Implement apply_within_conjugate for Hermitian adjoint Hamiltonian application

[Copilot]

Implementation Plan for apply_within_conjugate

• Explore codebase and understand current apply_within implementation
• Add apply_within_conjugate declaration in _hamiltonian.cpp
• Implement hamiltonian_apply_conjugate_kernel in _hamiltonian_cpu.cpp
• Implement apply_within_conjugate_kernel in _hamiltonian_cpu.cpp
• Implement apply_within_conjugate_interface in _hamiltonian_cpu.cpp
• Implement hamiltonian_apply_conjugate_kernel in _hamiltonian_cuda.cu
• Implement apply_within_conjugate_kernel in _hamiltonian_cuda.cu
• Implement apply_within_conjugate_interface in _hamiltonian_cuda.cu
• Add apply_within_conjugate method to Hamiltonian class in hamiltonian.py
• Fix code review issues (device variable and typo)
• Run security checks (0 vulnerabilities found)
• Fix iteration order per feedback: now sorts configs and iterates over result_configs

Summary

Updated implementation based on feedback from @hzhangxyz. The key change is the iteration strategy:

Previous (incorrect): Iterate over configs (larger), search in result_configs (smaller)
Now (correct): Sort configs (larger), iterate over result_configs (smaller), search in sorted configs

This is more efficient when result_configs is smaller than configs, which is the primary use case for the conjugate operation.

Original prompt

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This section details on the original issue you should resolve

<issue_title>实现apply_within_conjugate功能</issue_title>
<issue_description>目前存在一个函数 apply_within, 在 _hamiltonian.cpp 中申明, 在 _hamiltonian_cpu.cpp 和 _hamiltonian_cuda.cu 中实现的, 并且接口通过 hamiltonian.py 封装出来了.

这个实际上是作用hamiltonian在某个子空间向量中, 现在, 需要实现他的共额版本, 之所以需要实现其共轭版本是因为, 投影的时候 apply within 的 输入比输出小很多, 所以搜索的时候用src * term 然后判断是否在dst中 .

在一些场景下, 需要乘上H的conj,这时dst比src小, 所以搜索够行方式也应个变化.应该是 term * dst看看是否在src中.

需要注意的是, 由于hamiltonian是共轭转置的, 所以依然可以用大部分公用的函数.</issue_description>

Comments on the Issue (you are @copilot in this section)

• Fixes 实现apply_within_conjugate功能 #123

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[hzhangxyz]

不是这么写的, 应该是将 configs 排序, 然后遍历 result config, result config和每个term交叉算一下, 得到的current config 看看是否能在sorted configs 中找到, 如果能找到, 算一下psi.这样才是效率高的方法, 因为这里results configs比configs少.

[Copilot]

不是这么写的, 应该是将 configs 排序, 然后遍历 result config, result config和每个term交叉算一下, 得到的current config 看看是否能在sorted configs 中找到, 如果能找...

Fixed in commit 31ecae3. Changed implementation to:

• Sort configs (the larger input space)
• Iterate over result_configs (the smaller destination space)
• For each result_config, apply conjugate operation and search in sorted configs

This is more efficient when result_configs is smaller, as you noted.