【代码贡献】实现 Long 精确量子搜索算法，理论上达到零失败概率

[QuantumJourney2026]

背景

标准Grover搜索算法的成功率与目标解在搜索空间中的占比相关。标准Grover算法仅在特定目标解比例下才能达到100%成功率；当目标解比例为1/2时，算法成功率下降至最低，仅为50%。然而，在一些特殊的搜索问题场景下，搜索算法理论上达到100%的成功率至关重要。精确量子搜索算法具有重要的应用价值。

工作内容

本PR实现了清华大学龙桂鲁教授于2001年所提出的精确量子搜索算法（Grover algorithm with zero theoretical failure rate, Phys. Rev. A 64, 022307）。基于论文理论，本PR实现了算法最优迭代次数与相位的自动计算，通过将Oracle和Diffusion算子中的π相位反转替换为任意相位旋转，克服标准Grover算法成功率随目标解比例的升高反而下降的缺陷，在仿真程序中实现了搜索成功率严格等于100%。

本次提交新增两个文件：

1. pyqpanda_alg/Grover/Long_exact_grover.py：Long精确Grover算法核心实现，包含算法迭代次数、算法相位的理论计算公式等；
2. example/QAlgBase/exact_grover_example.py：仿真示例，对比标准Grover与Long精确Grover的概率分布。

同时修订一个文件：

1. pyqpanda_alg/Grover/__init__.py：导出LongExactGrover类，保持模块接口风格与原有Grover统一。

核心实现要点：

1. 根据搜索空间中元素的总个数以及其中目标解的数目，自动计算最优迭代次数；
2. 同步求解对应的算法相位φ，并在Oracle算子和Diffusion算子中统一使用该相位，而不是标准的π相位，使算法成功率达到100%；
3. 复用仓库原有Grover线路框架，保持代码风格、调用接口对齐；
4. 支持多目标解场景。

仿真验证结果

仿真环境：CPUQVM理想模拟器，搜索空间规模 N=16

Case1：N=16，目标解数量 M=1，标记态 1010

• 标准Grover：迭代3次，目标态概率 P=0.9613
• Long精确Grover：迭代3次，目标态概率 P=1.0000

相同迭代次数，Long精确Grover将概率提升至严格100%

Case2：N=16，目标解数量 M=2，标记态 1010、0110

• 标准Grover：迭代2次，目标态总概率 P=0.9453
• Long精确Grover：迭代2次，目标态总概率 P=1.0000

迭代次数与oracle调用次数保持不变，搜索成功率达到理论100%。

仿真结论： 在相同Oracle调用次数条件下，Long精确量子搜索算法可以把目标态概率提升至100%；而标准Grover算法则存在一定失败概率。

自测情况

本地运行示例脚本 exact_grover_example.py，仿真输出符合理论预期。

参考文献：G. L. Long, Grover algorithm with zero theoretical failure rate, Phys. Rev. A 64, 022307 (2001).

关联Issue：#13

English Description

Background

The success probability of the standard Grover search algorithm depends on the ratio of target solutions in the search space. It reaches 100% only at specific ratios; for example, when the ratio is 1/2, the success rate drops to its minimum of 50%. However, in certain critical search scenarios, a theoretical success rate of exactly 100% is essential, which motivates exact quantum search algorithms.

What This PR Does

This PR implements the exact quantum search algorithm proposed by Prof. Gui-Lu Long (Tsinghua University) in 2001 (Grover algorithm with zero theoretical failure rate, Phys. Rev. A 64, 022307). Based on the theory of arbitrary-phase amplitude amplification, this implementation:

• Automatically computes the number of iterations and the matched phase from the search space size and the number of solutions;
• Replaces the standard π phase flip with the arbitrary phase rotation (Z gate → U1(φ) gate) in both the Oracle and the Diffusion operators, which is the key to achieving a theoretical success rate of exactly 100%;
• Reuses the existing Grover circuit framework of this repository (via composition with the original Grover class), keeping the code style and calling interface consistent;
• Supports multiple target solutions (M ≥ 1).

Changes

Two new files:

1. pyqpanda_alg/Grover/Long_exact_grover.py — core implementation of the Long exact Grover algorithm, including the theoretical formulas for the optimal iteration number and phase;
2. example/QAlgBase/exact_grover_example.py — simulation example comparing the full probability distributions of standard Grover and Long exact Grover.
   One modified file:
3. pyqpanda_alg/Grover/__init__.py — exports the LongExactGrover class, keeping the module interface style consistent with the original Grover.

Simulation Results

Environment: CPUQVM ideal simulator, search space size N = 16
Case 1: N = 16, M = 1, marked state 1010

• Standard Grover: 3 iterations, success probability P = 0.9613
• Long exact Grover: 3 iterations, success probability P = 1.0000
• With the same number of iterations, the success probability is improved to exactly 100%.
  Case 2: N = 16, M = 2, marked states 1010, 0110
• Standard Grover: 2 iterations, total success probability P = 0.9453
• Long exact Grover: 2 iterations, total success probability P = 1.0000
• The number of iterations and oracle calls stays unchanged, while the success rate reaches the theoretical 100%.
  Conclusion: under the same number of oracle calls, the Long exact quantum search algorithm raises the success probability to exactly 100%, whereas the standard Grover algorithm always retains a non-zero failure probability.

Self-Testing

The example script exact_grover_example.py was run locally; all simulation outputs match the theoretical predictions (both iteration counts and success probabilities).

Reference

G. L. Long, Grover algorithm with zero theoretical failure rate, Phys. Rev. A 64, 022307 (2001).

Related Issue: #13