qrisp.app_sb_phase_polynomial#

app_sb_phase_polynomial(*args, permeability='args', is_qfree=True, verify=False, **kwargs)#

Applies a phase function specified by a semi-Boolean polynomial acting on a list of QuantumVariables. That is, this method implements the transformation

$$|y_1⟩\cdots |y_n⟩\to e^{itP(y_1,\dots ,y_n)}|y_1⟩\cdots |y_n⟩$$

where $|y_1⟩,\dots ,|y_n⟩$ are QuantumVariables and $P(y_1,\dots ,y_n)=P(y_{1,1},\dots ,y_{1,m_1},\dots ,y_{n,1}\dots ,y_{n,m_n})$ is a semi-Boolean polynomial in variables $y_{1,1},\dots ,y_{1,m_1},\dots ,y_{n,1}\dots ,y_{n,m_n}$. Here, $m_i$ is the size of the $i$ th variable.

Parameters:

qv_listlist[QuantumVariable] or QuantumArray

The list of QuantumVariables to evaluate the semi-Boolean polynomial on.

polySymPy expression

The semi-Boolean polynomial to evaluate.

symbol_listlist, optional

An ordered list of SymPy symbols associated to the qubits of the QuantumVariables of qv_list. For each QuantumVariable in qv_list a number of symbols according to its size is required. By default, the symbols of the polynomial will be ordered alphabetically and then matched to the order in qv_list.

tFloat or SymPy expression, optional

The argument t in the expression $\exp (itP)$. The default is 1.

Raises:

Exception

Provided QuantumVariable list does not include the appropriate amount of elements to evaluate the given polynomial.

Examples

We apply the phase function specified by the polynomial $P(x,y,z)=\pi xyz$ on a QuantumVariable:

import sympy as sp
import numpy as np
from qrisp import QuantumVariable, app_sb_phase_polynomial

x, y, z = sp.symbols('x y z')
P = np.pi*x*y*z

qv = QuantumVariable(3)
qv.init_state({'000': 0.5, '111': 0.5})

app_sb_phase_polynomial([qv], P)

We print the statevector:

>>> print(qv.qs.statevector())
sqrt(2)*(|000> - |111>)/2