{ "cells": [ { "cell_type": "markdown", "id": "aab9ba3c", "metadata": {}, "source": [ "# Fibonacci States" ] }, { "cell_type": "markdown", "source": [ "ZPGenerator is designed to simulate sources of light that require complicated pulse sequences to produce the photonic state. To demonstrate this capability, this example explores constructing and simulating a source of entangled photonic Fibonacci states that were first proposed and demonstrated in a Quandela research paper [[S. C. Wein et al., Nature Photonics 16, 374–379 (2022)](https://www.nature.com/articles/s41566-022-00979-z)]." ], "metadata": { "collapsed": false } }, { "cell_type": "markdown", "id": "f32ab5ac", "metadata": {}, "source": [ "## Theory background" ] }, { "cell_type": "markdown", "id": "4671b23b", "metadata": {}, "source": [ "Two-level atoms, or artificial atoms such as quantum dots, have been widely studied as a source of single photons. To deterministically generate entangled states of light, usually we must turn to sources of light based on multi-level systems, such as charged exciton containing the trion state (see the [Quantum Dots](quantum_dots.ipynb) and [Entanglement Generation](entanglement_generation.ipynb) tutorials). Surprisingly, a two-level system composed of a ground state $|g\\rangle$ and an excited state $|e\\rangle$ _can_ be used to deterministically generate entangled states of light encoded in the photon-number basis. This relies on the fact that the interaction between a two-level system and the electromagnetic field is essentially an entangling gate that preserves quantum coherence [[J. C. Loredo et al., Nature Photonics 13, 803–808 (2019)](https://www.nature.com/articles/s41566-019-0506-3)].\n", "\n", "The basic idea is to apply a sequence of well-timed excitation pulses to re-excite the atom before it has had time to fully decay. These excitation pulses play the role of single-qubit bit-flip gates on an ancillary qubit (the source) that is used to entangled the electromagnetic field. The photonic qubits are then the occupation of time bin modes defined between each subsequent pulse.\n", "\n", "As an example, the state of the source after a single $\\pi$ pulse is $|e\\rangle$. After a delay exactly equal to the atomic half-life $\\tau = T_1\\ln(2)$ where $T_1$ is the source lifetime, the atom may or may not have emitted a photon. Since the light-matter interaction is coherent, the total source-field system enters into an entangled state $|\\Psi\\rangle = (|e\\rangle|0\\rangle + |g\\rangle|1\\rangle)/\\sqrt{2}$. If, at this moment, we apply a second $\\pi$ pulse, the state of the source is flipped and the total light-matter state becomes $|\\Psi\\rangle = (|g\\rangle|0\\rangle + |e\\rangle|1\\rangle)/\\sqrt{2}$. Now, if we let the atom finish decaying to the ground state, we are left with the separable state $|\\Psi\\rangle = |g\\rangle|\\psi\\rangle$ where the state of the light is a maximally entangled Bell state $|\\psi\\rangle = (|00\\rangle + |11\\rangle)/\\sqrt{2}$.\n", "\n", "This idea can be extended to $N$ $\\pi$ pulses where each subsequent pulse adds a qubit to the state of light. It turns out that the delay between each pulse that maximises the entanglement in the state of light are determined by the Fibonacci sequence:\n", "\\begin{equation}\n", "\\tau_i = T_1\\ln\\left(\\frac{F_{N+2-i}}{F_{N-i}}\\right)\n", "\\end{equation}\n", "where $F_i = F_{i-1}+F_{i-2}$, $F_{0} = 0$, and $F_{1}=1$. Applying a pulse sequence based on this pattern will produce a sequence of entangled states that are expressed as an equally-weighted superposition of $F_N$ basis states:\n", " \n", "$$\n", "\\begin{aligned}\n", " |\\psi_0\\rangle &= |0\\rangle\\\\\n", " |\\psi_1\\rangle &= |1\\rangle\\\\\n", " |\\psi_2\\rangle &= \\left(|00\\rangle+|11\\rangle\\right)/\\sqrt{2}\\\\\n", " |\\psi_3\\rangle &= \\left(|001\\rangle+|100\\rangle+|111\\rangle\\right)/\\sqrt{3}\\\\\n", " |\\psi_4\\rangle &= \\left(|0000\\rangle+|0011\\rangle+|1001\\rangle+|1100\\rangle+|1111\\rangle\\right)/\\sqrt{5}\\\\\n", " &\\vdots\n", "\\end{aligned}\n", "$$\n", " \n", "We can also notice that $|\\psi_N\\rangle$ is a superposition state of photon number states with the same parity as $N$. Either $N$ is odd and $|\\psi_N\\rangle$ is a superposition of odd-numbers of photons or $N$ is even and $|\\psi_N\\rangle$ is a superposition of even-numbers of photons. Furthermore, the number of states composing $|\\psi_N\\rangle$ with the same total number of photons will follow Pascal's triangle:\n", "\n", "
\n", "\n", "
" ] }, { "cell_type": "markdown", "id": "43194ca3", "metadata": {}, "source": [ "## Fibonacci pulse sequence" ] }, { "cell_type": "markdown", "id": "ff28eeeb", "metadata": {}, "source": [ "To test our theory and replicate some experimental results, we can define a Fibonacci pulse sequence and simulate photon statistics using ZPGenerator." ] }, { "cell_type": "code", "execution_count": 32, "id": "b1d3ef4f", "metadata": { "ExecuteTime": { "end_time": "2024-02-09T13:19:01.589276Z", "start_time": "2024-02-09T13:19:01.177009Z" } }, "outputs": [], "source": [ "from zpgenerator import *\n", "from functools import reduce\n", "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "id": "4373218d", "metadata": {}, "source": [ "First, we define a function to generate the Fibonacci sequence. In this case, we can take the answer to [this Stack Overflow question](https://stackoverflow.com/questions/4935957/fibonacci-numbers-with-an-one-liner-in-python-3)." ] }, { "cell_type": "code", "execution_count": 33, "id": "6fdd4b66", "metadata": { "ExecuteTime": { "end_time": "2024-02-09T13:19:01.590192Z", "start_time": "2024-02-09T13:19:01.189866Z" } }, "outputs": [], "source": [ "def fibonacci(n: int) -> int:\n", " return reduce(lambda x, n: [x[1], x[0] + x[1]], range(n), [0, 1])[0]" ] }, { "cell_type": "markdown", "id": "9e6c9b40", "metadata": {}, "source": [ "Second, we can make a function that generates a list of delay times $\\tau_i$ defined in the previous section." ] }, { "cell_type": "code", "execution_count": 34, "id": "a5fd581c", "metadata": { "ExecuteTime": { "end_time": "2024-02-09T13:19:01.697456Z", "start_time": "2024-02-09T13:19:01.202208Z" } }, "outputs": [], "source": [ "def fibonacci_delays(N: int) -> list:\n", " delays = [0.] # initialise the list of pulse delay times starting with the initial time of 0.\n", " \n", " # Loop through each pulse and add up the delay, append to the list\n", " for i in range(1, N):\n", " delay = np.log(fibonacci(N - i + 2) / fibonacci(N - i)) # tau_i in units of T1\n", " delays.append(delays[-1] + delay)\n", " \n", " return delays" ] }, { "cell_type": "markdown", "id": "287ac09f", "metadata": {}, "source": [ "Third, we can use the Pulse class to define a function that builds a sequence of $N$ $\\pi$ pulses separated by the delay $\\tau_i$ defined in the previous section." ] }, { "cell_type": "code", "execution_count": 35, "id": "fa0544c8", "metadata": { "ExecuteTime": { "end_time": "2024-02-09T13:19:01.698362Z", "start_time": "2024-02-09T13:19:01.215350Z" } }, "outputs": [], "source": [ "def fibonacci_sequence(N: int, # the number of pulses\n", " shape: str = 'dirac', # dirac, gaussian, or square.\n", " width: float = 0.1 # the pulse width (irrelevant for dirac) in units of T1.\n", " ) -> Pulse:\n", " sequence = Pulse() # initialise the pulse object\n", "\n", " delays = fibonacci_delays(N) # generate the list of pulse times\n", "\n", " for i in range(0, N): # loop over each pulse and add it to our sequence\n", "\n", " # define the new pulse we want to add\n", " pulse_shape = Pulse.square if shape == 'square' else Pulse.gaussian if shape == 'gaussian' else Pulse.dirac\n", " pulse = pulse_shape({'delay': delays[i], 'area': np.pi, 'width': width}, name='pulse ' + str(i))\n", "\n", " sequence.add(pulse) # we add the pulse to our sequence\n", "\n", " return sequence" ] }, { "cell_type": "markdown", "id": "854ff5f0", "metadata": {}, "source": [ "To get a quick idea of what our pulse sequence looks like, we can use the plot() method. Note that, by default, evaluating a pulse shape will ignore any Dirac pulses." ] }, { "cell_type": "code", "execution_count": 36, "outputs": [ { "data": { "text/plain": "
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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sequence = fibonacci_sequence(4, shape = 'gaussian', width=0.1) # define our sequence\n", "sequence.plot().show()" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2024-02-09T13:19:01.712677Z", "start_time": "2024-02-09T13:19:01.278955Z" } } }, { "cell_type": "markdown", "source": [ "Note that we can always change the pulse parameters afterward making analysis easy!" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 37, "outputs": [ { "data": { "text/plain": "
", "image/png": 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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sequence.plot(parameters={'width': 0.1}, label='width = 0.1')\n", "sequence.plot(parameters={'width': 0.2}, label='width = 0.2')\n", "sequence.plot(parameters={'width': 0.3}, label='width = 0.3').show()" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2024-02-09T13:19:01.729527Z", "start_time": "2024-02-09T13:19:01.342083Z" } } }, { "cell_type": "markdown", "source": [ "Since we named each pulse in the sequence, we can also modify the pulse parameters individually." ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 38, "outputs": [ { "data": { "text/plain": "
", "image/png": 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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sequence.plot(parameters={'pulse 0/width': 0.10, 'pulse/area 0': np.pi/2,\n", " 'pulse 1/width': 0.12,\n", " 'pulse 2/width': 0.09,\n", " 'pulse 3/width': 0.14}).show()" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2024-02-09T13:19:01.731871Z", "start_time": "2024-02-09T13:19:01.597187Z" } } }, { "cell_type": "markdown", "id": "2706ac01", "metadata": { "ExecuteTime": { "end_time": "2023-06-01T11:45:01.256763Z", "start_time": "2023-06-01T11:45:01.252376Z" } }, "source": [ "## Fibonacci source" ], "outputs": [], "execution_count": 8 }, { "cell_type": "markdown", "id": "50c17469", "metadata": {}, "source": [ "Now that we have our pulse sequence, we must build our source by applying the sequence to generate photons." ] }, { "cell_type": "code", "execution_count": 39, "outputs": [], "source": [ "source = Source.two_level(pulse=sequence)" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2024-02-09T13:19:01.731960Z", "start_time": "2024-02-09T13:19:01.699750Z" } } }, { "cell_type": "markdown", "id": "97725777", "metadata": {}, "source": [ "Once we defined our source, we can simulate various figures of merit. One of the first things to look at is the source \"lifetime\", which is the instantaneous probability that the two-level system is in its excited state. This quantity is proportional to the shape of the emitted photonic wavepacket. For visualisation, let's use a Gaussian pulse shape." ] }, { "cell_type": "code", "execution_count": 40, "id": "753ee7ed", "metadata": { "ExecuteTime": { "end_time": "2024-02-09T13:19:01.937385Z", "start_time": "2024-02-09T13:19:01.715806Z" } }, "outputs": [ { "data": { "text/plain": "
", "image/png": 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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Evaluate the source lifetime between t = -1 and t = 8 for 600 points.\n", "source.plot_lifetime(start = -1, end = 8, resolution = 600)\n", "sequence.plot(scale=1/50).show()" ] }, { "cell_type": "markdown", "id": "c572e299", "metadata": {}, "source": [ "Now that we have verified our source emission intensity looks consistent with our applied pulse sequence, let's look at the photon statistics. To make things simpler, let's make a function that returns a Fibonacci source." ] }, { "cell_type": "code", "execution_count": 41, "outputs": [], "source": [ "def fibonacci_source(N: int, # the number of pulses\n", " shape: str = 'dirac', # dirac, gaussian, or square.\n", " width: float = 0.1, # the pulse width (irrelevant for dirac) in units of T1.\n", " efficiency: float = 1. # the efficiency of collecting a photon from the source.\n", " ) -> Source:\n", " return Source.two_level(pulse=fibonacci_sequence(N, shape, width), efficiency=efficiency)" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2024-02-09T13:19:01.939020Z", "start_time": "2024-02-09T13:19:01.936699Z" } } }, { "cell_type": "markdown", "source": [ "Let's continue on by first analysing the ideal case where we use Dirac $\\pi$ pulses to compare to our theory. Using the photon_statistics() method, we can automatically and efficiently compute the total integrated photon statistics produced over the entire wavepacket lifetime." ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 42, "id": "045373f8", "metadata": { "ExecuteTime": { "end_time": "2024-02-09T13:19:02.278342Z", "start_time": "2024-02-09T13:19:01.942110Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Figure of Merit | Value\n", "Brightness | 0.8000\n", "Average photon number | 2.0000\n", "Intensity correlation | 0.9000\n", "\n", "Number | Probability\n", "0 | 0.20000\n", "1 | 0.00000\n", "2 | 0.60000\n", "3 | 0.00000\n", "4 | 0.20000\n", "5 | 0.00000\n", "6 | 0.00000\n", "\n" ] } ], "source": [ "source = fibonacci_source(4, shape='dirac')\n", "pn = source.photon_statistics()\n", "pn.display_figures()\n", "pn.display()" ] }, { "cell_type": "markdown", "id": "4b697f5b", "metadata": {}, "source": [ "We can see that the average number of photons (mu $=\\mu$ ) produced by our source per excitation pulse sequence is $2$. The source brightness (beta $=\\beta$), which is the probability of producing at least one photon per excitation pulse sequence, is $0.8$. The integrated intensity correlation (g2 $= g^{(2)}$), which characterises the amount of multi-photon emission, is $0.9$. These figures of merit seem to be almost classical in nature, but in fact the photon number probabilities show very clearly that the photonic state produced by our source is not at all a coherent state. As predicted in the Theory background section, we see non-zero probabilities only for even numbers of photons, which is the same parity as the number of pulses that we applied. Furthermore, we can see that $1/5$ of the time we measure no photons, $3/5$ of the time we measure two photons and the remaining $1/5$ of the time we measure four photons. This 1, 3, 1 pattern follows the shallow diagonal of Pascale's triangle shown in the Theory background section for $|\\psi_4\\rangle$.\n", "\n", "To demonstrate how fast ZPGenerator is for computing integrated photon number probabilities, let's take a quick look at the photon distribution of the $|\\psi_{40}\\rangle$ and $|\\psi_{41}\\rangle$ Fibonacci states. Note that, these highly-entangled photonic states live in a total Hilbert space of up to $2^{41}=2.2$ trillion in size. However, since we are only obtaining the integrated (averaged) photon number statistics of the state, the simulation can be performed in polynomial time using the ZPG method." ] }, { "cell_type": "code", "execution_count": 43, "outputs": [], "source": [ "source = fibonacci_source(40, shape='dirac')\n", "psi40 = source.photon_statistics(truncation=40)\n", "\n", "source = fibonacci_source(41, shape='dirac')\n", "psi41 = source.photon_statistics(truncation=41)" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2024-02-09T13:19:24.538909Z", "start_time": "2024-02-09T13:19:02.299805Z" } } }, { "cell_type": "code", "execution_count": 44, "outputs": [ { "data": { "text/plain": "
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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "psi40.plot(label='|$\\psi_{40}$>', color='b')\n", "psi41.plot(label='|$\\psi_{41}$>', color='r').show()" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2024-02-09T13:19:24.658217Z", "start_time": "2024-02-09T13:19:24.546663Z" } } }, { "cell_type": "markdown", "source": [ "In the above plot, we can see clearly that for $N=40$, only even-$n$ probabilities are nonzero. Likewise for $N=41$, only odd-$n$ probabilities are nonzero. Interestingly, the shape of the distribution when neglecting the parity, follows a Gaussian distribution." ], "metadata": { "collapsed": false } }, { "cell_type": "markdown", "source": [ "To be sure that we are generating states with individual qubits occupying the time bin modes, and not just a single mode with an interesting photon-number distribution, we must resolve the possible Fock states contributing to the total Fibonacci state. For $|\\psi_4\\rangle$, this means we must resolve the three states: $|0011\\rangle$, $|1001\\rangle$, and $|1100\\rangle$ that contribute to the two-photon subspace. To do this, we can measure time-bin correlations." ], "metadata": { "collapsed": false } }, { "cell_type": "markdown", "id": "bf3652ec", "metadata": { "ExecuteTime": { "end_time": "2023-06-01T11:45:01.490136Z", "start_time": "2023-06-01T11:45:01.486717Z" } }, "source": [ "

4. Time Bin Correlations

" ], "outputs": [], "execution_count": 12 }, { "cell_type": "markdown", "id": "490dc42e", "metadata": {}, "source": [ "Once we have designed our source, we can monitor its emission into different time bins using the Processor class to add detectors explicitly. In this case, we have a very simple Processor composed of a single mode collecting emission from our Fibonacci source, an identity linear-optical circuit, but a more complex set of time bin detectors counting photons in defined time bins. Since we already built our source in the previous sections, let's build a detector that partitions time following the same time bin thresholds that we used to define the pulse sequence. This kind of time-bin partitioned detector can easily be created using the partition() class method of Detector. See [Detectors](detectors.ipynb) for more information about this catalogue detector type." ] }, { "cell_type": "code", "execution_count": 45, "outputs": [], "source": [ "def fibonacci_detector(pulse_number: int):\n", " return Detector.partition(thresholds=fibonacci_delays(pulse_number), name='fibo')" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2024-02-09T13:19:24.663594Z", "start_time": "2024-02-09T13:19:24.662280Z" } } }, { "cell_type": "markdown", "source": [ "Now, let's add it to a processor following the Fibonacci source." ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 46, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " _____________\n", "|0>----| Component |----D~ [fibo bin 0, fibo bin 1, fibo bin 2, fibo bin 3]\n", " ‾‾‾‾‾‾‾‾‾‾‾‾‾\n" ] } ], "source": [ "pulse_number = 4\n", "p = Processor() // fibonacci_source(pulse_number) // fibonacci_detector(pulse_number)\n", "p.display()" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2024-02-09T13:19:24.691402Z", "start_time": "2024-02-09T13:19:24.680703Z" } } }, { "cell_type": "markdown", "id": "cd222553", "metadata": {}, "source": [ "Using the display() method, we can see that our processor is composed of a single source with emission collected into a single mode, and monitored by a single detector. However, there are 4 detection bins associated with the detector. Note that we can always check how many measurement bins the processor contains by looking at the 'bins' property." ] }, { "cell_type": "code", "execution_count": 47, "outputs": [ { "data": { "text/plain": "4" }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p.bins" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2024-02-09T13:19:24.691663Z", "start_time": "2024-02-09T13:19:24.683923Z" } } }, { "cell_type": "markdown", "source": [ "Let's take a look at the probabilities for detecting photons across these four time bins." ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 48, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Pattern | Probability\n", "0 0 0 0 | 0.20000\n", "0 0 1 1 | 0.20000\n", "1 0 0 1 | 0.20000\n", "1 1 0 0 | 0.20000\n", "1 1 1 1 | 0.20000\n", "\n" ] } ], "source": [ "pn = p.probs()\n", "pn.display()" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2024-02-09T13:19:24.864488Z", "start_time": "2024-02-09T13:19:24.690186Z" } } }, { "cell_type": "markdown", "id": "e31365e2", "metadata": {}, "source": [ "As predicted in the Theory background section, we can now resolve all five possible outcomes of our Fibonacci source, and they each occur with $1/5$ probability! As a general rule, the outcome labels of Processor give the photon number listed chronologically from left to right for each detection time bin. Luckily, we assigned a name to our time partition detector, which labels each bin chronologically, so we can always double-check the ordering by looking at the 'bin_labels' property of the processor." ] }, { "cell_type": "code", "execution_count": 49, "id": "36ec235f", "metadata": { "ExecuteTime": { "end_time": "2024-02-09T13:19:24.867448Z", "start_time": "2024-02-09T13:19:24.865446Z" } }, "outputs": [ { "data": { "text/plain": "['fibo bin 0', 'fibo bin 1', 'fibo bin 2', 'fibo bin 3']" }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p.bin_labels" ] }, { "cell_type": "markdown", "id": "aa04fb2d", "metadata": { "ExecuteTime": { "end_time": "2023-06-01T11:45:01.930591Z", "start_time": "2023-06-01T11:45:01.782455Z" } }, "source": [ "## Interference" ], "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Figure of Merit: Measurement\n", "mu: 1.00000\n", "g2: 1.00000\n", "VHOM: -0.51994\n", "M: 0.48507\n", "c1: 0.00126\n", "c2: 0.50826\n", "beta: 0.50000\n", "\n", "Photon number: Probability\n", "0: 0.500000\n", "1: 0.000000\n", "2: 0.500000\n", "3: 0.000000\n", "4: 0.000000\n" ] } ], "execution_count": 16 }, { "cell_type": "markdown", "id": "3146175f", "metadata": {}, "source": [ "Now that we have confirmed our source produces the correct photon statistics, we should also ensure that we have coherence between Fock states. To do this, we can follow the method used in [[S. C. Wein et al., Nature Photonics 16, 374–379 (2022)](https://www.nature.com/articles/s41566-022-00979-z)] to characterise the $N=2$ Bell state using Hong-Ou-Mandel interference and measuring the second-order number coherence ($c^{(2)}$) between $|00\\rangle$ and $|11\\rangle$. Using ZPGenerator, we can make quick estimates of figures of merit obtained from Hong-Ou-Mandel interference using the hom() method of the Processor class. Since we only want to view these figures of merit, let's use the display_hom() method, which computes hom() and then displays the results." ] }, { "cell_type": "code", "execution_count": 50, "id": "b46e3db7", "metadata": { "ExecuteTime": { "end_time": "2024-02-09T13:19:25.141577Z", "start_time": "2024-02-09T13:19:24.868694Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Figure of Merit | Value\n", "First order number coherence | 0.0013\n", "Second order number coherence | 0.5076\n", "Hong-Ou-Mandel visibility | -0.5176\n", "Mean wavepacket overlap | 0.4850\n", "\n" ] } ], "source": [ "p = Processor() // fibonacci_source(2)\n", "p.display_hom(pseudo_limit=0.005)" ] }, { "cell_type": "markdown", "id": "02139456", "metadata": {}, "source": [ "The hom() method applies a pseudo-lossy regime algorithm using threshold detectors and so, although it is fast to evaluate, it can be quite sensitive to the 'pseudo_limit' efficiency regime parameter. For an appropriate choice of pseudo_limit, we can see that ZPGenerator predicts very close to the ideal values expected from the ideal Bell state in [[S. C. Wein et al., Nature Photonics 16, 374–379 (2022)](https://www.nature.com/articles/s41566-022-00979-z)]. That is, we get $c^{(2)}\\simeq 1/2$, $c^{(1)}\\simeq 0$, and $V_\\text{HOM}= M - g^{(2)} \\simeq -1/2$ implying $M\\simeq 1/2$. To do better than this quick estimation algorithm, we can manually build a Hong-Ou-Mandel processor and do our own virtual experiment using photon-number resolving detectors." ] }, { "cell_type": "code", "execution_count": 51, "id": "6c630301", "metadata": { "ExecuteTime": { "end_time": "2024-02-09T13:19:25.144969Z", "start_time": "2024-02-09T13:19:25.143467Z" } }, "outputs": [], "source": [ "def fibonacci_hom(phase: float = 0, shape: str = 'dirac', width: float = 0.1, efficiency: float = 1.) -> Processor:\n", " p = Processor() # initialise a processor with two modes\n", " \n", " p.add([0, 1], fibonacci_source(2, shape, width, efficiency)) # add an N=2 Fibonacci source to modes 0 and 1\n", " p.add(0, Circuit.ps(phase)) # add a phase shifter on mode 0 to tune the relate phases of the interfering photonic states\n", " p.add(0, Circuit.bs()) # add the beam splitter to perform Hong-Ou-Mandel interference\n", " p.add(0, Detector.pnr(4), bin_name='output 0') # Add number resolving detectors monitoring output modes with maximum resolution of 4\n", " p.add(1, Detector.pnr(4), bin_name='output 1')\n", " \n", " return p" ] }, { "cell_type": "markdown", "id": "6a880bd5", "metadata": {}, "source": [ "Now that we have built our Hong-Ou-Mandel processor, we can take a look at the probabilities from interference when there is no relative phase between our input states. Note that, in this case, our detectors are not time bin arrays, so we will look at the time-integrated properties of our state." ] }, { "cell_type": "code", "execution_count": 52, "id": "4bd286ba", "metadata": { "ExecuteTime": { "end_time": "2024-02-09T13:19:25.696824Z", "start_time": "2024-02-09T13:19:25.145969Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Pattern | Probability\n", "0 0 | 0.25000\n", "4 0 | 0.06250\n", "1 1 | 0.50000\n", "2 2 | 0.12500\n", "0 4 | 0.06250\n", "\n" ] } ], "source": [ "p = fibonacci_hom(0)\n", "p.probs().display()" ] }, { "cell_type": "markdown", "id": "b613d1c1", "metadata": {}, "source": [ "The outcomes of a Processor are automatically arranged in chronological order based on the initial time of each detection time bin. If two bins share the same initial time, as in this case, they will be arranged according to the order that the detectors were added to the processor. Since we named our arrays based on the output port they were added to, we can double-check the ordering by looking at the bin_labels properties of our Processor." ] }, { "cell_type": "code", "execution_count": 53, "id": "d26354c7", "metadata": { "ExecuteTime": { "end_time": "2024-02-09T13:19:25.699542Z", "start_time": "2024-02-09T13:19:25.697515Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Bin labels: ['output 0', 'output 1']\n" ] } ], "source": [ "print('Bin labels: ', p.bin_labels)" ] }, { "cell_type": "markdown", "id": "04d370b3", "metadata": {}, "source": [ "To get a better estimate of the second-order coherence $c^{(2)}$, we can look at how the two-photon coincidence (1, 1) depends on the relative phase of the input states. Note that this type of exact numerical simulation would usually take an extremely long time to compute, because it requires simulating conditional time evolution of source states in the tensor product space of two source Hilbert spaces, evaluating $4^2 = 16$ possible detection outcomes for two detectors each resolving up to 4 photons, and then again for multiple different measurement configurations of our linear-optical circuit. Standard time-integration techniques would require recursive integration over multi-time correlation functions up to 8 dimensions in time. Using the ZPG method, however, we bypass this high-dimensional integration such that the simulation takes only a handful of seconds." ] }, { "cell_type": "code", "execution_count": 54, "id": "8c98095c", "metadata": { "ExecuteTime": { "end_time": "2024-02-09T13:19:38.961101Z", "start_time": "2024-02-09T13:19:25.815155Z" } }, "outputs": [ { "data": { "text/plain": "
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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "phases = np.linspace(0, np.pi, 25) # define some phases\n", "probs = [fibonacci_hom(phi).probs() for phi in phases] # evaluate the HOM probabilities for each phase\n", "\n", "# Let's extract coincidence probabilities only\n", "coinc_labels = [(1, 1), (1, 2), (2, 1), (2, 2)]\n", "coinc = [[pr[c] for c in coinc_labels] for pr in probs]\n", "\n", "# Plot each coincidence event\n", "for i, c in enumerate(coinc_labels):\n", " plt.plot(phases, list(zip(*coinc))[i], label='Pr(' + ''.join([str(n) for n in c]) + ')')\n", "\n", "plt.xlabel('Relative phase, $\\phi$')\n", "plt.ylabel('Coincidence probability')\n", "plt.legend(loc='upper center')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "6a84131c", "metadata": {}, "source": [ "As expected, we can see a clear fringe in the two-photon (1, 1) coincidence events due to interference between the vacuum of one input state and the two-photon state of the other, indicating coherence. On the other hand, the four-photon outcomes shows no such fringe, which is expected because there is only one possible input state combination giving rise to that outcome for a $|\\psi_2\\rangle$ state. Also, we can see that we never observe odd photon number coincidence events because our source is producing an even Fibonacci state!\n", "\n", "The value of $c^{(2)}$ can now be directly determined by taking the difference in the coincidence intensity at the minimum and maximum of the fringe, and then normalising by the squared average photon number of our source: $c^{(2)} = \\frac{1}{\\mu^2}\\sum_{n,m}nm|Pr_{\\phi=0}(nm) - Pr_{\\phi=\\pi/2}(nm)|$. Using either $\\mu=1$ from before or $\\mu=\\frac{1}{2}\\sum_{n,m}(n+m)Pr(nm)$, we can confirm $c^{(2)}=\\frac{1}{2}$ which, along with verifying that our source is indeed producing a photon-number Bell state." ] }, { "cell_type": "code", "execution_count": 55, "id": "5d1c6c63", "metadata": { "ExecuteTime": { "end_time": "2024-02-09T13:19:40.016858Z", "start_time": "2024-02-09T13:19:38.962474Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.5000022420571637\n" ] } ], "source": [ "def c2(shape: str = 'dirac', width: float = 0.1, efficiency: float = 1., args: dict = None) -> float:\n", " # Simulate HOM for max and min of the fringe\n", " probs0 = fibonacci_hom(0, shape, width, efficiency).probs(args)\n", " probs1 = fibonacci_hom(np.pi/2, shape, width, efficiency).probs(args)\n", " \n", " # Estimate mu from half the average photon number of both ouputs\n", " mu = sum((int(k[0]) + int(k[1]))*pr for k, pr in probs0.items())/2\n", " \n", " # Compute c2\n", " return sum(int(k[0])*int(k[1])*abs(probs0[k] - probs1[k]) for k in probs0.keys())/mu**2\n", "\n", "print(c2())" ] }, { "cell_type": "markdown", "id": "2329d63c", "metadata": { "ExecuteTime": { "end_time": "2023-06-01T11:45:08.035534Z", "start_time": "2023-06-01T11:45:08.027041Z" } }, "source": [ "## Imperfections" ], "outputs": [], "execution_count": 22 }, { "cell_type": "markdown", "id": "9db5056f", "metadata": {}, "source": [ "In reality, we are not able to apply perfect Dirac pulses to our emitter and our setup may not have perfect collection or detection efficiency. ZPGenerator is designed to take many physical imperfections into account in a natural way. To study imperfections, we can make a function that simulates the classical Bhattacharyya coefficient. This coefficient is an upper bound on the quantum state fidelity." ] }, { "cell_type": "code", "execution_count": 56, "id": "dda3db66", "metadata": { "ExecuteTime": { "end_time": "2024-02-09T13:19:40.020311Z", "start_time": "2024-02-09T13:19:40.019067Z" } }, "outputs": [], "source": [ "def bhatt_fidelity(N: int, # the number of pulses\n", " shape: str = 'dirac', # dirac, gaussian, or square.\n", " width: float = 0.1, # the pulse width (irrelevant for dirac) in units of T1.\n", " efficiency: float = 1. # the end-to-end efficiency\n", " ):\n", "\n", " # First, we simulate the ideal case as before\n", " p = Processor() // fibonacci_source(N) // fibonacci_detector(N)\n", " ideal_probs = p.probs()\n", " \n", " # next, we simulate the imperfect case\n", " p = Processor() // fibonacci_source(N, shape=shape, width=width, efficiency=efficiency) // fibonacci_detector(N)\n", " probs = p.probs()\n", "\n", " # we estimate an upper bound on the quantum state fidelity using squared classical Bhattacharyya coefficient\n", " bhatt = 0\n", " for k, v in ideal_probs.items():\n", " bhatt += np.sqrt(v * probs[k]) if k in probs.keys() else 0\n", "\n", " return bhatt ** 2" ] }, { "cell_type": "markdown", "id": "d4b7ecbb", "metadata": {}, "source": [ "Using this function, we can increase the Gaussian pulse width and see how the fidelity bound decreases." ] }, { "cell_type": "code", "execution_count": 57, "id": "6cdf0c99", "metadata": { "ExecuteTime": { "end_time": "2024-02-09T13:19:49.534026Z", "start_time": "2024-02-09T13:19:40.022480Z" } }, "outputs": [ { "data": { "text/plain": "
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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pulse_widths = np.linspace(0.001, 0.501, 20)\n", "\n", "fidelity_set = [bhatt_fidelity(4, shape='gaussian', width=width) for width in pulse_widths]\n", "\n", "plt.plot(pulse_widths, fidelity_set)\n", "plt.xlabel(\"Gaussian pulse standard deviation ($T_1$)\")\n", "plt.ylabel(\"Bhattacharyya coefficient\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "3f3cbd7f", "metadata": {}, "source": [ "Similarly, we can see how inefficiency decreases the fidelity bound even using perfect pulses." ], "outputs": [] }, { "cell_type": "code", "execution_count": 58, "id": "594c4bd0", "metadata": { "ExecuteTime": { "end_time": "2024-02-09T13:19:56.063837Z", "start_time": "2024-02-09T13:19:49.536380Z" } }, "outputs": [ { "data": { "text/plain": "
", "image/png": 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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "efficiency_set = np.linspace(0, 1, 20)\n", "\n", "fidelity_set = [bhatt_fidelity(4, shape='dirac', efficiency=efficiency) for efficiency in efficiency_set]\n", "\n", "plt.plot(efficiency_set, fidelity_set)\n", "plt.xlabel(\"Efficiency, $\\eta$\")\n", "plt.ylabel(\"Bhattacharyya coefficient\")\n", "plt.show()" ] }, { "cell_type": "markdown", "source": [], "metadata": { "collapsed": false } } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.9.6" } }, "nbformat": 4, "nbformat_minor": 5 }