qit.examples.qft_circuit

qit.examples.qft_circuit(dim=(2, 3, 3, 2))

Quantum Fourier transform circuit demo.

Parameters

dim (Sequence[int]) – dimension vector of the subsystems

Simulate the quadratic quantum circuit for QFT.

NOTE: If dim is not palindromic the resulting circuit also reverses the order of the dimensions in the SWAP cascade.

$$U|x_1,x_2,\dots ,x_n⟩=\frac{1}{\sqrt{d}}\sum _{k_i}|k_n,\dots ,k_2,k_1⟩\exp \left(i2\pi (\sum _{r=1}^n{k}_{r}0.x_r{x}_{r+1}\dots x_n)\right)=\frac{1}{\sqrt{d}}\sum _{k_i}|k_n,\dots ,k_2,k_1⟩\exp (i2\pi 0.x_1{x}_2\dots x_n(\sum _{r=1}^n{d}_1{d}_2\cdots d_{r-1}{k}_r)).$$