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\n", + "* Step3: Alice then performs certain operations on her qubit ($q_1$) with $\\psi$ as control and measures both qubits. The result is then sent to Bob via classical channel.\n", + "* Step4: Based on the classical information, Bob performation certain operations to recover state $\\psi$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Step 1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let $\\phi$ represent the entangled qubit pair. This can be acheived by applying a Hadamard gate followed by a CNOT gate.
\n", + "$$|\\phi \\rangle=\\frac{1}{\\sqrt 2}(|00\\rangle+|11\\rangle)$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Step 2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Alice keeps the first qubit and Bob keeps the second one." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### State of three qubit pair" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Qubit state that Alice wants to send to Bob.$$|\\psi \\rangle = a|0\\rangle+b|1\\rangle$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Three Qubit State: $$|\\phi \\rangle \\times |\\psi \\rangle = \\frac{1}{\\sqrt 2}(|00\\rangle+|11\\rangle)\\times (a|0\\rangle+b|1\\rangle)$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\\frac{1}{\\sqrt 2}(a|000\\rangle+b|001\\rangle+a|110\\rangle+b|111\\rangle)$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Remember, Alice has first two qubits and Bob has the 3rd qubit" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Step 3" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Alice Applies CNOT gate to $q_1$ (middle qubit in above representation), controlled by $q_0$ (rightmost qubit in above representation), followed by Hadamard gate to $q_0$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "CNOT$\\frac{1}{\\sqrt 2}(a|000\\rangle+b|001\\rangle+a|110\\rangle+b|111\\rangle)$ = $\\frac{1}{\\sqrt 2}(a|000\\rangle+b|011\\rangle+a|110\\rangle+b|101\\rangle)$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "H$\\frac{1}{\\sqrt 2}(a|000\\rangle+b|011\\rangle+a|110\\rangle+b|101\\rangle)$ = $\\frac{1}{\\sqrt 2}(a|00+\\rangle+b|01-\\rangle+a|11+\\rangle+b|10-\\rangle)$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Remember, $$|+\\rangle = \\frac{1}{\\sqrt{2}}(|0\\rangle+|1\\rangle)$$\n", + " $$|-\\rangle = \\frac{1}{\\sqrt{2}}(|0\\rangle-|1\\rangle)$$\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This will result in:\n", + "\n", + "$$\\frac{1}{2}((a|0\\rangle+b|1\\rangle)|00\\rangle\\\\+(a|1\\rangle-b|0\\rangle)|01\\rangle\\\\+(a|1\\rangle+b|0\\rangle)|10\\rangle\\\\+(b|0\\rangle-a|1\\rangle)|11\\rangle)$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Alice will measure the first two qubits. The result she will obtain will always be one of four standard basis states. $|00\\rangle, 01\\rangle, 10\\rangle, 11\\rangle$\n", + "This information is sent to Bob through classical channel." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Step 4" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Upon receiving the information, Bob can recover state $|\\psi\\rangle$ by applying appropriate gates\n", + "\n", + "00 → Do nothing\n", + "\n", + "01 → Apply X gate\n", + "\n", + "10 → Apply Z gate\n", + "\n", + "11 → Apply ZX gate" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "https://www.nature.com/news/quantum-teleportation-is-even-weirder-than-you-think-1.22321" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Quantum Teleportation Protocol" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Create our Quantum Circuit" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "def create_bell_pair(qc, a, b):\n", + " \"\"\"Creates a bell pair in qc using qubits a & b\"\"\"\n", + " qc.h(a) # Put qubit a into state |+>\n", + " qc.cx(a,b) # CNOT with a as control and b as target" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "def alice_gates(qc, psi, a):\n", + " qc.cx(psi, a)\n", + " qc.h(psi)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "def measure_and_send(qc, a, b):\n", + " \"\"\"Measures qubits a & b and 'sends' the results to Bob\"\"\"\n", + " qc.barrier()\n", + " qc.measure(a,0)\n", + " qc.measure(b,1)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "## SETUP\n", + "# Protocol uses 3 qubits and 2 classical bits in 2 different registers\n", + "\n", + "qr = QuantumRegister(3, name=\"q\") # Protocol uses 3 qubits\n", + "crz = ClassicalRegister(1, name=\"crz\") # and 2 classical bits\n", + "crx = ClassicalRegister(1, name=\"crx\") # in 2 different registers\n", + "teleportation_circuit = QuantumCircuit(qr, crz, crx)\n", + "\n", + "# STEP 1\n", + "# In our case, Telamon entangles qubits q1 and q2\n", + "# Let's apply this to our circuit:\n", + "create_bell_pair(teleportation_circuit, 1, 2)\n", + "# And view the circuit so far:\n", + "teleportation_circuit.draw('mpl')\n", + "\n", + "## STEP 2\n", + "teleportation_circuit.barrier() # Use barrier to separate steps\n", + "alice_gates(teleportation_circuit, 0, 1)\n", + "teleportation_circuit.draw('mpl')\n", + "\n", + "## STEP 3\n", + "measure_and_send(teleportation_circuit, 0 ,1)\n", + "teleportation_circuit.draw('mpl')" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "# This function takes a QuantumCircuit (qc), integer (qubit)\n", + "# and ClassicalRegisters (crz & crx) to decide which gates to apply\n", + "def bob_gates(qc, qubit, crz, crx):\n", + " # Here we use c_if to control our gates with a classical\n", + " # bit instead of a qubit\n", + " qc.x(qubit).c_if(crx, 1) # Apply gates if the registers \n", + " qc.z(qubit).c_if(crz, 1) # are in the state '1'" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Protocol uses 3 qubits and 2 classical bits in 2 different registers\n", + "qr = QuantumRegister(3, name=\"q\")\n", + "crz, crx = ClassicalRegister(1, name=\"crz\"), ClassicalRegister(1, name=\"crx\")\n", + "teleportation_circuit = QuantumCircuit(qr, crz, crx)\n", + "\n", + "## STEP 1\n", + "create_bell_pair(teleportation_circuit, 1, 2)\n", + "\n", + "## STEP 2\n", + "teleportation_circuit.barrier() # Use barrier to separate steps\n", + "alice_gates(teleportation_circuit, 0, 1)\n", + "\n", + "## STEP 3\n", + "measure_and_send(teleportation_circuit, 0, 1)\n", + "\n", + "## STEP 4\n", + "teleportation_circuit.barrier() # Use barrier to separate steps\n", + "bob_gates(teleportation_circuit, 2, crz, crx)\n", + "teleportation_circuit.draw('mpl')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Simulating the Teleportation protocol" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \n", + "|\\psi\\rangle =\\begin{bmatrix}\n", + "0.71618 - 0.4504i \\\\\n", + "0.23441 + 0.47884i\n", + "\\end{bmatrix}\n", + "$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Create random 1-qubit state\n", + "psi = random_state(1)\n", + "\n", + "# Display it nicely\n", + "array_to_latex(psi, pretext=\"|\\\\psi\\\\rangle =\")\n", + "# Show it on a Bloch sphere\n", + "plot_bloch_multivector(psi)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "init_gate = Initialize(psi)\n", + "init_gate.label = \"init\"" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "## SETUP\n", + "qr = QuantumRegister(3, name=\"q\") # Protocol uses 3 qubits\n", + "crz = ClassicalRegister(1, name=\"crz\") # and 2 classical registers\n", + "crx = ClassicalRegister(1, name=\"crx\")\n", + "qc = QuantumCircuit(qr, crz, crx)\n", + "\n", + "## STEP 0\n", + "# First, let's initialize Alice's q0\n", + "qc.append(init_gate, [0])\n", + "qc.barrier()\n", + "\n", + "## STEP 1\n", + "# Now begins the teleportation protocol\n", + "create_bell_pair(qc, 1, 2)\n", + "qc.barrier()\n", + "\n", + "## STEP 2\n", + "# Send q1 to Alice and q2 to Bob\n", + "alice_gates(qc, 0, 1)\n", + "\n", + "## STEP 3\n", + "# Alice then sends her classical bits to Bob\n", + "measure_and_send(qc, 0, 1)\n", + "\n", + "## STEP 4\n", + "# Bob decodes qubits\n", + "bob_gates(qc, 2, crz, crx)\n", + "\n", + "# Display the circuit\n", + "qc.draw('mpl')" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "sv_sim = Aer.get_backend('statevector_simulator')\n", + "qobj = assemble(qc)\n", + "out_vector = sv_sim.run(qobj).result().get_statevector()\n", + "plot_bloch_multivector(out_vector)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Using the QASM Simulator" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [], + "source": [ + "inverse_init_gate = init_gate.gates_to_uncompute()" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "## SETUP\n", + "qr = QuantumRegister(3, name=\"q\") # Protocol uses 3 qubits\n", + "crz = ClassicalRegister(1, name=\"crz\") # and 2 classical registers\n", + "crx = ClassicalRegister(1, name=\"crx\")\n", + "qc = QuantumCircuit(qr, crz, crx)\n", + "\n", + "## STEP 0\n", + "# First, let's initialize Alice's q0\n", + "qc.append(init_gate, [0])\n", + "qc.barrier()\n", + "\n", + "## STEP 1\n", + "# Now begins the teleportation protocol\n", + "create_bell_pair(qc, 1, 2)\n", + "qc.barrier()\n", + "\n", + "## STEP 2\n", + "# Send q1 to Alice and q2 to Bob\n", + "alice_gates(qc, 0, 1)\n", + "\n", + "## STEP 3\n", + "# Alice then sends her classical bits to Bob\n", + "measure_and_send(qc, 0, 1)\n", + "\n", + "## STEP 4\n", + "# Bob decodes qubits\n", + "bob_gates(qc, 2, crz, crx)\n", + "\n", + "## STEP 5\n", + "# reverse the initialization process\n", + "qc.append(inverse_init_gate, [2])\n", + "\n", + "# Display the circuit\n", + "qc.draw('mpl')" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Need to add a new ClassicalRegister\n", + "# to see the result\n", + "cr_result = ClassicalRegister(1)\n", + "qc.add_register(cr_result)\n", + "qc.measure(2,2)\n", + "qc.draw('mpl')" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qasm_sim = Aer.get_backend('qasm_simulator')\n", + "t_qc = transpile(qc, qasm_sim)\n", + "qobj = assemble(t_qc)\n", + "counts = qasm_sim.run(qobj).result().get_counts()\n", + "plot_histogram(counts)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Teleportation on a Real Quantum Computer " + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [], + "source": [ + "def new_bob_gates(qc, a, b, c):\n", + " qc.cx(b, c)\n", + " qc.cz(a, c)" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc = QuantumCircuit(3,1)\n", + "\n", + "# First, let's initialize Alice's q0\n", + "qc.append(init_gate, [0])\n", + "qc.barrier()\n", + "\n", + "# Now begins the teleportation protocol\n", + "create_bell_pair(qc, 1, 2)\n", + "qc.barrier()\n", + "# Send q1 to Alice and q2 to Bob\n", + "alice_gates(qc, 0, 1)\n", + "qc.barrier()\n", + "# Alice sends classical bits to Bob\n", + "new_bob_gates(qc, 0, 1, 2)\n", + "\n", + "# We undo the initialization process\n", + "qc.append(inverse_init_gate, [2])\n", + "\n", + "# See the results, we only care about the state of qubit 2\n", + "qc.measure(2,0)\n", + "\n", + "# View the results:\n", + "qc.draw('mpl')" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Library/Frameworks/Python.framework/Versions/3.7/lib/python3.7/site-packages/qiskit/providers/ibmq/ibmqfactory.py:192: UserWarning: Timestamps in IBMQ backend properties, jobs, and job results are all now in local time instead of UTC.\n", + " warnings.warn('Timestamps in IBMQ backend properties, jobs, and job results '\n" + ] + } + ], + "source": [ + "# First, see what devices we are allowed to use by loading our saved accounts\n", + "IBMQ.load_account()\n", + "provider = IBMQ.get_provider(hub='ibm-q')" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Job Status: job has successfully run\n" + ] + } + ], + "source": [ + "# get the least-busy backend at IBM and run the quantum circuit there\n", + "from qiskit.providers.ibmq import least_busy\n", + "from qiskit.tools.monitor import job_monitor\n", + "backend = least_busy(provider.backends(filters=lambda b: b.configuration().n_qubits >= 3 and\n", + " not b.configuration().simulator and b.status().operational==True))\n", + "t_qc = transpile(qc, backend, optimization_level=3)\n", + "qobj = assemble(t_qc)\n", + "job = backend.run(qobj)\n", + "job_monitor(job) # displays job status under cell" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'0': 962, '1': 62}\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Get the results and display them\n", + "exp_result = job.result()\n", + "exp_counts = exp_result.get_counts(qc)\n", + "print(exp_counts)\n", + "plot_histogram(exp_counts)" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The experimental error rate : 0.061%\n" + ] + } + ], + "source": [ + "print(f\"The experimental error rate : {exp_counts['1']/sum(exp_counts.values()):.3f}%\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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": "3.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +}