算子使用示例¶
本教程展示各类算子的使用方法。
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import pysparq as ps
import numpy as np
算术算子¶
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ps.System.clear()
ps.System.add_register("a", ps.UnsignedInteger, 4)
ps.System.add_register("b", ps.UnsignedInteger, 4)
ps.System.add_register("result", ps.UnsignedInteger, 4)
state = ps.SparseState()
ps.Init_Unsafe("a", 7)(state)
ps.Init_Unsafe("b", 10)(state)
加法¶
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# 外置加法: result ^= a + b
ps.Add_UInt_UInt("a", "b", "result")(state)
print("Add_UInt_UInt:")
ps.pprint(state)
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# 内置加法: b += a
ps.System.clear()
ps.System.add_register("a", ps.UnsignedInteger, 4)
ps.System.add_register("b", ps.UnsignedInteger, 4)
state = ps.SparseState()
ps.Init_Unsafe("a", 7)(state)
ps.Init_Unsafe("b", 10)(state)
op = ps.Add_UInt_UInt_InPlace("a", "b")
op(state)
print("Add_UInt_UInt_InPlace:")
ps.pprint(state)
# b = (10 + 7) % 16 = 1
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# 撤销
op.dag(state)
print("dagger 后:")
ps.pprint(state)
乘法¶
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ps.System.clear()
ps.System.add_register("x", ps.UnsignedInteger, 4)
ps.System.add_register("triple", ps.UnsignedInteger, 4)
state = ps.SparseState()
ps.Init_Unsafe("x", 5)(state)
# 乘以奇数常量（保证双射）
ps.Mult_UInt_ConstUInt("x", 3, "triple")(state)
print("Mult_UInt_ConstUInt(x, 3):")
ps.pprint(state)
比较与标志¶
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ps.System.clear()
ps.System.add_register("a", ps.UnsignedInteger, 4)
ps.System.add_register("b", ps.UnsignedInteger, 4)
ps.System.add_register("less", ps.Boolean, 1)
ps.System.add_register("equal", ps.Boolean, 1)
state = ps.SparseState()
ps.Init_Unsafe("a", 3)(state)
ps.Init_Unsafe("b", 5)(state)
ps.Compare_UInt_UInt("a", "b", "less", "equal")(state)
print("Compare_UInt_UInt:")
ps.pprint(state)
量子门¶
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ps.System.clear()
ps.System.add_register("q", ps.Boolean, 1)
state = ps.SparseState()
print("初始:")
ps.pprint(state)
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# X 门（NOT）
ps.Xgate_Bool("q", 0)(state)
print("X 门后:")
ps.pprint(state)
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# Hadamard
ps.Hadamard_Bool("q")(state)
print("Hadamard 后:")
ps.pprint(state)
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# 相位门
ps.Phase_Bool("q", 0, np.pi/4)(state)
print("Phase(π/4) 后:")
ps.pprint(state)
QFT¶
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ps.System.clear()
ps.System.add_register("q", ps.UnsignedInteger, 3)
state = ps.SparseState()
ps.Init_Unsafe("q", 1)(state)
print("初始:")
ps.pprint(state)
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# QFT
ps.QFT("q")(state)
print("QFT 后:")
ps.pprint(state)
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# inverseQFT
ps.inverseQFT("q")(state)
print("inverseQFT 后:")
ps.pprint(state)
条件操作¶
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ps.System.clear()
ps.System.add_register("x", ps.UnsignedInteger, 2)
ps.System.add_register("result", ps.UnsignedInteger, 2)
ps.System.add_register("ctrl", ps.Boolean, 1)
state = ps.SparseState()
ps.Init_Unsafe("x", 3)(state)
ps.Init_Unsafe("ctrl", 1)(state)
# 当 ctrl = 1 时执行加法
ps.Add_UInt_ConstUInt("x", 5, "result").conditioned_by_nonzeros("ctrl")(state)
print("条件加法 (ctrl=1):")
ps.pprint(state)
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# ctrl = 0 时条件不触发
ps.System.clear()
ps.System.add_register("x", ps.UnsignedInteger, 2)
ps.System.add_register("result", ps.UnsignedInteger, 2)
ps.System.add_register("ctrl", ps.Boolean, 1)
state = ps.SparseState()
ps.Init_Unsafe("x", 3)(state)
ps.Init_Unsafe("ctrl", 0)(state) # ctrl = 0
ps.Add_UInt_ConstUInt("x", 5, "result").conditioned_by_nonzeros("ctrl")(state)
print("条件加法 (ctrl=0):")
ps.pprint(state)
# result 保持 0
Block Encoding：三对角矩阵¶
Block Encoding 将经典矩阵编码为酉矩阵，是量子线性代数算法的核心。下面的例子使用 pysparq.algorithms.block_encoding 中的 BlockEncodingTridiagonal 对三对角矩阵 :math:A = \alpha I + \beta T 进行块编码。
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from pysparq.algorithms.block_encoding import (
get_tridiagonal_matrix,
BlockEncodingTridiagonal,
)
alpha, beta, dim = 0.5, 0.3, 4
A = get_tridiagonal_matrix(alpha, beta, dim)
print(f"三对角矩阵 A:\n{A}")
# 构建 Block Encoding 电路
ps.System.clear()
ps.System.add_register("main_reg", ps.UnsignedInteger, 2) # dim = 2^2
ps.System.add_register("anc_UA", ps.UnsignedInteger, 4)
state = ps.SparseState()
ps.Init_Unsafe("main_reg", 0)(state)
ps.Init_Unsafe("anc_UA", 0)(state)
block_enc = BlockEncodingTridiagonal("main_reg", "anc_UA", alpha, beta)
block_enc(state)
print(f"Block Encoding 应用成功，基态数: {state.size()}")
block_enc.dag(state) # 释放辅助寄存器
print(f"逆 Block Encoding 后，基态数: {state.size()}")
Python 侧自定义算子¶
当需要组合多个已有算子时，在 Python 侧直接封装：
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class MyIncrement:
"""对寄存器值加 1（外置结果寄存器）。"""
def __init__(self, src: str, dst: str):
self.src = src
self.dst = dst
def __call__(self, state: ps.SparseState):
ps.Add_UInt_UInt(self.src, self.dst)(state)
def dag(self, state: ps.SparseState):
ps.Add_UInt_UInt(self.src, self.dst)(state) # XOR 语义，加两次恢复
ps.System.clear()
ps.System.add_register("counter", ps.UnsignedInteger, 4)
ps.System.add_register("result", ps.UnsignedInteger, 4)
state = ps.SparseState()
ps.Init_Unsafe("counter", 5)(state)
ps.Init_Unsafe("result", 0)(state)
my_inc = MyIncrement("counter", "result")
my_inc(state) # result = 0 + 5 = 5
print(f"加法后 result = {state.basis_states[0].get(ps.System.get_id('result')).value}")
my_inc.dag(state) # result = 5 + 5 = 0，恢复
print(f"dagger 后 result = {state.basis_states[0].get(ps.System.get_id('result')).value}")
如需新 primitives（超出已有算子表达能力），使用 compile_operator 将 C++ 代码编译为动态链接库：
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from pysparq.dynamic_operator import compile_operator
cpp_code = '''
class FlipOp : public SelfAdjointOperator {
size_t reg_id;
public:
FlipOp(size_t r) : reg_id(r) {}
void operator()(std::vector<System>& state) const override {
for (auto& s : state) {
s.get(reg_id).value ^= 1;
}
}
};
'''
FlipOp = compile_operator(
name="FlipOp",
cpp_code=cpp_code,
base_class="SelfAdjointOperator",
constructor_args=[("size_t", "reg_id")],
)
ps.System.clear()
ps.System.add_register("q", ps.UnsignedInteger, 4)
state = ps.SparseState()
ps.Init_Unsafe("q", 1)(state)
print("初始:", state.basis_states[0].get(ps.System.get_id("q")).value)
flip = FlipOp(reg_id=0)
flip(state) # 第 0 比特翻转
print("翻转后:", state.basis_states[0].get(ps.System.get_id("q")).value)
总结¶
本教程展示了：
算术算子：Add, Mult, Compare
量子门：X, Hadamard, Phase
QFT / inverseQFT
条件操作
Block Encoding：用
BlockEncodingTridiagonal对三对角矩阵进行块编码自定义算子：Python 侧组合已有算子，或通过
compile_operator编译 C++ 代码