费米子算符类
==============

我们用如下的记号标识来表示费米子的两个形态，
湮没: :math:`X`  表示 :math:`a_x` ，
创建: :math:`X +` 表示 :math:`a_x^\dagger` ，
例如: "1 + 3 5 + 1"则代表 :math:`a_1^\dagger \ a_3 \ a_5^\dagger \ a_1`

整理规则如下

**1.** 不同数字

.. math:: "1\quad 2" = -1 * "2\quad 1"
.. math:: "1 + 2 +" = -1 * "2 + 1 +"
.. math:: "1 + 2" = -1 * "2\quad 1 +"

**2.** 相同数字

.. math:: "1\quad 1 +" =  1 + "1 + 1"
.. math:: "1 + 1 +" = 0
.. math:: "1\quad 1" = 0

跟 ``PauliOperator`` 类似，``FermionOperator`` 类也提供了费米子算符之间加、减和乘的基础的运算操作。通过整理功能可以得到一份有序排列的结果。


实例
--------------

.. code-block:: cpp

    #include "Components/Operator/FermionOperator.h"

    int main()
    {
        QPanda::FermionOperator a("0 1+", 2);
        QPanda::FermionOperator b("2+ 3", 3);

        auto plus = a + b;
        auto minus = a - b;
        auto muliply = a * b;

        std::cout << "a + b = " << plus << std::endl << std::endl;
        std::cout << "a - b = " << minus << std::endl << std::endl;
        std::cout << "a * b = " << muliply << std::endl << std::endl;

        std::cout << "normal_ordered(a + b) = " << plus.normal_ordered() << std::endl << std::endl;
        std::cout << "normal_ordered(a - b) = " << minus.normal_ordered() << std::endl << std::endl;
        std::cout << "normal_ordered(a * b) = " << muliply.normal_ordered() << std::endl << std::endl;

        return 0;
    }

.. image:: images/FermionOperatorTest.png