qrisp.QuantumVariable.app_phase_function#

QuantumVariable.app_phase_function(phi)[source]#

Applies a previously specified phase function to each computational basis state of the QuantumVariable using Gray-Synthesis.

For a given phase function $\varphi (x)$ and a QuantumVariable in state $|\psi ⟩=\sum _{x\in \text{Labels}}{a}_x|x⟩$ this method acts as:

$$U_{\varphi }\sum _{x\in \text{Labels}}{a}_x|x⟩=\sum _{x\in \text{Labels}}\text{exp}(i\varphi (x))a_x|x⟩$$

Parameters:

phiPython function

A Python function which turns the labels of the QuantumVariable into floats.

Examples

We create a QuantumFloat and encode the k-th basis state of the Fourier basis. Finally, we will apply an inverse Fourier transformation to measure k in the computational basis.

>>> import numpy as np
>>> from qrisp import QuantumFloat, h, QFT
>>> n = 5
>>> qf = QuantumFloat(n, signed = False)
>>> h(qf)

After this, qf is in the state

$$|\text{qf}⟩=\frac{1}{\sqrt{2^n}}\sum _{x=0}^{2^n}|x⟩$$

We specify phi

>>> k = 4
>>> def phi(x):
>>>     return 2*np.pi*x*k/2**n

And apply phi as a phase function

>>> qf.app_phase_function(phi)

qf is now in the state

$$|\text{qf}⟩=\frac{1}{\sqrt{2^n}}\sum _{x=0}^{2^n}\text{exp}\left(\frac{2\pi ikx}{2^n}\right)|x⟩$$

Finally we apply the inverse Fourier transformation and measure:

>>> QFT(qf, inv = True)
>>> print(qf)
{4: 1.0}