paddle_quantum.qchem.fermionic_state

Wave function module.

class paddle_quantum.qchem.fermionic_state.WaveFunction(data, convention='mixed', backend=None, dtype=None, override=False)

Bases: State

clone()

Return a copy of the wavefunction.

Returns:

A new state which is identical to this state.

swap(p, q)

Switching p-th qubit and q-th qubit.

Note

Since qubit represents fermion state, exchanging them will results in a minus sign.

Parameters:

• p (int) – index of the qubit being exchanged.

• q (int) – index of another qubit being exchanged.

to_spin_mixed()

If the wavefunction is in convention “separated”, convert it to a “mixed” convention state.

to_spin_separated()

If the wavefunction is in convention “mixed”, convert it to a “separated” convention state.

classmethod slater_determinant_state(num_qubits, num_elec, mz, backend=None, dtype=None)

Construct a single Slater determinant state whose length is num_qubits . The number of “1” in the Slater determinant state equals num_elec, the difference between number of spin up electrons and the number of spin down electrons is mz . The prepared Slater determinant is in mixed spin orbital mode, which is “updownupdown…”.

Parameters:

• num_qubits (int) – number of qubits used in preparing Slater determinant state.

• num_elec (int) – number of electrons in Slater determinant state.

• mz (int) – $n_{\uparrow }-n_{\downarrow }$ .

Returns:

WaveFunction.

classmethod zero_state(num_qubits, backend=None, dtype=None)

Construct a zero state, $|0000....⟩$ .

num_elec(shots=0)

Calculate the total number of electrons in the wave function.

$$⟨\mathrm{\Psi }|\sum _{i\sigma }{\hat{a}}_{i\sigma }^{†}{\hat{a}}_{i\sigma }|\mathrm{\Psi }⟩.$$

total_SpinZ(shots=0)

Calculate the total spin Z component of the wave function.

$$\begin{array}{r}⟨\mathrm{\Psi }|\sum _i{\hat{S}}_z|\mathrm{\Psi }⟩\\ {\hat{S}}_z=0.5\ast \sum _p({\hat{n}}_{p\alpha }-{\hat{n}}_{p\beta })\\ \alpha \equiv \uparrow ,\beta \equiv \downarrow ,{\hat{n}}_{p\sigma }={\hat{a}}_{p\sigma }^{†}{\hat{a}}_{p\sigma }\end{array}$$

total_Spin2(shots=0)

Calculate the expectation value of ${\hat{S}}^2$ operator on the wave function.

$$\begin{array}{r}⟨\mathrm{\Psi }|{\hat{S}}_{+}{\hat{S}}_{-}+{\hat{S}}_z({\hat{S}}_z-1)|\mathrm{\Psi }⟩\\ {\hat{S}}_{+}=\sum _p{\hat{a}}_{p\alpha }^{†}{\hat{a}}_{p\beta }\\ {\hat{S}}_{-}=\sum _p{\hat{a}}_{p\beta }^{†}{\hat{a}}_{p\alpha }\\ {\hat{S}}_z=0.5\ast \sum _p({\hat{n}}_{p\alpha }-{\hat{n}}_{p\beta })\\ \alpha \equiv \uparrow ,\beta \equiv \downarrow ,{\hat{n}}_{p\sigma }={\hat{a}}_{p\sigma }^{†}{\hat{a}}_{p\sigma }\end{array}$$