{
"cells": [
{
"cell_type": "markdown",
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"source": [
"# Schrödinger's Worm and 2-qubit gates\n",
"\n",
"## Objectives\n",
"* Design, build, and test quantum circuits that model systems in superposition and entanglement.\n",
"* Learn additional error mitigation & reduction techniques"
]
},
{
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"
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"## Superposition\n",
"\n",
"The worm is alive when all five squares are black and dead when only four are black. Use a 0 to represent a white square and 1 to represent a black square as in the figure:\n",
"\n",
"![Screenshot%20from%202021-07-14%2013-25-21.png](attachment:Screenshot%20from%202021-07-14%2013-25-21.png)\n",
"\n",
"Representing the five segments as a state $|q_4 q_3 q_2 q_1 q_0\\rangle$ were the segments are number in descending order from left to right.\n",
"\n",
"* What is the classical state of the live 5-bit worm?"
]
},
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"source": [
"=============================\n",
"\n",
"$|q_4 q_3 q_2 q_1 q_0\\rangle=$ ???????\n",
"\n",
"============================="
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"* What is the classical state of the dead 5-bit worm?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"=============================\n",
"\n",
"$|q_4 q_3 q_2 q_1 q_0\\rangle=$ ???????\n",
"\n",
"============================="
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"* Use IBM Composer to create a worm in a superposition state of alive and dead. Let q[0] correspond to the bit on the far right. (Hint, remember that the composer initializes all qubits to 0)\n",
"* Can you modify the circuit so that the worm is first put in a superposition state and then brought to life?\n",
"* Can you modify the circuit so that the worm in a superposition state becomes definitely dead?"
]
},
{
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}
},
"cell_type": "markdown",
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"source": [
"## Entanglement\n",
"\n",
"The worm is next to a hungry bird, such that the worm is either alive or chomped to pieces\n",
"\n",
"![Screenshot%20from%202021-07-14%2013-25-27.png](attachment:Screenshot%20from%202021-07-14%2013-25-27.png)\n",
"\n",
"7. What is the classical state of the very dead worm?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"=============================\n",
"\n",
"$|q_4 q_3 q_2 q_1 q_0\\rangle=$ ???????\n",
"\n",
"============================="
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"* Create a circuit in IBM Composer that produces a worm in a superposition state of alive and very dead. (Hint: Two of the qubits are entangled.)\n",
"* Can you modify the circuit so that the worm in a superposition state becomes either definitely dead or definitely alive?"
]
},
{
"attachments": {
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"
}
},
"cell_type": "markdown",
"metadata": {},
"source": [
"# Working with real machines\n",
"\n",
"If I've understood what the previous sections asked, then the IBM Composer circuit for the worm near the bird is given by:\n",
"\n",
"![Screenshot%20from%202021-07-14%2021-59-11.png](attachment:Screenshot%20from%202021-07-14%2021-59-11.png)\n",
"\n",
"Unlike the circuits yesterday, this one has a 2-qubit gate (the CNOT). On real hardware, these gates typically have 100s or 1000s times gate errors. So lets investigate this by running our circuit on one of the devices.\n",
"\n",
"In order to run on actual devices, we need to perform at least 1 measurement. If we want to know the state of the entire worm, we need to measure every qubit\n",
"\n",
"* Add 5 measurement \"gates\" at the end of your circuit, one for each qubit\n",
"* Run your circuit on the ibmq_jakarta with 1024 shots. Name it something memorable! We will be doing multiple calculations\n",
"* In the cell below, record the frequency observed for the alive state and the dead state. (Don't count the spurious states that correspond to some other state)\n",
"* How does this probabilities compare to your theoretical expectations ($p_{alive}=p_{dead}=0.5$)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Alive: 0.380859375\n",
"Dead: 0.44140625\n"
]
}
],
"source": [
"num_shots=1024\n",
"\n",
"freq_alive=390\n",
"freq_dead=452\n",
"\n",
"prob_alive=freq_alive/num_shots\n",
"prob_dead=freq_dead/num_shots\n",
"\n",
"print(\"Alive: \", prob_alive)\n",
"print(\"Dead: \", prob_dead)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"During our lab yesterday, we discussed how often there is an asymmetry in the readout error -- measuring $|0\\rangle$ is typically easier to do more accurately then $|1\\rangle$. For this reason, if you can reduce the number of qubits in the $|1\\rangle$ state at the end, typically you will be more accurate.\n",
"\n",
"* Reconfigure your circuit such that dead segements are $|1\\rangle$ and live segments are $|0\\rangle$.\n",
"* Run this new circuit on ibmq_jakarta with 1024 shots.\n",
"* Record the results below, do you see a difference from your original results?\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Alive: 0.4501953125\n",
"Dead: 0.435546875\n"
]
}
],
"source": [
"num_shots=1024\n",
"\n",
"freq_alive=461\n",
"freq_dead=446\n",
"\n",
"prob_alive=freq_alive/num_shots\n",
"prob_dead=freq_dead/num_shots\n",
"\n",
"print(\"Alive: \", prob_alive)\n",
"print(\"Dead: \", prob_dead)"
]
},
{
"attachments": {
"Screenshot%20from%202021-07-14%2019-12-38.png": {
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"
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"
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}
},
"cell_type": "markdown",
"metadata": {},
"source": [
"When you look at your circuit, you might assume that all qubits are created equal. This is not true for two reasons: connectivity and gate fidelities. \n",
"\n",
"Connectiviy refers to the graph connecting each qubit to the rest of the computer. All-to-All connectivity refers to the ability of any set of qubits to be operated upon by a multi-qubit gate. This requires a substantial amount of hard work on the engineers part, and we don't expect it to be true for large computers. Instead, we expect qubits to be able to act directly with only a limited number of neighbors, and if nonlocal interactions are needed, multiple SWAP gates will be used to move the state of a given qubit closer to perform the operation.\n",
"\n",
"The graph connecting the qubits of ibmq_jakarta is shown in the figure\n",
"\n",
"![Screenshot%20from%202021-07-14%2019-16-12.png](attachment:Screenshot%20from%202021-07-14%2019-16-12.png)\n",
"\n",
"In this graph, 3 of the 7 qubits can talk to 2 other qubits. The remaining 4 only communicate with a single qubit.\n",
"\n",
"In addition to connectivity, different qubits on the same device can have dramatically different 1 and 2 qubit gate fidelities. So when optimizing circuits, qubits which are heavily utilized should be mapped to the ones on the architecture with high gate fidelity.\n",
"\n",
"Perhaps you can appreciate how, when you have large devices and complicated algorithms, optimizing the mapping from your code to the actual qubits can be highly nontrivial. Many engineers, postdocs, graduate students, and undergraduates spend good portions of their time trying to find better mappings for their problems! Some of this can be performed by a transpiler, but often these aren't as effective as a human looking at the code. \n",
"\n",
"Lets see if we can do anything to improve your code. To proceed, open your jobs menu and look at the last result. You should have something like\n",
"\n",
"![Screenshot%20from%202021-07-14%2019-12-38.png](attachment:Screenshot%20from%202021-07-14%2019-12-38.png)\n",
"\n",
"* Click the See more details\n",
"* Scroll to the bottom of the page that pops up.\n",
"* To the left, you should see your circuit as written\n",
"* On the right, you see how your code was transpiled to run on ibmq_jakarta. It probably looks like\n",
"![Screenshot%20from%202021-07-14%2022-43-47.png](attachment:Screenshot%20from%202021-07-14%2022-43-47.png)\n",
"\n",
"The 2 sets of 3 CNOT gates that appear are transpiled versions of the $SWAP$ gate. These $SWAP$ gates are being used to move the two qubits that you are entangling to be close enough that a CNOT can be acted on between them.\n",
"\n",
"This immediately suggest an optimization. Since the transpiler seems to be unable to change the initial positions of qubits, let us do it explicitly.\n",
"\n",
"From a mathematical point of view, \n",
"\n",
"![newdead.png](attachment:newdead.png)\n",
"\n",
"is equivalent to the previous model of the worm and bird, except different states are associated with alive and very dead.\n",
"\n",
"* Modify your circuit to put the two entangle qubits directly beside each other\n",
"* Run this new circuit on ibmq_jakarta with 1024 shots.\n",
"* Record the results below, do you see a difference from your previous results?\n",
"* Inspect the transpiled version of this new code. Is it substantially simpler?\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Alive: 0.484375\n",
"Dead: 0.4462890625\n"
]
}
],
"source": [
"num_shots=1024\n",
"\n",
"freq_alive=496\n",
"freq_dead=457\n",
"\n",
"prob_alive=freq_alive/num_shots\n",
"prob_dead=freq_dead/num_shots\n",
"\n",
"print(\"Alive: \", prob_alive)\n",
"print(\"Dead: \", prob_dead)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Sometimes, there are theoretical reasons to exclude certain final states from the final result because they obviously indicate an error has occured. Removing these states from your count and normalizing the total number of remain shots can be used to boost your results. This is called postselection.\n",
"\n",
"In your current code, any state besides $|00000\\rangle$ and $|00011\\rangle$ could be considered a state that can only occur by qubit errors. So lets recompute your probabilities.\n",
"\n",
"* Put your previous frequency of alive and dead into the next cell\n",
"* How do your probabilities compare to each previous case and the theoretical result?"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Alive: 0.5204616998950682\n",
"Dead: 0.4795383001049318\n"
]
}
],
"source": [
"freq_alive=496\n",
"freq_dead=457\n",
"\n",
"num_postselected_shots=freq_alive+freq_dead\n",
"\n",
"prob_alive=freq_alive/num_postselected_shots\n",
"prob_dead=freq_dead/num_postselected_shots\n",
"\n",
"print(\"Alive: \", prob_alive)\n",
"print(\"Dead: \", prob_dead)"
]
}
],
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