_style = function(el){\n", " var fig = this\n", " el.on(\"remove\", function(){\n", "\tfig.close_ws(fig, {});\n", " });\n", "}\n", "\n", "mpl.figure.prototype._canvas_extra_style = function(el){\n", " // this is important to make the div 'focusable\n", " el.attr('tabindex', 0)\n", " // reach out to IPython and tell the keyboard manager to turn it's self\n", " // off when our div gets focus\n", "\n", " // location in version 3\n", " if (IPython.notebook.keyboard_manager) {\n", " IPython.notebook.keyboard_manager.register_events(el);\n", " }\n", " else {\n", " // location in version 2\n", " IPython.keyboard_manager.register_events(el);\n", " }\n", "\n", "}\n", "\n", "mpl.figure.prototype._key_event_extra = function(event, name) {\n", " var manager = IPython.notebook.keyboard_manager;\n", " if (!manager)\n", " manager = IPython.keyboard_manager;\n", "\n", " // Check for shift+enter\n", " if (event.shiftKey && event.which == 13) {\n", " this.canvas_div.blur();\n", " event.shiftKey = false;\n", " // Send a \"J\" for go to next cell\n", " event.which = 74;\n", " event.keyCode = 74;\n", " manager.command_mode();\n", " manager.handle_keydown(event);\n", " }\n", "}\n", "\n", "mpl.figure.prototype.handle_save = function(fig, msg) {\n", " fig.ondownload(fig, null);\n", "}\n", "\n", "\n", "mpl.find_output_cell = function(html_output) {\n", " // Return the cell and output element which can be found *uniquely* in the notebook.\n", " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", " // IPython event is triggered only after the cells have been serialised, which for\n", " // our purposes (turning an active figure into a static one), is too late.\n", " var cells = IPython.notebook.get_cells();\n", " var ncells = cells.length;\n", " for (var i=0; i