{
"cells": [
{
"cell_type": "markdown",
"id": "be565231",
"metadata": {},
"source": [
"# 电路基础"
]
},
{
"cell_type": "markdown",
"id": "fcdfed33",
"metadata": {},
"source": [
"## 概述\n",
"\n",
"在这篇笔记中，我们将了解 TensorCircuit 中核心对象的基本操作-``tc.Circuit``，它支持无噪声仿真和基于蒙特卡洛轨迹的噪声仿真。更重要的是，几乎所有对 Circuit 对象的操作都是可微分的和可即时编译的，这是成功高效地进行变分量子算法模拟的关键。\n",
"[WIP note]"
]
},
{
"cell_type": "markdown",
"id": "c51c024b",
"metadata": {},
"source": [
"## 设置"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "98f21e9b",
"metadata": {},
"outputs": [],
"source": [
"from functools import partial\n",
"import inspect\n",
"import sys\n",
"import numpy as np\n",
"import tensorflow as tf\n",
"\n",
"import tensorcircuit as tc"
]
},
{
"cell_type": "markdown",
"id": "558cdc17",
"metadata": {},
"source": [
"## “Hello World\" 样例"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "b83f24f4",
"metadata": {},
"outputs": [],
"source": [
"def get_circuit(n):\n",
" c = tc.Circuit(n) # 用 n 个量子比特初始化一个电路对象\n",
" for i in range(n):\n",
" c.H(i) # 在每个量子比特上使用 Hadamard 门\n",
" c.cnot(0, 1) # 在第 0 个量子比特上应用带有控制量子比特的 cnot 门\n",
" c.CNOT(n - 1, n - 2) # 大写的 API 也可以正常使用\n",
" return c"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "601a072c",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"['i', 'x', 'y', 'z', 'h', 't', 's', 'td', 'sd', 'wroot', 'cnot', 'cz', 'swap', 'cy', 'iswap', 'ox', 'oy', 'oz', 'toffoli', 'fredkin']\n"
]
}
],
"source": [
"# 打印不含参数的有可能的门\n",
"print(tc.Circuit.sgates)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "c191ea53",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"i\n",
"[[1.+0.j 0.+0.j]\n",
" [0.+0.j 1.+0.j]]\n",
"x\n",
"[[0.+0.j 1.+0.j]\n",
" [1.+0.j 0.+0.j]]\n",
"y\n",
"[[0.+0.j 0.-1.j]\n",
" [0.+1.j 0.+0.j]]\n",
"z\n",
"[[ 1.+0.j 0.+0.j]\n",
" [ 0.+0.j -1.+0.j]]\n",
"h\n",
"[[ 0.70710677+0.j 0.70710677+0.j]\n",
" [ 0.70710677+0.j -0.70710677+0.j]]\n",
"t\n",
"[[1. +0.j 0. +0.j ]\n",
" [0. +0.j 0.70710677+0.70710677j]]\n",
"s\n",
"[[1.+0.j 0.+0.j]\n",
" [0.+0.j 0.+1.j]]\n",
"td\n",
"[[1. +0.j 0. +0.j ]\n",
" [0. +0.j 0.70710677-0.70710677j]]\n",
"sd\n",
"[[1.+0.j 0.+0.j]\n",
" [0.+0.j 0.-1.j]]\n",
"wroot\n",
"[[ 0.70710677+0.j -0.5 -0.5j]\n",
" [ 0.5 -0.5j 0.70710677+0.j ]]\n",
"cnot\n",
"[[1.+0.j 0.+0.j 0.+0.j 0.+0.j]\n",
" [0.+0.j 1.+0.j 0.+0.j 0.+0.j]\n",
" [0.+0.j 0.+0.j 0.+0.j 1.+0.j]\n",
" [0.+0.j 0.+0.j 1.+0.j 0.+0.j]]\n",
"cz\n",
"[[ 1.+0.j 0.+0.j 0.+0.j 0.+0.j]\n",
" [ 0.+0.j 1.+0.j 0.+0.j 0.+0.j]\n",
" [ 0.+0.j 0.+0.j 1.+0.j 0.+0.j]\n",
" [ 0.+0.j 0.+0.j 0.+0.j -1.+0.j]]\n",
"swap\n",
"[[1.+0.j 0.+0.j 0.+0.j 0.+0.j]\n",
" [0.+0.j 0.+0.j 1.+0.j 0.+0.j]\n",
" [0.+0.j 1.+0.j 0.+0.j 0.+0.j]\n",
" [0.+0.j 0.+0.j 0.+0.j 1.+0.j]]\n",
"cy\n",
"[[1.+0.j 0.+0.j 0.+0.j 0.+0.j]\n",
" [0.+0.j 1.+0.j 0.+0.j 0.+0.j]\n",
" [0.+0.j 0.+0.j 0.+0.j 0.-1.j]\n",
" [0.+0.j 0.+0.j 0.+1.j 0.+0.j]]\n",
"iswap\n",
"[[1.+0.j 0.+0.j 0.+0.j 0.+0.j]\n",
" [0.+0.j 0.+0.j 0.+1.j 0.+0.j]\n",
" [0.+0.j 0.+1.j 0.+0.j 0.+0.j]\n",
" [0.+0.j 0.+0.j 0.+0.j 1.+0.j]]\n",
"ox\n",
"[[0.+0.j 1.+0.j 0.+0.j 0.+0.j]\n",
" [1.+0.j 0.+0.j 0.+0.j 0.+0.j]\n",
" [0.+0.j 0.+0.j 1.+0.j 0.+0.j]\n",
" [0.+0.j 0.+0.j 0.+0.j 1.+0.j]]\n",
"oy\n",
"[[0.+0.j 0.-1.j 0.+0.j 0.+0.j]\n",
" [0.+1.j 0.+0.j 0.+0.j 0.+0.j]\n",
" [0.+0.j 0.+0.j 1.+0.j 0.+0.j]\n",
" [0.+0.j 0.+0.j 0.+0.j 1.+0.j]]\n",
"oz\n",
"[[ 1.+0.j 0.+0.j 0.+0.j 0.+0.j]\n",
" [ 0.+0.j -1.+0.j 0.+0.j 0.+0.j]\n",
" [ 0.+0.j 0.+0.j 1.+0.j 0.+0.j]\n",
" [ 0.+0.j 0.+0.j 0.+0.j 1.+0.j]]\n",
"toffoli\n",
"[[1.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]\n",
" [0.+0.j 1.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]\n",
" [0.+0.j 0.+0.j 1.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]\n",
" [0.+0.j 0.+0.j 0.+0.j 1.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]\n",
" [0.+0.j 0.+0.j 0.+0.j 0.+0.j 1.+0.j 0.+0.j 0.+0.j 0.+0.j]\n",
" [0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 1.+0.j 0.+0.j 0.+0.j]\n",
" [0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 1.+0.j]\n",
" [0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 1.+0.j 0.+0.j]]\n",
"fredkin\n",
"[[1.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]\n",
" [0.+0.j 1.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]\n",
" [0.+0.j 0.+0.j 1.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]\n",
" [0.+0.j 0.+0.j 0.+0.j 1.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]\n",
" [0.+0.j 0.+0.j 0.+0.j 0.+0.j 1.+0.j 0.+0.j 0.+0.j 0.+0.j]\n",
" [0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 1.+0.j 0.+0.j]\n",
" [0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 1.+0.j 0.+0.j 0.+0.j]\n",
" [0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 1.+0.j]]\n"
]
}
],
"source": [
"# 这些门定义的相应矩阵\n",
"for g in tc.Circuit.sgates:\n",
" gf = getattr(tc.gates, g)\n",
" print(g)\n",
" print(tc.gates.matrix_for_gate(gf()))"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "96c15225",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[{'gatef': h,\n",
" 'gate': Gate(\n",
" name: 'h',\n",
" tensor:\n",
" array([[ 0.70710677+0.j, 0.70710677+0.j],\n",
" [ 0.70710677+0.j, -0.70710677+0.j]], dtype=complex64),\n",
" edges: [\n",
" Edge('cnot'[2] -> 'h'[0] ),\n",
" Edge('h'[1] -> 'qb-1'[0] )\n",
" ]),\n",
" 'index': (0,),\n",
" 'name': 'h',\n",
" 'split': None,\n",
" 'mpo': False},\n",
" {'gatef': h,\n",
" 'gate': Gate(\n",
" name: 'h',\n",
" tensor:\n",
" array([[ 0.70710677+0.j, 0.70710677+0.j],\n",
" [ 0.70710677+0.j, -0.70710677+0.j]], dtype=complex64),\n",
" edges: [\n",
" Edge('cnot'[3] -> 'h'[0] ),\n",
" Edge('h'[1] -> 'qb-2'[0] )\n",
" ]),\n",
" 'index': (1,),\n",
" 'name': 'h',\n",
" 'split': None,\n",
" 'mpo': False},\n",
" {'gatef': h,\n",
" 'gate': Gate(\n",
" name: 'h',\n",
" tensor:\n",
" array([[ 0.70710677+0.j, 0.70710677+0.j],\n",
" [ 0.70710677+0.j, -0.70710677+0.j]], dtype=complex64),\n",
" edges: [\n",
" Edge('cnot'[2] -> 'h'[0] ),\n",
" Edge('h'[1] -> 'qb-3'[0] )\n",
" ]),\n",
" 'index': (2,),\n",
" 'name': 'h',\n",
" 'split': None,\n",
" 'mpo': False},\n",
" {'gatef': cnot,\n",
" 'gate': Gate(\n",
" name: 'cnot',\n",
" tensor:\n",
" array([[[[1.+0.j, 0.+0.j],\n",
" [0.+0.j, 0.+0.j]],\n",
" \n",
" [[0.+0.j, 1.+0.j],\n",
" [0.+0.j, 0.+0.j]]],\n",
" \n",
" \n",
" [[[0.+0.j, 0.+0.j],\n",
" [0.+0.j, 1.+0.j]],\n",
" \n",
" [[0.+0.j, 0.+0.j],\n",
" [1.+0.j, 0.+0.j]]]], dtype=complex64),\n",
" edges: [\n",
" Edge(Dangling Edge)[0],\n",
" Edge('cnot'[3] -> 'cnot'[1] ),\n",
" Edge('cnot'[2] -> 'h'[0] ),\n",
" Edge('cnot'[3] -> 'h'[0] )\n",
" ]),\n",
" 'index': (0, 1),\n",
" 'name': 'cnot',\n",
" 'split': None,\n",
" 'mpo': False},\n",
" {'gatef': cnot,\n",
" 'gate': Gate(\n",
" name: 'cnot',\n",
" tensor:\n",
" array([[[[1.+0.j, 0.+0.j],\n",
" [0.+0.j, 0.+0.j]],\n",
" \n",
" [[0.+0.j, 1.+0.j],\n",
" [0.+0.j, 0.+0.j]]],\n",
" \n",
" \n",
" [[[0.+0.j, 0.+0.j],\n",
" [0.+0.j, 1.+0.j]],\n",
" \n",
" [[0.+0.j, 0.+0.j],\n",
" [1.+0.j, 0.+0.j]]]], dtype=complex64),\n",
" edges: [\n",
" Edge(Dangling Edge)[0],\n",
" Edge(Dangling Edge)[1],\n",
" Edge('cnot'[2] -> 'h'[0] ),\n",
" Edge('cnot'[3] -> 'cnot'[1] )\n",
" ]),\n",
" 'index': (2, 1),\n",
" 'name': 'cnot',\n",
" 'split': None,\n",
" 'mpo': False}]"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"c = get_circuit(3)\n",
"ir = c.to_qir() # 电路的中间表示\n",
"ir"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "9ab7fd6e",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(array([[ 0.70710677+0.j, 0.70710677+0.j],\n",
" [ 0.70710677+0.j, -0.70710677+0.j]], dtype=complex64),\n",
" array([[[[1.+0.j, 0.+0.j],\n",
" [0.+0.j, 0.+0.j]],\n",
" \n",
" [[0.+0.j, 1.+0.j],\n",
" [0.+0.j, 0.+0.j]]],\n",
" \n",
" \n",
" [[[0.+0.j, 0.+0.j],\n",
" [0.+0.j, 1.+0.j]],\n",
" \n",
" [[0.+0.j, 0.+0.j],\n",
" [1.+0.j, 0.+0.j]]]], dtype=complex64))"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ir[0][\"gatef\"]().tensor, ir[-1][\"gate\"].tensor # 每个门的实际幺正矩阵"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "ecdc0f1a",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([0.35355335+0.j, 0.35355335+0.j, 0.35355335+0.j, 0.35355335+0.j,\n",
" 0.35355335+0.j, 0.35355335+0.j, 0.35355335+0.j, 0.35355335+0.j],\n",
" dtype=complex64)"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# 计算电路的最终输出量子态\n",
"c.state()"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "64fa321b",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(0.9999998+0j) 0j\n"
]
}
],
"source": [
"# 计算一些期望值，比如 <X1>\n",
"x1 = c.expectation([tc.gates.x(), [1]])\n",
"\n",
"# 或 <Z1Z2>\n",
"z1z2 = c.expectation([tc.gates.z(), [1]], [tc.gates.z(), [2]])\n",
"\n",
"print(x1, z1z2)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "c8292569",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(array([1., 1., 1.], dtype=float32), 0.1250001713634208)\n",
"(array([0., 0., 1.], dtype=float32), 0.12499997764825821)\n",
"(array([0., 1., 1.], dtype=float32), 0.12499997764825821)\n",
"(array([1., 1., 0.], dtype=float32), 0.1249999776482098)\n",
"(array([1., 1., 0.], dtype=float32), 0.1249999776482098)\n",
"(array([1., 0., 1.], dtype=float32), 0.12499997019766829)\n",
"(array([0., 1., 0.], dtype=float32), 0.12499997764825821)\n",
"(array([1., 1., 0.], dtype=float32), 0.1249999776482098)\n",
"(array([0., 0., 0.], dtype=float32), 0.12499997764825821)\n",
"(array([0., 1., 1.], dtype=float32), 0.12499997764825821)\n"
]
}
],
"source": [
"# 做一些随机取样\n",
"for _ in range(10):\n",
" print(c.perfect_sampling())"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "c2c0bb84",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"tf.Tensor(\n",
"[0.35355335+0.j 0.35355335+0.j 0.35355335+0.j 0.35355335+0.j\n",
" 0.35355335+0.j 0.35355335+0.j 0.35355335+0.j 0.35355335+0.j], shape=(8,), dtype=complex64)\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"WARNING:absl:No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"[0.35355335+0.j 0.35355335+0.j 0.35355335+0.j 0.35355335+0.j\n",
" 0.35355335+0.j 0.35355335+0.j 0.35355335+0.j 0.35355335+0.j]\n",
"tensor([0.3536+0.j, 0.3536+0.j, 0.3536+0.j, 0.3536+0.j, 0.3536+0.j, 0.3536+0.j, 0.3536+0.j,\n",
" 0.3536+0.j])\n"
]
}
],
"source": [
"# 我们可以轻松地从 NumPy 切换模拟后端！\n",
"\n",
"with tc.runtime_backend(\"tensorflow\") as K:\n",
" c = get_circuit(3)\n",
" print(c.state())\n",
"\n",
"with tc.runtime_backend(\"jax\") as K:\n",
" c = get_circuit(3)\n",
" print(c.state())\n",
"\n",
"with tc.runtime_backend(\"pytorch\") as K:\n",
" # pytorch 后端无法保证最佳性能和完整功能\n",
" c = get_circuit(3)\n",
" print(c.state())"
]
},
{
"cell_type": "markdown",
"id": "0cbe17e7",
"metadata": {},
"source": [
"## 参数化量子电路(PQC)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "66192a2d",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"['r', 'cr', 'rx', 'ry', 'rz', 'crx', 'cry', 'crz', 'orx', 'ory', 'orz', 'any', 'exp', 'exp1']\n"
]
}
],
"source": [
"# 接受参数的量子电路门\n",
"\n",
"print(tc.Circuit.vgates)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "bae96276",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"r (theta: float = 0, alpha: float = 0, phi: float = 0) -> tensorcircuit.gates.Gate\n",
"cr (theta: float = 0, alpha: float = 0, phi: float = 0) -> tensorcircuit.gates.Gate\n",
"rx (theta: float = 0) -> tensorcircuit.gates.Gate\n",
"ry (theta: float = 0) -> tensorcircuit.gates.Gate\n",
"rz (theta: float = 0) -> tensorcircuit.gates.Gate\n",
"crx (*args: Any, **kws: Any) -> Any\n",
"cry (*args: Any, **kws: Any) -> Any\n",
"crz (*args: Any, **kws: Any) -> Any\n",
"orx (*args: Any, **kws: Any) -> Any\n",
"ory (*args: Any, **kws: Any) -> Any\n",
"orz (*args: Any, **kws: Any) -> Any\n",
"any (unitary: Any, name: str = 'any') -> tensorcircuit.gates.Gate\n",
"exp (unitary: Any, theta: float, name: str = 'none') -> tensorcircuit.gates.Gate\n",
"exp1 (unitary: Any, theta: float, name: str = 'none') -> tensorcircuit.gates.Gate\n"
]
}
],
"source": [
"# 查看每种类型的变量门的关键字参数（类型为浮点数）\n",
"for g in tc.Circuit.vgates:\n",
" print(g, inspect.signature(getattr(tc.gates, g).f))"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "55df5ffa",
"metadata": {},
"outputs": [],
"source": [
"def get_circuit(n, params):\n",
" c = tc.Circuit(n) # 用 n 个量子比特初始化一个电路对象\n",
" for i in range(n):\n",
" c.rx(i, theta=params[i]) # 应用 rx 门\n",
" c.cnot(0, 1)\n",
" return c"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "84392f01",
"metadata": {},
"outputs": [],
"source": [
"K = tc.set_backend(\"tensorflow\")"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "24ba6d64",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"tf.Tensor(\n",
"[ 0.6758712 +0.j 0. -0.36923012j 0. -0.36923015j\n",
" -0.20171136-0.j -0.20171136+0.j 0. +0.11019541j\n",
" 0. -0.36923015j -0.20171136-0.j ], shape=(8,), dtype=complex64)\n"
]
}
],
"source": [
"n = 3\n",
"params = K.ones([n])\n",
"c = get_circuit(n, params)\n",
"print(c.state())"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "c85cb07f",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[{'gatef': rx,\n",
" 'index': (0,),\n",
" 'name': 'rx',\n",
" 'split': None,\n",
" 'mpo': False,\n",
" 'parameters': {'theta': <tf.Tensor: shape=(), dtype=complex64, numpy=(1+0j)>},\n",
" 'gate': Gate(\n",
" name: '__unnamed_node__',\n",
" tensor:\n",
" <tf.Tensor: shape=(2, 2), dtype=complex64, numpy=\n",
" array([[0.87758255+0.j , 0. -0.47942555j],\n",
" [0. -0.47942555j, 0.87758255+0.j ]], dtype=complex64)>,\n",
" edges: [\n",
" Edge('cnot'[2] -> '__unnamed_node__'[0] ),\n",
" Edge('__unnamed_node__'[1] -> 'qb-1'[0] )\n",
" ])},\n",
" {'gatef': rx,\n",
" 'index': (1,),\n",
" 'name': 'rx',\n",
" 'split': None,\n",
" 'mpo': False,\n",
" 'parameters': {'theta': <tf.Tensor: shape=(), dtype=complex64, numpy=(1+0j)>},\n",
" 'gate': Gate(\n",
" name: '__unnamed_node__',\n",
" tensor:\n",
" <tf.Tensor: shape=(2, 2), dtype=complex64, numpy=\n",
" array([[0.87758255+0.j , 0. -0.47942555j],\n",
" [0. -0.47942555j, 0.87758255+0.j ]], dtype=complex64)>,\n",
" edges: [\n",
" Edge('cnot'[3] -> '__unnamed_node__'[0] ),\n",
" Edge('__unnamed_node__'[1] -> 'qb-2'[0] )\n",
" ])},\n",
" {'gatef': rx,\n",
" 'index': (2,),\n",
" 'name': 'rx',\n",
" 'split': None,\n",
" 'mpo': False,\n",
" 'parameters': {'theta': <tf.Tensor: shape=(), dtype=complex64, numpy=(1+0j)>},\n",
" 'gate': Gate(\n",
" name: '__unnamed_node__',\n",
" tensor:\n",
" <tf.Tensor: shape=(2, 2), dtype=complex64, numpy=\n",
" array([[0.87758255+0.j , 0. -0.47942555j],\n",
" [0. -0.47942555j, 0.87758255+0.j ]], dtype=complex64)>,\n",
" edges: [\n",
" Edge(Dangling Edge)[0],\n",
" Edge('__unnamed_node__'[1] -> 'qb-3'[0] )\n",
" ])},\n",
" {'gatef': cnot,\n",
" 'gate': Gate(\n",
" name: 'cnot',\n",
" tensor:\n",
" <tf.Tensor: shape=(2, 2, 2, 2), dtype=complex64, numpy=\n",
" array([[[[1.+0.j, 0.+0.j],\n",
" [0.+0.j, 0.+0.j]],\n",
" \n",
" [[0.+0.j, 1.+0.j],\n",
" [0.+0.j, 0.+0.j]]],\n",
" \n",
" \n",
" [[[0.+0.j, 0.+0.j],\n",
" [0.+0.j, 1.+0.j]],\n",
" \n",
" [[0.+0.j, 0.+0.j],\n",
" [1.+0.j, 0.+0.j]]]], dtype=complex64)>,\n",
" edges: [\n",
" Edge(Dangling Edge)[0],\n",
" Edge(Dangling Edge)[1],\n",
" Edge('cnot'[2] -> '__unnamed_node__'[0] ),\n",
" Edge('cnot'[3] -> '__unnamed_node__'[0] )\n",
" ]),\n",
" 'index': (0, 1),\n",
" 'name': 'cnot',\n",
" 'split': None,\n",
" 'mpo': False}]"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ir = c.to_qir()\n",
"ir"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "71ca41e2",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<tf.Tensor: shape=(2, 2), dtype=complex64, numpy=\n",
"array([[0.87758255+0.j , 0. -0.47942555j],\n",
" [0. -0.47942555j, 0.87758255+0.j ]], dtype=complex64)>"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# 查看量子门对应的矩阵\n",
"ir[0][\"gatef\"](**ir[0][\"parameters\"]).tensor"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "eb13a4ef",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(<tf.Tensor: shape=(), dtype=float32, numpy=0.2919265>, <tf.Tensor: shape=(3,), dtype=complex64, numpy=\n",
"array([-4.5464873e-01+0.j, -4.5464873e-01+0.j, 2.2351742e-08+0.j],\n",
" dtype=complex64)>)\n"
]
}
],
"source": [
"# 让我们组成一个可微分的量子函数\n",
"\n",
"\n",
"def energy(params):\n",
" c = get_circuit(n, params)\n",
" return K.real(c.expectation([tc.gates.z(), [1]]))\n",
"\n",
"\n",
"energy_vag = K.value_and_grad(energy)\n",
"\n",
"print(energy_vag(params))\n",
"\n",
"# 一旦我们有了梯度，我们就可以运行基于梯度的下降的变分优化"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "1a82a3a1",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(<tf.Tensor: shape=(), dtype=float32, numpy=0.2919265>, <tf.Tensor: shape=(3,), dtype=complex64, numpy=\n",
"array([-4.5464873e-01+0.j, -4.5464873e-01+0.j, 2.2351742e-08+0.j],\n",
" dtype=complex64)>)\n"
]
}
],
"source": [
"# 并且使其可即时编译以加速\n",
"\n",
"energy_vag_jit = K.jit(K.value_and_grad(energy))\n",
"\n",
"print(energy_vag_jit(params))\n",
"# 第一次运行可即时编译的函数会很慢，但是后面的测量会超级快"
]
},
{
"cell_type": "markdown",
"id": "36c710ef",
"metadata": {},
"source": [
"## 电路的高级用法"
]
},
{
"cell_type": "markdown",
"id": "d4e55e05",
"metadata": {},
"source": [
"### 输入状态\n",
"\n",
"我们可以从默认的 |0^n> 替换输入状态"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "49865f13",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<tf.Tensor: shape=(8,), dtype=complex64, numpy=\n",
"array([0.49999997+0.j, 0.49999997+0.j, 0.49999997+0.j, 0.49999997+0.j,\n",
" 0. +0.j, 0. +0.j, 0. +0.j, 0. +0.j],\n",
" dtype=complex64)>"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"input_state = K.ones([2**n])\n",
"input_state /= K.norm(input_state)\n",
"\n",
"c = tc.Circuit(n, inputs=input_state)\n",
"c.H(0)\n",
"c.state()"
]
},
{
"cell_type": "markdown",
"id": "47f2a348",
"metadata": {},
"source": [
"### 蒙特卡罗方法噪声模拟\n",
"\n",
"``tc.Circuit`` 支持使用蒙特卡罗方法进行噪声模拟，并且它也是可即时编译的！ 此外，``tc.DMCircuit`` 支持使用全密度矩阵方法进行噪声模拟。"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "e17b0b8b",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"tf.Tensor(0j, shape=(), dtype=complex64)\n"
]
}
],
"source": [
"c = tc.Circuit(n)\n",
"for i in range(n):\n",
" c.H(i)\n",
"for i in range(n - 1):\n",
" c.cnot(i, i + 1)\n",
" c.depolarizing(i, px=0.1, py=0.1, pz=0.1)\n",
" c.apply_general_kraus(tc.channels.phasedampingchannel(gamma=0.2), i + 1)\n",
"print(c.expectation([tc.gates.y(), [1]]))"
]
},
{
"cell_type": "markdown",
"id": "ae498792",
"metadata": {},
"source": [
"### 应用任意幺正门\n",
"\n",
"只需直接使用 ``any`` API 通过提供相应的幺正矩阵"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "1fed32f3",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<tf.Tensor: shape=(8,), dtype=complex64, numpy=\n",
"array([0.25+0.j, 0. +0.j, 0.25+0.j, 0. +0.j, 0.25+0.j, 0. +0.j,\n",
" 0.25+0.j, 0. +0.j], dtype=complex64)>"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"c = tc.Circuit(n)\n",
"c.any(0, 1, unitary=K.ones([4, 4]) / K.norm(K.ones([4, 4])))\n",
"c.state()"
]
},
{
"cell_type": "markdown",
"id": "1d64546c",
"metadata": {},
"source": [
"### 指数门\n",
"\n",
"如果我们想将门模拟为 $e^{i\\theta G}$ ，其中 $G^2=1$ 是一个矩阵，我们有一个快速有效的门实现，例如\n",
"`exp1`"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "32f50d3a",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<tf.Tensor: shape=(8,), dtype=complex64, numpy=\n",
"array([-0.14713009-3.2148516e-01j, 0.35355335+1.4901161e-08j,\n",
" -0.14713009+3.2148516e-01j, 0.35355335-1.4901161e-08j,\n",
" 0.35355335-1.4901161e-08j, -0.14713009+3.2148516e-01j,\n",
" 0.35355335+1.4901161e-08j, -0.14713009-3.2148516e-01j],\n",
" dtype=complex64)>"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"c = tc.Circuit(n)\n",
"for i in range(n):\n",
" c.H(i)\n",
"for i in range(n - 1):\n",
" c.exp1(i, i + 1, theta=K.ones([]), unitary=tc.gates._zz_matrix)\n",
"c.state()"
]
},
{
"cell_type": "markdown",
"id": "934c3885",
"metadata": {},
"source": [
"在上面的例子中 $G=Z\\otimes Z$"
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "409ed76b",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[[ 1. 0. 0. 0.]\n",
" [ 0. -1. 0. -0.]\n",
" [ 0. 0. -1. -0.]\n",
" [ 0. -0. -0. 1.]]\n"
]
}
],
"source": [
"print(tc.gates._zz_matrix)"
]
},
{
"cell_type": "markdown",
"id": "ce35316b",
"metadata": {},
"source": [
"下面列出了门模块中的常用矩阵"
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "f8c647b0",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"_cnot_matrix :\n",
" [[1. 0. 0. 0.]\n",
" [0. 1. 0. 0.]\n",
" [0. 0. 0. 1.]\n",
" [0. 0. 1. 0.]]\n",
"_cy_matrix :\n",
" [[ 1.+0.j 0.+0.j 0.+0.j 0.+0.j]\n",
" [ 0.+0.j 1.+0.j 0.+0.j 0.+0.j]\n",
" [ 0.+0.j 0.+0.j 0.+0.j -0.-1.j]\n",
" [ 0.+0.j 0.+0.j 0.+1.j 0.+0.j]]\n",
"_cz_matrix :\n",
" [[ 1. 0. 0. 0.]\n",
" [ 0. 1. 0. 0.]\n",
" [ 0. 0. 1. 0.]\n",
" [ 0. 0. 0. -1.]]\n",
"_fredkin_matrix :\n",
" [[1. 0. 0. 0. 0. 0. 0. 0.]\n",
" [0. 1. 0. 0. 0. 0. 0. 0.]\n",
" [0. 0. 1. 0. 0. 0. 0. 0.]\n",
" [0. 0. 0. 1. 0. 0. 0. 0.]\n",
" [0. 0. 0. 0. 1. 0. 0. 0.]\n",
" [0. 0. 0. 0. 0. 0. 1. 0.]\n",
" [0. 0. 0. 0. 0. 1. 0. 0.]\n",
" [0. 0. 0. 0. 0. 0. 0. 1.]]\n",
"_h_matrix :\n",
" [[ 0.70710678 0.70710678]\n",
" [ 0.70710678 -0.70710678]]\n",
"_i_matrix :\n",
" [[1. 0.]\n",
" [0. 1.]]\n",
"_ii_matrix :\n",
" [[1. 0. 0. 0.]\n",
" [0. 1. 0. 0.]\n",
" [0. 0. 1. 0.]\n",
" [0. 0. 0. 1.]]\n",
"_s_matrix :\n",
" [[1.+0.j 0.+0.j]\n",
" [0.+0.j 0.+1.j]]\n",
"_swap_matrix :\n",
" [[1. 0. 0. 0.]\n",
" [0. 0. 1. 0.]\n",
" [0. 1. 0. 0.]\n",
" [0. 0. 0. 1.]]\n",
"_t_matrix :\n",
" [[1. +0.j 0. +0.j ]\n",
" [0. +0.j 0.70710678+0.70710678j]]\n",
"_toffoli_matrix :\n",
" [[1. 0. 0. 0. 0. 0. 0. 0.]\n",
" [0. 1. 0. 0. 0. 0. 0. 0.]\n",
" [0. 0. 1. 0. 0. 0. 0. 0.]\n",
" [0. 0. 0. 1. 0. 0. 0. 0.]\n",
" [0. 0. 0. 0. 1. 0. 0. 0.]\n",
" [0. 0. 0. 0. 0. 1. 0. 0.]\n",
" [0. 0. 0. 0. 0. 0. 0. 1.]\n",
" [0. 0. 0. 0. 0. 0. 1. 0.]]\n",
"_wroot_matrix :\n",
" [[ 0.70710678+0.j -0.5 -0.5j]\n",
" [ 0.5 -0.5j 0.70710678+0.j ]]\n",
"_x_matrix :\n",
" [[0. 1.]\n",
" [1. 0.]]\n",
"_xx_matrix :\n",
" [[0. 0. 0. 1.]\n",
" [0. 0. 1. 0.]\n",
" [0. 1. 0. 0.]\n",
" [1. 0. 0. 0.]]\n",
"_y_matrix :\n",
" [[ 0.+0.j -0.-1.j]\n",
" [ 0.+1.j 0.+0.j]]\n",
"_yy_matrix :\n",
" [[ 0.+0.j 0.-0.j 0.-0.j -1.+0.j]\n",
" [ 0.+0.j 0.+0.j 1.-0.j 0.-0.j]\n",
" [ 0.+0.j 1.-0.j 0.+0.j 0.-0.j]\n",
" [-1.+0.j 0.+0.j 0.+0.j 0.+0.j]]\n",
"_z_matrix :\n",
" [[ 1. 0.]\n",
" [ 0. -1.]]\n",
"_zz_matrix :\n",
" [[ 1. 0. 0. 0.]\n",
" [ 0. -1. 0. -0.]\n",
" [ 0. 0. -1. -0.]\n",
" [ 0. -0. -0. 1.]]\n"
]
}
],
"source": [
"for name in dir(tc.gates):\n",
" if name.endswith(\"_matrix\"):\n",
" print(name, \":\\n\", getattr(tc.gates, name))"
]
},
{
"cell_type": "markdown",
"id": "7851cdcd",
"metadata": {},
"source": [
"### 非幺正门\n",
"\n",
"``tc.Circuit``由于其张量网络引擎性质而自动支持非幺正电路仿真"
]
},
{
"cell_type": "code",
"execution_count": 26,
"id": "e1805a84",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<tf.Tensor: shape=(8,), dtype=complex64, numpy=\n",
"array([0.83373 -0.9888977j, 0. +0.j ,\n",
" 0.63496387-1.2984576j, 0. +0.j ,\n",
" 0. +0.j , 0. +0.j ,\n",
" 0. +0.j , 0. +0.j ], dtype=complex64)>"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"c = tc.Circuit(n)\n",
"c.exp1(1, unitary=tc.gates._x_matrix, theta=K.ones([]) + 1.0j * K.ones([]))\n",
"c.state()"
]
},
{
"cell_type": "markdown",
"id": "28222612",
"metadata": {},
"source": [
"请注意，在这种情况下，最终量子态不再归一化。"
]
},
{
"cell_type": "code",
"execution_count": 27,
"id": "1581cf4f",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Not equal to tolerance rtol=1e-07, atol=0\n",
"\n",
"Mismatched elements: 1 / 1 (100%)\n",
"Max absolute difference: 0.93963802\n",
"Max relative difference: 0.93963802\n",
" x: array(1.939638+0.j, dtype=complex64)\n",
" y: array(1.)\n"
]
}
],
"source": [
"try:\n",
" np.testing.assert_allclose(K.norm(c.state()), 1.0)\n",
"except AssertionError as e:\n",
" print(e)"
]
}
],
"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": "3.8.0"
}
},
"nbformat": 4,
"nbformat_minor": 5
}