{ "cells": [ { "cell_type": "code", "execution_count": 1, "outputs": [ { "data": { "text/plain": "", "text/html": "

Version Information

Qiskit SoftwareVersion
qiskit-terra0.19.2
qiskit-aer0.10.3
qiskit-ignis0.7.0
qiskit-ibmq-provider0.18.3
qiskit0.34.2
qiskit-nature0.3.1
qiskit-optimization0.3.1
qiskit-machine-learning0.3.1
System information
Python version3.8.12
Python compilerGCC 7.5.0
Python builddefault, Oct 12 2021 13:49:34
OSLinux
CPUs12
Memory (Gb)125.78773498535156
Wed Mar 23 23:16:23 2022 +03
" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import qiskit.tools.jupyter\n", "%qiskit_version_table" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "# Hands-on 2\n", "\n", "Single qubits are interesting, but individually they offer no computational advantage. We will now look at how we represent multiple qubits, and how these qubits can interact with each other. We have seen how we can represent the state of a qubit using a 2D-vector, now we will see how we can represent the state of multiple qubits." ], "metadata": {} }, { "cell_type": "markdown", "source": [ "### Representing Multi-Qubit States\n", "\n", "We saw that a single bit has two possible states, and a qubit state has two complex amplitudes. Similarly, two bits have four possible states:\n", "\n", "`00` `01` `10` `11`\n", "\n", "And to describe the state of two qubits requires four complex amplitudes. We store these amplitudes in a 4D-vector like so:\n", "\n", "$$ |a\\rangle = a_{00}|00\\rangle + a_{01}|01\\rangle + a_{10}|10\\rangle + a_{11}|11\\rangle = \\begin{bmatrix} a_{00} \\\\ a_{01} \\\\ a_{10} \\\\ a_{11} \\end{bmatrix} $$\n", "\n", "The rules of measurement still work in the same way:\n", "\n", "$$ p(|00\\rangle) = |\\langle 00 | a \\rangle |^2 = |a_{00}|^2$$\n", "\n", "And the same implications hold, such as the normalisation condition:\n", "\n", "$$ |a_{00}|^2 + |a_{01}|^2 + |a_{10}|^2 + |a_{11}|^2 = 1$$\n", "\n", "If we have two separated qubits, we can describe their collective state using the kronecker product:\n", "\n", "$$ |a\\rangle = \\begin{bmatrix} a_0 \\\\ a_1 \\end{bmatrix}, \\quad |b\\rangle = \\begin{bmatrix} b_0 \\\\ b_1 \\end{bmatrix} $$\n", "\n", "$$ \n", "|ba\\rangle = |b\\rangle \\otimes |a\\rangle = \\begin{bmatrix} b_0 \\times \\begin{bmatrix} a_0 \\\\ a_1 \\end{bmatrix} \\\\ b_1 \\times \\begin{bmatrix} a_0 \\\\ a_1 \\end{bmatrix} \\end{bmatrix} = \\begin{bmatrix} b_0 a_0 \\\\ b_0 a_1 \\\\ b_1 a_0 \\\\ b_1 a_1 \\end{bmatrix}\n", "$$\n", "\n", "And following the same rules, we can use the kronecker product to describe the collective state of any number of qubits. Here is an example with three qubits:\n", "\n", "$$ \n", "|cba\\rangle = \\begin{bmatrix} c_0 b_0 a_0 \\\\ c_0 b_0 a_1 \\\\ c_0 b_1 a_0 \\\\ c_0 b_1 a_1 \\\\\n", " c_1 b_0 a_0 \\\\ c_1 b_0 a_1 \\\\ c_1 b_1 a_0 \\\\ c_1 b_1 a_1 \\\\\n", " \\end{bmatrix}\n", "$$\n", "\n", "If we have $n$ qubits, we will need to keep track of $2^n$ complex amplitudes. As we can see, these vectors grow exponentially with the number of qubits. This is the reason quantum computers with large numbers of qubits are so difficult to simulate. A modern laptop can easily simulate a general quantum state of around 20 qubits, but simulating 100 qubits is too difficult for the largest supercomputers.\n", "\n", "Let's look at an example circuit:" ], "metadata": {} }, { "cell_type": "code", "execution_count": 2, "source": [ "from qiskit import QuantumCircuit, Aer, assemble\n", "import numpy as np\n", "from qiskit.visualization import plot_histogram, plot_bloch_multivector" ], "outputs": [], "metadata": { "tags": [ "thebelab-init" ] } }, { "cell_type": "code", "execution_count": 3, "source": [ "qc = QuantumCircuit(3)\n", "# Apply H-gate to each qubit:\n", "for qubit in range(3):\n", " qc.h(qubit)\n", "# See the circuit:\n", "qc.draw('mpl')" ], "outputs": [ { "data": { "text/plain": "
", "image/png": "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\n" }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "metadata": {} }, { "cell_type": "markdown", "source": [ "Each qubit is in the state $|+\\rangle$, so we should see the vector:\n", "\n", "$$ \n", "|{+++}\\rangle = \\frac{1}{\\sqrt{8}}\\begin{bmatrix} 1 \\\\ 1 \\\\ 1 \\\\ 1 \\\\\n", " 1 \\\\ 1 \\\\ 1 \\\\ 1 \\\\\n", " \\end{bmatrix}\n", "$$" ], "metadata": {} }, { "cell_type": "code", "execution_count": 4, "source": [ "# Let's see the result\n", "svsim = Aer.get_backend('aer_simulator')\n", "qc.save_statevector()\n", "qobj = assemble(qc)\n", "final_state = svsim.run(qobj).result().get_statevector()\n", "\n", "# In Jupyter Notebooks we can display this nicely using Latex.\n", "# If not using Jupyter Notebooks you may need to remove the \n", "# array_to_latex function and use print(final_state) instead.\n", "from qiskit.visualization import array_to_latex\n", "array_to_latex(final_state, prefix=\"\\\\text{Statevector} = \")" ], "outputs": [ { "data": { "text/plain": "", "text/latex": "$$\n\\text{Statevector} = \n\\begin{bmatrix}\n\\tfrac{1}{\\sqrt{8}} & \\tfrac{1}{\\sqrt{8}} & \\tfrac{1}{\\sqrt{8}} & \\tfrac{1}{\\sqrt{8}} & \\tfrac{1}{\\sqrt{8}} & \\tfrac{1}{\\sqrt{8}} & \\tfrac{1}{\\sqrt{8}} & \\tfrac{1}{\\sqrt{8}} \\\\\n \\end{bmatrix}\n$$" }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "metadata": {} }, { "cell_type": "markdown", "source": [ "And we have our expected result." ], "metadata": {} }, { "cell_type": "markdown", "source": [ "### Single Qubit Gates on Multi-Qubit Statevectors\n", "\n", "We have seen that an X-gate is represented by the matrix:\n", "\n", "$$\n", "X = \\begin{bmatrix} 0 & 1 \\\\ 1 & 0 \\end{bmatrix}\n", "$$\n", "\n", "And that it acts on the state $|0\\rangle$ as so:\n", "\n", "$$\n", "X|0\\rangle = \\begin{bmatrix} 0 & 1 \\\\ 1 & 0 \\end{bmatrix}\\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix} = \\begin{bmatrix} 0 \\\\ 1\\end{bmatrix}\n", "$$\n", "\n", "but it may not be clear how an X-gate would act on a qubit in a multi-qubit vector. Fortunately, the rule is quite simple; just as we used the kronecker product to calculate multi-qubit statevectors, we use the tensor product to calculate matrices that act on these statevectors. For example, in the circuit below:" ], "metadata": {} }, { "cell_type": "code", "execution_count": 5, "source": [ "qc = QuantumCircuit(2)\n", "qc.h(0)\n", "qc.x(1)\n", "qc.draw('mpl')" ], "outputs": [ { "data": { "text/plain": "
", "image/png": "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\n" }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "metadata": {} }, { "cell_type": "markdown", "source": [ "we can represent the simultaneous operations (H & X) using their kronecker product:\n", "\n", "$$\n", "X|q_1\\rangle \\otimes H|q_0\\rangle = (X\\otimes H)|q_1 q_0\\rangle\n", "$$\n", "\n", "The operation looks like this:\n", "\n", "$$\n", "X\\otimes H = \\begin{bmatrix} 0 & 1 \\\\ 1 & 0 \\end{bmatrix} \\otimes \\tfrac{1}{\\sqrt{2}}\\begin{bmatrix} 1 & 1 \\\\ 1 & -1 \\end{bmatrix}\n", "$$\n", "\n", "$$\n", "= \\frac{1}{\\sqrt{2}}\n", "\\begin{bmatrix} 0 \\times \\begin{bmatrix} 1 & 1 \\\\ 1 & -1 \\end{bmatrix}\n", " & 1 \\times \\begin{bmatrix} 1 & 1 \\\\ 1 & -1 \\end{bmatrix}\n", " \\\\ \n", " 1 \\times \\begin{bmatrix} 1 & 1 \\\\ 1 & -1 \\end{bmatrix}\n", " & 0 \\times \\begin{bmatrix} 1 & 1 \\\\ 1 & -1 \\end{bmatrix}\n", "\\end{bmatrix} \n", "$$\n", "\n", "$$\n", "= \\frac{1}{\\sqrt{2}}\n", "\\begin{bmatrix} 0 & 0 & 1 & 1 \\\\\n", " 0 & 0 & 1 & -1 \\\\\n", " 1 & 1 & 0 & 0 \\\\\n", " 1 & -1 & 0 & 0 \\\\\n", "\\end{bmatrix}\n", "$$\n", "\n", "Which we can then apply to our 4D statevector $|q_1 q_0\\rangle$. This can become quite messy, you will often see the clearer notation:\n", "\n", "$$\n", "X\\otimes H = \n", "\\begin{bmatrix} 0 & H \\\\\n", " H & 0\\\\\n", "\\end{bmatrix}\n", "$$\n", "\n", "Instead of calculating this by hand, we can use Qiskit’s `aer_simulator` to calculate this for us. The Aer simulator multiplies all the gates in our circuit together to compile a single unitary matrix that performs the whole quantum circuit:" ], "metadata": {} }, { "cell_type": "code", "execution_count": 6, "source": [ "usim = Aer.get_backend('aer_simulator')\n", "qc.save_unitary()\n", "qobj = assemble(qc)\n", "unitary = usim.run(qobj).result().get_unitary()" ], "outputs": [], "metadata": {} }, { "cell_type": "markdown", "source": [ "and view the results:" ], "metadata": {} }, { "cell_type": "code", "execution_count": 7, "source": [ "# In Jupyter Notebooks we can display this nicely using Latex.\n", "# If not using Jupyter Notebooks you may need to remove the \n", "# array_to_latex function and use print(unitary) instead.\n", "from qiskit.visualization import array_to_latex\n", "array_to_latex(unitary, prefix=\"\\\\text{Circuit = }\\n\")" ], "outputs": [ { "data": { "text/plain": "", "text/latex": "$$\n\\text{Circuit = }\n\n\\begin{bmatrix}\n0 & 0 & \\tfrac{1}{\\sqrt{2}} & \\tfrac{1}{\\sqrt{2}} \\\\\n 0 & 0 & \\tfrac{1}{\\sqrt{2}} & -\\tfrac{1}{\\sqrt{2}} \\\\\n \\tfrac{1}{\\sqrt{2}} & \\tfrac{1}{\\sqrt{2}} & 0 & 0 \\\\\n \\tfrac{1}{\\sqrt{2}} & -\\tfrac{1}{\\sqrt{2}} & 0 & 0 \\\\\n \\end{bmatrix}\n$$" }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "metadata": {} }, { "cell_type": "markdown", "source": [ "If we want to apply a gate to only one qubit at a time (such as in the circuit below), we describe this using kronecker product with the identity matrix, e.g.:\n", "\n", "$$ X \\otimes I $$" ], "metadata": {} }, { "cell_type": "code", "execution_count": 8, "source": [ "qc = QuantumCircuit(2)\n", "qc.x(1)\n", "qc.draw('mpl')" ], "outputs": [ { "data": { "text/plain": "
", "image/png": "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\n" }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "metadata": {} }, { "cell_type": "code", "execution_count": 9, "source": [ "# Simulate the unitary\n", "usim = Aer.get_backend('aer_simulator')\n", "qc.save_unitary()\n", "qobj = assemble(qc)\n", "unitary = usim.run(qobj).result().get_unitary()\n", "# Display the results:\n", "array_to_latex(unitary, prefix=\"\\\\text{Circuit = } \")" ], "outputs": [ { "data": { "text/plain": "", "text/latex": "$$\n\\text{Circuit = } \n\\begin{bmatrix}\n0 & 0 & 1 & 0 \\\\\n 0 & 0 & 0 & 1 \\\\\n 1 & 0 & 0 & 0 \\\\\n 0 & 1 & 0 & 0 \\\\\n \\end{bmatrix}\n$$" }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "metadata": {} }, { "cell_type": "markdown", "source": [ "We can see Qiskit has performed the kronecker product:\n", "$$\n", "X \\otimes I =\n", "\\begin{bmatrix} 0 & I \\\\\n", " I & 0\\\\\n", "\\end{bmatrix} = \n", "\\begin{bmatrix} 0 & 0 & 1 & 0 \\\\\n", " 0 & 0 & 0 & 1 \\\\\n", " 1 & 0 & 0 & 0 \\\\\n", " 0 & 1 & 0 & 0 \\\\\n", "\\end{bmatrix}\n", "$$\n", "\n" ], "metadata": {} }, { "cell_type": "markdown", "source": [ "#### Send it after class 1\n", "\n", "Calculate the single qubit unitary ($U$) created by the sequence of gates: $U = XZH$. Use Qiskit's Aer simulator to check your results.\n", "\n", "**Note:** Different books, softwares and websites order their qubits differently. This means the kronecker product of the same circuit can look very different. Try to bear this in mind when consulting other sources.\n" ], "metadata": { "collapsed": false } }, { "cell_type": "markdown", "source": [ "### Multi-Qubit Gates\n", "\n", "Now we know how to represent the state of multiple qubits, we are now ready to learn how qubits interact with each other. An important two-qubit gate is the CNOT-gate.\n", "\n", "#### The CNOT-Gate\n", "\n", "CNOT gate is a conditional gate that performs an X-gate on the second qubit (target), if the state of the first qubit (control) is $|1\\rangle$. The gate is drawn on a circuit like this, with `q0` as the control and `q1` as the target:" ], "metadata": {} }, { "cell_type": "code", "execution_count": 10, "source": [ "qc = QuantumCircuit(2)\n", "# Apply CNOT\n", "qc.cx(0,1)\n", "# See the circuit:\n", "qc.draw('mpl')" ], "outputs": [ { "data": { "text/plain": "
", "image/png": "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\n" }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "metadata": {} }, { "cell_type": "markdown", "source": [ "When our qubits are not in superposition of $|0\\rangle$ or $|1\\rangle$ (behaving as classical bits), this gate is very simple and intuitive to understand. We can use the classical truth table:\n", "\n", "| Input (t,c) | Output (t,c) |\n", "|:-----------:|:------------:|\n", "| 00 | 00 |\n", "| 01 | 11 |\n", "| 10 | 10 |\n", "| 11 | 01 |\n", "\n", "And acting on our 4D-statevector, it has one of the two matrices:\n", "\n", "$$\n", "\\text{CNOT} = \\begin{bmatrix} 1 & 0 & 0 & 0 \\\\\n", " 0 & 0 & 0 & 1 \\\\\n", " 0 & 0 & 1 & 0 \\\\\n", " 0 & 1 & 0 & 0 \\\\\n", " \\end{bmatrix}, \\quad\n", "\\text{CNOT} = \\begin{bmatrix} 1 & 0 & 0 & 0 \\\\\n", " 0 & 1 & 0 & 0 \\\\\n", " 0 & 0 & 0 & 1 \\\\\n", " 0 & 0 & 1 & 0 \\\\\n", " \\end{bmatrix}\n", "$$\n", "\n", "depending on which qubit is the control and which is the target. Different books, simulators and papers order their qubits differently. In our case, the left matrix corresponds to the CNOT in the circuit above. This matrix swaps the amplitudes of $|01\\rangle$ and $|11\\rangle$ in our statevector:\n", "\n", "$$ \n", "|a\\rangle = \\begin{bmatrix} a_{00} \\\\ a_{01} \\\\ a_{10} \\\\ a_{11} \\end{bmatrix}, \\quad \\text{CNOT}|a\\rangle = \\begin{bmatrix} a_{00} \\\\ a_{11} \\\\ a_{10} \\\\ a_{01} \\end{bmatrix} \\begin{matrix} \\\\ \\leftarrow \\\\ \\\\ \\leftarrow \\end{matrix}\n", "$$\n", "\n", "We have seen how this acts on classical states, but let’s now see how it acts on a qubit in superposition. We will put one qubit in the state $|+\\rangle$:" ], "metadata": {} }, { "cell_type": "code", "execution_count": 11, "source": [ "qc = QuantumCircuit(2)\n", "# Apply H-gate to the first:\n", "qc.h(0)\n", "qc.draw('mpl')" ], "outputs": [ { "data": { "text/plain": "
", "image/png": "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\n" }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "metadata": {} }, { "cell_type": "code", "execution_count": 12, "source": [ "# Let's see the result:\n", "svsim = Aer.get_backend('aer_simulator')\n", "qc.save_statevector()\n", "qobj = assemble(qc)\n", "final_state = svsim.run(qobj).result().get_statevector()\n", "# Print the statevector neatly:\n", "array_to_latex(final_state, prefix=\"\\\\text{Statevector = }\")" ], "outputs": [ { "data": { "text/plain": "", "text/latex": "$$\n\\text{Statevector = }\n\\begin{bmatrix}\n\\tfrac{1}{\\sqrt{2}} & \\tfrac{1}{\\sqrt{2}} & 0 & 0 \\\\\n \\end{bmatrix}\n$$" }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "metadata": {} }, { "cell_type": "markdown", "source": [ "As expected, this produces the state $|0\\rangle \\otimes |{+}\\rangle = |0{+}\\rangle$:\n", "\n", "$$\n", "|0{+}\\rangle = \\tfrac{1}{\\sqrt{2}}(|00\\rangle + |01\\rangle)\n", "$$\n", "\n", "And let’s see what happens when we apply the CNOT gate:" ], "metadata": {} }, { "cell_type": "code", "execution_count": 13, "source": [ "qc = QuantumCircuit(2)\n", "# Apply H-gate to the first:\n", "qc.h(0)\n", "# Apply a CNOT:\n", "qc.cx(0,1)\n", "qc.draw('mpl')" ], "outputs": [ { "data": { "text/plain": "
", "image/png": "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\n" }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "metadata": {} }, { "cell_type": "code", "execution_count": 14, "source": [ "# Let's get the result:\n", "qc.save_statevector()\n", "qobj = assemble(qc)\n", "result = svsim.run(qobj).result()\n", "# Print the statevector neatly:\n", "final_state = result.get_statevector()\n", "array_to_latex(final_state, prefix=\"\\\\text{Statevector = }\")" ], "outputs": [ { "data": { "text/plain": "", "text/latex": "$$\n\\text{Statevector = }\n\\begin{bmatrix}\n\\tfrac{1}{\\sqrt{2}} & 0 & 0 & \\tfrac{1}{\\sqrt{2}} \\\\\n \\end{bmatrix}\n$$" }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "metadata": {} }, { "cell_type": "markdown", "source": [ "We see we have the state:\n", "\n", "$$\n", "\\text{CNOT}|0{+}\\rangle = \\tfrac{1}{\\sqrt{2}}(|00\\rangle + |11\\rangle)\n", "$$ \n", "\n", "This state is very interesting to us, because it is _entangled._ This leads us neatly on to the next section." ], "metadata": {} }, { "cell_type": "markdown", "source": [ "#### Entangled States\n", "\n", "We saw in the previous section we could create the state:\n", "\n", "$$\n", "\\tfrac{1}{\\sqrt{2}}(|00\\rangle + |11\\rangle)\n", "$$ \n", "\n", "This is known as a _Bell_ state. We can see that this state has 50% probability of being measured in the state $|00\\rangle$, and 50% chance of being measured in the state $|11\\rangle$. Most interestingly, it has a **0%** chance of being measured in the states $|01\\rangle$ or $|10\\rangle$. We can see this in Qiskit:" ], "metadata": {} }, { "cell_type": "code", "execution_count": 15, "source": [ "plot_histogram(result.get_counts())" ], "outputs": [ { "data": { "text/plain": "
", "image/png": 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\n" }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "metadata": {} }, { "cell_type": "markdown", "source": [ "This combined state cannot be written as two separate qubit states, which has interesting implications. Although our qubits are in superposition, measuring one will tell us the state of the other and collapse its superposition. For example, if we measured the top qubit and got the state $|1\\rangle$, the collective state of our qubits changes like so:\n", "\n", "$$\n", "\\tfrac{1}{\\sqrt{2}}(|00\\rangle + |11\\rangle) \\quad \\xrightarrow[]{\\text{measure}} \\quad |11\\rangle\n", "$$\n", "\n", "Even if we separated these qubits light-years away, measuring one qubit collapses the superposition and appears to have an immediate effect on the other. This is the [‘spooky action at a distance’](https://en.wikipedia.org/wiki/Quantum_nonlocality) that upset so many physicists in the early 20th century.\n", "\n", "It’s important to note that the measurement result is random, and the measurement statistics of one qubit are **not** affected by any operation on the other qubit. Because of this, there is **no way** to use shared quantum states to communicate. This is known as the no-communication theorem." ], "metadata": {} }, { "cell_type": "markdown", "source": [ "#### Visualizing Entangled States\n", "\n", "We have seen that this state cannot be written as two separate qubit states, this also means we lose information when we try to plot our state on separate Bloch spheres:" ], "metadata": {} }, { "cell_type": "code", "execution_count": 16, "source": [ "plot_bloch_multivector(final_state)" ], "outputs": [ { "data": { "text/plain": "
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\n" }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "metadata": {} }, { "cell_type": "markdown", "source": [ "Given how we defined the Bloch sphere in the earlier chapters, it may not be clear how Qiskit even calculates the Bloch vectors with entangled qubits like this. In the single-qubit case, the position of the Bloch vector along an axis nicely corresponds to the expectation value of measuring in that basis. If we take this as _the_ rule of plotting Bloch vectors, we arrive at this conclusion above. This shows us there is _no_ single-qubit measurement basis for which a specific measurement is guaranteed. This contrasts with our single qubit states, in which we could always pick a single-qubit basis. Looking at the individual qubits in this way, we miss the important effect of correlation between the qubits. We cannot distinguish between different entangled states. For example, the two states:\n", "\n", "$$\\tfrac{1}{\\sqrt{2}}(|01\\rangle + |10\\rangle) \\quad \\text{and} \\quad \\tfrac{1}{\\sqrt{2}}(|00\\rangle + |11\\rangle)$$\n", "\n", "will both look the same on these separate Bloch spheres, despite being very different states with different measurement outcomes.\n", "\n", "How else could we visualize this statevector? This statevector is simply a collection of four amplitudes (complex numbers), and there are endless ways we can map this to an image. One such visualization is the _Q-sphere,_ here each amplitude is represented by a blob on the surface of a sphere. The size of the blob is proportional to the magnitude of the amplitude, and the colour is proportional to the phase of the amplitude. The amplitudes for $|00\\rangle$ and $|11\\rangle$ are equal, and all other amplitudes are 0:" ], "metadata": {} }, { "cell_type": "code", "execution_count": 17, "source": [ "from qiskit.visualization import plot_state_qsphere\n", "plot_state_qsphere(final_state)" ], "outputs": [ { "data": { "text/plain": "
", "image/png": 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\n" }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "metadata": {} }, { "cell_type": "markdown", "source": [ "Here we can clearly see the correlation between the qubits. The Q-sphere's shape has no significance, it is simply a nice way of arranging our blobs; the number of `0`s in the state is proportional to the states position on the Z-axis, so here we can see the amplitude of $|00\\rangle$ is at the top pole of the sphere, and the amplitude of $|11\\rangle$ is at the bottom pole of the sphere." ], "metadata": {} }, { "cell_type": "markdown", "source": [ "#### Send it after class 2\n", "1. Create a quantum circuit that produces the Bell state: $\\tfrac{1}{\\sqrt{2}}(|01\\rangle + |10\\rangle)$.\n", " Use the statevector simulator to verify your result.\n", " \n", "2. The circuit you created in question 1 transforms the state $|00\\rangle$ to $\\tfrac{1}{\\sqrt{2}}(|01\\rangle + |10\\rangle)$, calculate the unitary of this circuit using Qiskit's simulator. Verify this unitary does in fact perform the correct transformation.\n" ], "metadata": {} }, { "cell_type": "markdown", "source": [ "### Exploring the CNOT-Gate\n", "\n", "We saw that we could entangle the two qubits by placing the control qubit in the state $|+\\rangle$:\n", "\n", "$$\n", "\\text{CNOT}|0{+}\\rangle = \\tfrac{1}{\\sqrt{2}}(|00\\rangle + |11\\rangle)\n", "$$\n", "\n", "But what happens if we put the second qubit in superposition?" ], "metadata": { "pycharm": { "name": "#%% md\n" } } }, { "cell_type": "code", "execution_count": 18, "outputs": [], "source": [ "from qiskit import QuantumCircuit, Aer, assemble\n", "from math import pi\n", "import numpy as np\n", "from qiskit.visualization import plot_bloch_multivector, plot_histogram, array_to_latex" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "code", "execution_count": 19, "outputs": [ { "data": { "text/plain": "
", "image/png": "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\n" }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(2)\n", "qc.h(0)\n", "qc.h(1)\n", "qc.cx(0,1)\n", "qc.draw('mpl')" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "In the circuit above, we have the CNOT acting on the state:\n", "\n", "$$ |{+}{+}\\rangle = \\tfrac{1}{2}(|00\\rangle + |01\\rangle + |10\\rangle + |11\\rangle) $$\n", "\n", "Since the CNOT swaps the amplitudes of $|01\\rangle$ and $|11\\rangle$, we see no change:" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 20, "outputs": [ { "data": { "text/plain": "
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\n" }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(2)\n", "qc.h(0)\n", "qc.h(1)\n", "qc.cx(0,1)\n", "display(qc.draw('mpl')) # `display` is a command for Jupyter notebooks\n", "# similar to `print`, but for rich content\n", "\n", "# Let's see the result\n", "svsim = Aer.get_backend('aer_simulator')\n", "qc.save_statevector()\n", "qobj = assemble(qc)\n", "final_state = svsim.run(qobj).result().get_statevector()\n", "display(array_to_latex(final_state, prefix=\"\\\\text{Statevector} = \"))\n", "plot_bloch_multivector(final_state)" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "Let’s put the target qubit in the state $|-\\rangle$, so it has a negative phase:" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 21, "outputs": [ { "data": { "text/plain": "
", "image/png": "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\n" }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(2)\n", "qc.h(0)\n", "qc.x(1)\n", "qc.h(1)\n", "qc.draw('mpl')" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "This creates the state:\n", "\n", "$$ |{-}{+}\\rangle = \\tfrac{1}{2}(|00\\rangle + |01\\rangle - |10\\rangle - |11\\rangle) $$" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 22, "outputs": [ { "data": { "text/plain": "
", "image/png": "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\n" }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": "", "text/latex": "$$\n\\text{Statevector} = \n\\begin{bmatrix}\n\\tfrac{1}{2} & \\tfrac{1}{2} & -\\tfrac{1}{2} & -\\tfrac{1}{2} \\\\\n \\end{bmatrix}\n$$" }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": "
", "image/png": 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\n" }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(2)\n", "qc.h(0)\n", "qc.x(1)\n", "qc.h(1)\n", "display(qc.draw('mpl'))\n", "# See the result\n", "qc1 = qc.copy()\n", "qc1.save_statevector()\n", "final_state = svsim.run(qc1).result().get_statevector()\n", "display(array_to_latex(final_state, prefix=\"\\\\text{Statevector} = \"))\n", "plot_bloch_multivector(final_state)" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "If the CNOT acts on this state, we will swap the amplitudes of $|01\\rangle$ and $|11\\rangle$, resulting in the state:\n", "\n", "$$\n", "\\begin{aligned}\n", "\\text{CNOT}|{-}{+}\\rangle & = \\tfrac{1}{2}(|00\\rangle - |01\\rangle - |10\\rangle + |11\\rangle) \\\\\n", " & = |{-}{-}\\rangle\n", "\\end{aligned}\n", "$$\n", "\n", "\n", "This is interesting, because it affects the state of the _control_ qubit while leaving the state of the _target_ qubit unchanged." ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 23, "outputs": [ { "data": { "text/plain": "
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\n" }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc.cx(0,1)\n", "display(qc.draw('mpl'))\n", "\n", "qc.save_statevector()\n", "qobj = assemble(qc)\n", "final_state = svsim.run(qobj).result().get_statevector()\n", "display(array_to_latex(final_state, prefix=\"\\\\text{Statevector} = \"))\n", "plot_bloch_multivector(final_state)" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "If you remember the H-gate transforms $|{+}\\rangle \\rightarrow |0\\rangle$ and $|{-}\\rangle \\rightarrow |1\\rangle$, we can see that wrapping a CNOT in H-gates has the equivalent behaviour of a CNOT acting in the opposite direction:\n", "\n", "![cnot_identity](images/identities_1.png)\n", "\n", "We can verify this using Qiskit's Aer simulator:" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 24, "outputs": [ { "data": { "text/plain": "
", "image/png": "iVBORw0KGgoAAAANSUhEUgAAANgAAAB7CAYAAAAWqE6tAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAAAJq0lEQVR4nO3df2zU9R3H8edd1x/MGqVepFIp0pZ289Z20K0STLw2UWzdVDYBIVsTK0kJZW7Mv9yk/kNtMtI/cC6ZZsskS7Rz7TrUWYluaw9IVVa7AXWbR4BSDqu2iJt1pUB7++Ok9oByd3Cffr/37euRfJPe5+4+3zef3IvP9z73vfu6QqFQCBExwm11ASJOpoCJGKSAiRikgIkYpICJGKSAiRikgIkYpICJGKSAiRikgIkYpICJGKSAiRikgIkYpICJGKSAiRikgIkYpICJGKSAiRikgIkYpICJGKSAiRikgIkYpICJGKSAiRikgIkYpICJGPQlqwuwu/YeOHHKmn3nzIXvfsOafVvBiWOtgEVx4hQc/sjqKmYHJ461DhFFDFLARAxSwEQMUsBEDFLARAxSwEQMUsBEDFLARAxSwCTC2Dn4dBTOjVtdiTPYOmATExM0NzezePFiMjIyKC0txe/3U1RURF1dndXlXVJbYwX7djbG3G4Xhz+CX3XBYy9CQzv8pBV+vw9Ojlhd2fSSYaxtfarU+vXraW9vp6GhgbKyMrq7u1m3bh1DQ0M8+uijVpfnGD1H4fnu8N+hz9vOjsObh+Afx+AHd8L8uZaVl9RsG7CWlhZ27NhBV1cXPp8PgMrKSnp7e2lvb2fp0qUWV+gMpz6DF978IlhThYDRs/CbPfDTe8Htmunqkp9tDxGbmpqoqqqaDNd5BQUFpKamUlJSAkB/fz8+n4/CwkKKi4vZs2ePFeUmre5DMHGpdH0uFILhT+HQBzNXk5PYMmDBYJC+vj5Wr1590X0DAwN4vV7S09MB2LBhAw8++CCBQIBnn32WtWvXcubMmaj7cLlcMW1+f1fc9e976Ul+WXd9xPZ+YG/c/fj9XTHXeaXbb3e+SSh0mYQBoVCI2h89abyWZBnreNjyEDEYDAKQnZ0d0T46Oorf76e6uhqA4eFh9u7dy8svvwzA8uXLmT9/Pp2dndx9990zW/QU5fc/TvnKLRFtbY0V1hQThcudEsOLJoTbnTIj9cTL7mNtyxnM4/EAEAgEItq3bdvG4OAgZWVlQHg2mzdv3uRsBrBo0SKOHTsWdR+hUCimzeerSNw/LE4+X0XMdV7ptqqqPGodLpebX/zsMeO1JMtYx8OWM1heXh4lJSU0NTWRlZVFTk4ObW1tdHR0AEwGTK7e7YWw99D097uAa9KheMGMleQotpzB3G43ra2teL1eNm7cSG1tLR6Ph02bNpGSkjK5wJGbm8uHH37I2NjY5HOPHj3KwoULrSo96dx0PVQVh/++8EDRBbhc8P3bIcWWrxT7c4XinfMsVFNTw/79+zlw4MBk24oVK1i5ciX19fV0d3ezatUq+vv7SUtLS8g+n37Duq+x598Ij9w1M/t6+zC80QfDUz5Yzr8RvlUKeTfOTA1OHGtbHiJOp6enh2XLlkW0PfPMMzz00ENs376dtLQ0WlpaEhau2eS2fCjPgx+/EL695T7wXGttTU6QNAEbGRkhEAhQX18f0Z6Xl8fu3bstqspZpi4mKlyJkTQBy8zMZHxcZ6BKctFbVxGDFDARgxQwEYMUMBGDFDARgxQwEYMUMBGDkuZzMKvkWPhVeSv3bQUnjrUCFsVsuj6X1Zw41jpEFDFIARMxSAETMUgBEzFIARMxSAETMUgBEzFIARMxSAETMUgBEzFIARMxSAETMUgBEzFIZ9NH0d4DJ05Zs++cuc48w3w6ThxrBSyKE6es+znn2caJY61DRBGDFDARg3SIKJz6DA4ch+DHX7T9/HWYPxdyb4CSBZCRal19yUwBm8UGP4FX98O7QbjwGlZHhsIbwB/+Bt9cBNWl4YvxSewUsFloIgR/eRd2HYTxieiPHzsXvgrm/uOw9jbw3my+RqfQe7BZZiIEL74dnrliCddUn56GX/vDF+uT2Chgs8yuA1cXkBDwu7fgX+8nrCRHU8Bmkf7h8GViL2f798Lb5YQIz4KjZxJWmmPZOmATExM0NzezePFiMjIyKC0txe/3U1RURF1dndXlJZ0/vnPxYsaV+uR/8Od3E9SZg9k6YOvXr2fr1q1s2LCB1157jTVr1rBu3TqOHDlCWVmZ1eVdUltjBft2NsbcPlOOn4Rjw4nt863DcM7Ci47adaynsu0qYktLCzt27KCrqwufzwdAZWUlvb29tLe3s3TpUosrTC69xxLf52dj8N6gVhUvx7YzWFNTE1VVVZPhOq+goIDU1FRKSkoAeOKJJygsLMTtdtPW1mZFqUlh4KShfj+O/pjZzJYBCwaD9PX1sXr16ovuGxgYwOv1kp4e/sSzqqqKXbt2cccdd8x0mUnlg/8Y6vcTM/06hS0PEYPBIADZ2dkR7aOjo/j9fqqrqyfbli9ffkX7cLlcMT3ugcc7ufmrFXH1ve+lJ3mnozmi7ezpEXK/dmdc/fj9XfxwRWVcz5lO/a9HSM24ZvJ2tJXC6e7f/Hzk7Z2vvMrDvm9fZXVhyTLWoVDsS0W2DJjH4wEgEAhwzz33TLZv27aNwcFB2y5wnFd+/+OUr9wS0dbWWGFNMZ87d/Z0RMASZfzM6YT3GQ87jvVUtgxYXl4eJSUlNDU1kZWVRU5ODm1tbXR0dAAkJGCx/i/09BvWfUfJ56ugrTExC+tPvQ5Hh764feFMdN75mWu6+y9U//AD/OmpxNTolLGeypbvwdxuN62trXi9XjZu3EhtbS0ej4dNmzaRkpIyucAhsVuQlVz9OoUtZzCAwsJCOjs7I9pqamq49dZbmTNnjkVVJa8lC2H3e4ntc04qFN2U2D6dxrYBu5Senh6WLVsW0dbQ0MBzzz3H0NAQBw8eZPPmzfj9fvLz8y2pcdWWrrjaZ8otHrh5LgQT+JsX5fmQZuEryK5jPZUtDxEvZWRkhEAgcNEHzFu3biUYDDI2NsbJkycJBoOWhcvOXC5YmcC1ocwMuMubuP6cKmlmsMzMTMbHLTwvxwEK5oHvK+D/9/SPiXVxY015OGRyeUkzg0li3LcEvp57dX18pyz8MwISXdLMYJIYKW6ouR1uyIS//jO+s+vnpMKqcii7xVR1zqOAzUIpbrh3CRQvgFf+Hv2zpxQ3LMkNP+e6L89MjU6hgM1it3jgkbvC5ykeGIDjH8NH/4VzE5CeCvOvD/+q1JKFcK3eb10RBUzIvg6yi62uwpm0yCFikAImYpAOEaPImTs7920FJ461KxTPl1tEJC46RBQxSAETMUgBEzFIARMxSAETMUgBEzFIARMxSAETMUgBEzFIARMxSAETMUgBEzFIARMxSAETMUgBEzFIARMxSAETMUgBEzHo/7zXcj2rYMp7AAAAAElFTkSuQmCC\n" }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": "", "text/latex": "$$\n\\text{Circuit = }\n\n\\begin{bmatrix}\n1 & 0 & 0 & 0 \\\\\n 0 & 1 & 0 & 0 \\\\\n 0 & 0 & 0 & 1 \\\\\n 0 & 0 & 1 & 0 \\\\\n \\end{bmatrix}\n$$" }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(2)\n", "qc.h(0)\n", "qc.h(1)\n", "qc.cx(0,1)\n", "qc.h(0)\n", "qc.h(1)\n", "display(qc.draw('mpl'))\n", "\n", "qc.save_unitary()\n", "usim = Aer.get_backend('aer_simulator')\n", "qobj = assemble(qc)\n", "unitary = usim.run(qobj).result().get_unitary()\n", "array_to_latex(unitary, prefix=\"\\\\text{Circuit = }\\n\")" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "code", "execution_count": 25, "outputs": [ { "data": { "text/plain": "
", "image/png": "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\n" }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": "", "text/latex": "$$\n\\text{Circuit = }\n\n\\begin{bmatrix}\n1 & 0 & 0 & 0 \\\\\n 0 & 1 & 0 & 0 \\\\\n 0 & 0 & 0 & 1 \\\\\n 0 & 0 & 1 & 0 \\\\\n \\end{bmatrix}\n$$" }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(2)\n", "qc.cx(1,0)\n", "display(qc.draw('mpl'))\n", "qc.save_unitary()\n", "\n", "qobj = assemble(qc)\n", "unitary = usim.run(qobj).result().get_unitary()\n", "array_to_latex(unitary, prefix=\"\\\\text{Circuit = }\\n\")" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "This identity is an example of _phase kickback,_ which leads us neatly on to the next section...\n", "\n", "### Phase Kickback\n", "\n", "#### Explaining the CNOT Circuit Identity\n", "In the previous section we saw this identity:\n", "\n", "![cnot_identity](images/identities_1.png)\n", "\n", "This is an example of _kickback_ (or, _phase kickback_ ) which is very important and is used in almost every quantum algorithm. Kickback is where the eigenvalue added by a gate to a qubit is ‘kicked back’ into a different qubit via a controlled operation. For example, we saw that performing an X-gate on a $|{-}\\rangle$ qubit gives it the phase $-1$:\n", "\n", "$$\n", "X|{-}\\rangle = -|{-}\\rangle\n", "$$\n", "\n", "When our control qubit is in either $|0\\rangle$ or $|1\\rangle$, this phase affects the whole state, however it is a global phase and has no observable effects:\n", "\n", "$$\n", "\\begin{aligned}\n", "\\text{CNOT}|{-}0\\rangle & = |{-}\\rangle \\otimes |0\\rangle \\\\\n", " & = |{-}0\\rangle \\\\\n", " \\quad & \\\\\n", "\\text{CNOT}|{-}1\\rangle & = X|{-}\\rangle \\otimes |1\\rangle \\\\\n", " & = -|{-}\\rangle \\otimes |1\\rangle \\\\\n", " & = -|{-}1\\rangle \\\\\n", "\\end{aligned}\n", "$$\n", "\n", "The interesting effect is when our control qubit is in superposition. The component of the control qubit that lies in the direction of $|1\\rangle$ applies this phase factor to the *corresponding* target qubit. This applied phase factor in turn introduces a relative phase into the control qubit:\n", "\n", "$$\n", "\\begin{aligned}\n", "\\text{CNOT}|{-}{+}\\rangle & = \\tfrac{1}{\\sqrt{2}}(\\text{CNOT}|{-}0\\rangle + \\text{CNOT}|{-}1\\rangle) \\\\\n", " & = \\tfrac{1}{\\sqrt{2}}(|{-}0\\rangle + X|{-}1\\rangle) \\\\\n", " & = \\tfrac{1}{\\sqrt{2}}(|{-}0\\rangle -|{-}1\\rangle) \\\\\n", "\\end{aligned}\n", "$$\n", "\n", "This can then be written as the two separable qubit states:\n", "\n", "$$\n", "\\begin{aligned}\n", "\\text{CNOT}|{-}{+}\\rangle & = |{-}\\rangle \\otimes \\tfrac{1}{\\sqrt{2}}(|{0}\\rangle - |1\\rangle )\\\\\n", " & = |{-}{-}\\rangle \\\\\n", "\\end{aligned}\n", "$$\n", "\n", "Wrapping the CNOT in H-gates transforms the qubits from the computational basis to the $(|+\\rangle, |-\\rangle)$ basis, where we see this effect. This identity is very useful in hardware, since some hardwares only allow for CNOTs in one direction between two specific qubits. We can use this identity to overcome this problem and allow CNOTs in both directions." ], "metadata": { "collapsed": false } }, { "cell_type": "markdown", "source": [ "#### Kickback with the T-gate \n", "\n", "Let’s look at another controlled operation, the controlled-T gate:" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "source": [ "qc = QuantumCircuit(2)\n", "qc.cp(pi/4, 0, 1)\n", "qc.draw('mpl')" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } }, "execution_count": 26, "outputs": [ { "data": { "text/plain": "
", "image/png": "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\n" }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ] }, { "cell_type": "markdown", "source": [ "The T-gate has the matrix:\n", "\n", "$$\n", "\\text{T} =\n", "\\begin{bmatrix}\n", "1 & 0 \\\\\n", "0 & e^{i\\pi/4}\\\\\n", "\\end{bmatrix}\n", "$$\n", "\n", "And the controlled-T gate has the matrix:\n", "\n", "$$\n", "\\text{Controlled-T} =\n", "\\begin{bmatrix}\n", "1 & 0 & 0 & 0 \\\\\n", "0 & 1 & 0 & 0 \\\\\n", "0 & 0 & 1 & 0 \\\\\n", "0 & 0 & 0 & e^{i\\pi/4}\\\\\n", "\\end{bmatrix}\n", "$$\n", "\n", "We can verify this using Qiskit's Aer simulator:" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 27, "outputs": [ { "data": { "text/plain": "
", "image/png": "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\n" }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": "", "text/latex": "$$\n\\text{Controlled-T} = \n\n\\begin{bmatrix}\n1 & 0 & 0 & 0 \\\\\n 0 & 1 & 0 & 0 \\\\\n 0 & 0 & 1 & 0 \\\\\n 0 & 0 & 0 & \\tfrac{1}{\\sqrt{2}}(1 + i) \\\\\n \\end{bmatrix}\n$$" }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(2)\n", "qc.cp(pi/4, 0, 1)\n", "display(qc.draw('mpl'))\n", "# See Results:\n", "qc.save_unitary()\n", "qobj = assemble(qc)\n", "unitary = usim.run(qobj).result().get_unitary()\n", "array_to_latex(unitary, prefix=\"\\\\text{Controlled-T} = \\n\")" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "More generally, we can find the matrix of any controlled-U operation using the rule:\n", "\n", "$$\n", "\\begin{aligned}\n", "\\text{U} & =\n", "\\begin{bmatrix}\n", "u_{00} & u_{01} \\\\\n", "u_{10} & u_{11}\\\\\n", "\\end{bmatrix} \\\\\n", "\\quad & \\\\\n", "\\text{Controlled-U} & =\n", "\\begin{bmatrix}\n", "I & 0 \\\\\n", "0 & U\\\\\n", "\\end{bmatrix}\n", " =\n", "\\begin{bmatrix}\n", "1 & 0 & 0 & 0 \\\\\n", "0 & 1 & 0 & 0 \\\\\n", "0 & 0 & u_{00} & u_{01} \\\\\n", "0 & 0 & u_{10} & u_{11}\\\\\n", "\\end{bmatrix}\n", "\\end{aligned}\n", "$$\n", "\n", "Qiskit puts the most significant bit (MSB) on the left, and the least significant bit (LSB) on the right. This is the standard ordering of binary bitstrings. We order the qubits in the same way (qubit representing the MSB has index 0), which is why Qiskit uses a non-standard tensor product order. Hence, in Qiskit, the above matrix looks like the following:\n", "\n", "$$\n", "\\text{Controlled-U} =\n", "\\begin{bmatrix}\n", "1 & 0 & 0 & 0 \\\\\n", "0 & u_{00} & 0 & u_{01} \\\\\n", "0 & 0 & 1 & 0 \\\\\n", "0 & u_{10} & 0 & u_{11}\\\\\n", "\\end{bmatrix}\n", "$$\n", "\n", "\n", "If we apply the T-gate to a qubit in the state $|1\\rangle$, we add a phase of $e^{i\\pi/4}$ to this qubit:\n", "\n", "$$\n", "T|1\\rangle = e^{i\\pi/4}|1\\rangle\n", "$$\n", "\n", "This is _global phase_ and is unobservable. But if we control this operation using another qubit in the $|{+}\\rangle$ state, the phase is no longer global but relative, which changes the _relative phase_ in our control qubit:\n", "\n", "$$\n", "\\begin{aligned}\n", "|1{+}\\rangle & = |1\\rangle \\otimes \\tfrac{1}{\\sqrt{2}}(|0\\rangle + |1\\rangle) \\\\\n", "& = \\tfrac{1}{\\sqrt{2}}(|10\\rangle + |11\\rangle) \\\\\n", "& \\\\\n", "\\text{Controlled-T}|1{+}\\rangle & = \\tfrac{1}{\\sqrt{2}}(|10\\rangle + e^{i\\pi/4}|11\\rangle) \\\\\n", "& \\\\\n", "& = |1\\rangle \\otimes \\tfrac{1}{\\sqrt{2}}(|0\\rangle + e^{i\\pi/4}|1\\rangle)\n", "\\end{aligned}\n", "$$\n", "\n", "This has the effect of rotating our control qubit around the Z-axis of the Bloch sphere, while leaving the target qubit unchanged. Let's see this in Qiskit:" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 28, "outputs": [ { "data": { "text/plain": "
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\n" }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(2)\n", "qc.h(0)\n", "qc.x(1)\n", "display(qc.draw('mpl'))\n", "# See Results:\n", "qc.save_statevector()\n", "qobj = assemble(qc)\n", "final_state = svsim.run(qobj).result().get_statevector()\n", "plot_bloch_multivector(final_state)" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "code", "execution_count": 29, "outputs": [ { "data": { "text/plain": "
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\n" }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(2)\n", "qc.h(0)\n", "qc.x(1)\n", "# Add Controlled-T\n", "qc.cp(pi/4, 0, 1)\n", "display(qc.draw('mpl'))\n", "# See Results:\n", "qc.save_statevector()\n", "qobj = assemble(qc)\n", "final_state = svsim.run(qobj).result().get_statevector()\n", "plot_bloch_multivector(final_state)" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "we can see the leftmost qubit has been rotated by $\\pi/4$ around the Z-axis of the Bloch sphere as expected. After exploring this behaviour, it may become clear why Qiskit draws the controlled-Z rotation gates in this symmetrical fashion (two controls instead of a control and a target). There is no clear control or target qubit for all cases.\n", "\n", "![](images/pkb_z_equiv.png)\n", "\n", "#### Send it after class 3:\n", "\n", "-What would be the resulting state of the control qubit (q0) if the target qubit (q1) was in the state $|0\\rangle$? (as shown in the circuit below)? Use Qiskit to check your answer.\n", "\n", "\n", "\n", "![](images/pkb_ex1.png)\n", "\n", "-What would happen to the control qubit (q0) if the target qubit (q1) was in the state $|1\\rangle$, and the circuit used a controlled-Sdg gate instead of the controlled-T (as shown in the circuit below)?\n", "\n", "\n", "\n", "![](images/pkb_ex2.png)\n", "\n", "-What would happen to the control qubit (q0) if it was in the state $|1\\rangle$ instead of the state $|{+}\\rangle$ before application of the controlled-T (as shown in the circuit below)?\n", "\n", "\n", "\n", "![](images/pkb_ex3.png)" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%% md\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": "3.7.7" } }, "nbformat": 4, "nbformat_minor": 4 }