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solution to lab 6 #1

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211 changes: 156 additions & 55 deletions task 1.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -38,33 +38,46 @@
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"metadata": {
"ExecuteTime": {
"end_time": "2025-10-09T17:17:26.193607Z",
"start_time": "2025-10-09T17:17:26.178663Z"
}
},
"source": [
"def toy_hash(x):\n",
" \"\"\"Hash function with unique preimages: (3*x + 5) mod 8.\"\"\"\n",
" return (3 * x + 5) % 8\n",
"\n"
]
],
"outputs": [],
"execution_count": 29
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"metadata": {
"ExecuteTime": {
"end_time": "2025-10-09T17:17:26.208993Z",
"start_time": "2025-10-09T17:17:26.194629Z"
}
},
"source": [
"# Setup\n",
"n_qubits = 3 # 3-bit password (values 0-7)\n",
"target_hash = 5 # The hash value we want to find a pre-image for\n",
"\n"
]
],
"outputs": [],
"execution_count": 30
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"metadata": {
"ExecuteTime": {
"end_time": "2025-10-09T17:17:26.234388Z",
"start_time": "2025-10-09T17:17:26.227422Z"
}
},
"source": [
"def classical_preimage_search():\n",
" \"\"\"Classically search for a pre-image of the target hash.\"\"\"\n",
Expand All @@ -77,25 +90,43 @@
"\n",
"actual_password = classical_preimage_search()\n",
"\n"
]
],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"h(0) = 5\n"
]
}
],
"execution_count": 31
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"metadata": {
"ExecuteTime": {
"end_time": "2025-10-09T17:17:26.272100Z",
"start_time": "2025-10-09T17:17:26.266483Z"
}
},
"source": [
"from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister, transpile\n",
"from qiskit.circuit.library import MCMTGate, ZGate\n",
"from qiskit_aer import AerSimulator\n",
"import numpy as np\n"
]
],
"outputs": [],
"execution_count": 32
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"metadata": {
"ExecuteTime": {
"end_time": "2025-10-09T19:06:48.610911Z",
"start_time": "2025-10-09T19:06:48.601493Z"
}
},
"source": [
"def create_oracle(n_qubits, target_hash):\n",
" \"\"\"\n",
Expand All @@ -115,38 +146,53 @@
"\n",
" # Step 1: Compute hash(x) = (3*x + 5) mod 8\n",
" # TODO: Multiply by 3. HINT: 3*x = 2*x + x, so use CNOTs for left shift plus addition\n",
"\n",
"\n",
" # We only care about the lower 3 qubits of hash\n",
" # We can throw the MSB away because of the mod 8\n",
" for i in range(n_qubits - 1):\n",
" oracle.cx(input_qubits[i],hash_qubits[i + 1])\n",
"\n",
" for i in range(n_qubits):\n",
" oracle.cx(input_qubits[i], hash_qubits[i])\n",
" \n",
" # TODO: Add 5. HINT: Use X gates to add constants in binary (5 = 101 in binary)\n",
"\n",
" oracle.x(n_qubits)\n",
" oracle.x(n_qubits+2)\n",
" # Step 2: Check if hash(x) == target_hash\n",
" target_binary = format(target_hash, f\"0{n_qubits}b\")\n",
"\n",
" # Flip qubits where target bit is 0 (so we match on |111...>)\n",
" for i, bit in enumerate(target_binary):\n",
" # TODO: Update here\n",
" pass \n",
" if bit == '0':\n",
" oracle.x(n_qubits+i)\n",
"\n",
" # TODO: Mark the state with multi-controlled NOT\n",
" oracle.mcx(hash_qubits, phase_qubit)\n",
"\n",
" # Unflip the checking bits\n",
" for i, bit in enumerate(target_binary):\n",
" # TODO: Update here\n",
" pass\n",
" if bit == '0':\n",
" oracle.x(n_qubits+i)\n",
"\n",
" # Step 3: Uncompute hash to clean up ancilla\n",
" # TODO: Reverse the hash computation steps\n",
"\n",
" \n",
" # The ancilla is unmodified in the hash calculation\n",
" \n",
" return oracle\n",
"\n"
]
],
"outputs": [],
"execution_count": 65
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"metadata": {
"ExecuteTime": {
"end_time": "2025-10-09T19:06:49.955583Z",
"start_time": "2025-10-09T19:06:49.943819Z"
}
},
"source": [
"def create_diffusion(n_qubits):\n",
" \"\"\"Create diffusion operator (inversion about average)\"\"\"\n",
Expand All @@ -155,43 +201,52 @@
" # TODO: Implement the diffusion operator\n",
"\n",
" # Step 1: Apply H to all qubits\n",
"\n",
" diffusion.h(range(n_qubits))\n",
"\n",
" # Step 2: Apply X to all qubits\n",
"\n",
" diffusion.x(range(n_qubits))\n",
"\n",
" # Step 3: Multi-controlled Z (using ancilla if needed)\n",
"\n",
"\n",
"\n",
" mcz = MCMTGate(ZGate(),n_qubits-1,1)\n",
" diffusion.append(mcz, range(n_qubits))\n",
"\n",
"\n",
" # Step 4: Apply X to all qubits\n",
"\n",
" diffusion.x(range(n_qubits))\n",
"\n",
" # Step 5: Apply H to all qubits\n",
"\n",
" diffusion.h(range(n_qubits))\n",
"\n",
" return diffusion\n",
"\n"
]
],
"outputs": [],
"execution_count": 66
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"metadata": {
"ExecuteTime": {
"end_time": "2025-10-09T19:06:50.296651Z",
"start_time": "2025-10-09T19:06:50.291068Z"
}
},
"source": [
"# Calculate number of Grover iterations\n",
"N = 2**n_qubits\n",
"optimal_iterations = int(np.pi / 4 * np.sqrt(N)) # Since there's 1 solution, otherwise use N/M, where M is the number of solutions\n"
]
],
"outputs": [],
"execution_count": 67
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"metadata": {
"ExecuteTime": {
"end_time": "2025-10-09T19:30:00.362049Z",
"start_time": "2025-10-09T19:30:00.342055Z"
}
},
"source": [
"# Build Grover circuit\n",
"\n",
Expand All @@ -202,30 +257,50 @@
"qc = QuantumCircuit(qr, cr)\n",
"\n",
"# TODO: Initialize input qubits to superposition\n",
"\n",
"qc.h(range(n_qubits))\n",
"\n",
"# TODO: Initialize phase qubit to |-⟩ for phase kickback\n",
"\n",
"qc.x(total_qubits-1)\n",
"qc.h(total_qubits-1)\n",
"qc.barrier()\n",
"\n",
"# Grover iterations\n",
"oracle = create_oracle(n_qubits, target_hash)\n",
"diffusion = create_diffusion(n_qubits)\n",
"\n",
"for _ in range(optimal_iterations):\n",
" # TODO: Apply oracle and diffusion\n",
" pass\n",
" qc.append(oracle, range(total_qubits))\n",
" qc.barrier()\n",
" qc.append(diffusion, range(n_qubits))\n",
" qc.barrier()\n",
"\n",
"# TODO: Measure input qubits\n",
"\n",
"# TODO: Measure input qubits\n",
"qc.measure(range(n_qubits), range(n_qubits))\n",
"\n"
]
],
"outputs": [
{
"data": {
"text/plain": [
"<qiskit.circuit.instructionset.InstructionSet at 0x1ac248da110>"
]
},
"execution_count": 79,
"metadata": {},
"output_type": "execute_result"
}
],
"execution_count": 79
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"metadata": {
"ExecuteTime": {
"end_time": "2025-10-09T19:30:00.963626Z",
"start_time": "2025-10-09T19:30:00.787853Z"
}
},
"source": [
"# Simulate the circuit\n",
"simulator = AerSimulator()\n",
Expand All @@ -250,7 +325,33 @@
"print(\n",
" f\"\\nMost likely password guess: {found_password} (h({found_password})={toy_hash(found_password)})\"\n",
")\n"
]
],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 000 (password=0): 1850 shots ( 45.2%) - h(0)=5 ✓✓✓\n",
" 111 (password=7): 339 shots ( 8.3%) - h(7)=2 \n",
" 010 (password=2): 339 shots ( 8.3%) - h(2)=3 \n",
" 011 (password=3): 336 shots ( 8.2%) - h(3)=6 \n",
" 100 (password=4): 333 shots ( 8.1%) - h(4)=1 \n",
" 110 (password=6): 307 shots ( 7.5%) - h(6)=7 \n",
" 001 (password=1): 301 shots ( 7.3%) - h(1)=0 \n",
" 101 (password=5): 291 shots ( 7.1%) - h(5)=4 \n",
"\n",
"Most likely password guess: 0 (h(0)=5)\n"
]
}
],
"execution_count": 80
},
{
"metadata": {},
"cell_type": "code",
"outputs": [],
"execution_count": null,
"source": ""
}
],
"metadata": {
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