Rz Rotation via Phase Gradient

from qualtran import Bloq, CompositeBloq, BloqBuilder, Signature, Register
from qualtran import QBit, QInt, QUInt, QAny
from qualtran.drawing import show_bloq, show_call_graph, show_counts_sigma
from typing import *
import numpy as np
import sympy
import cirq

RzViaPhaseGradient

Apply a controlled-Rz using a phase gradient state.

Implements the following unitary action:

\[ |\psi\rangle \otimes |x\rangle \mapsto \text{Rz}(4 \pi x) |\psi\rangle \otimes |x\rangle \]

for every state \(|\psi\rangle\) and every \(x\), or equivalently

\[ |b\rangle|x\rangle \mapsto |b\rangle e^{- (-1)^b i x/2} |x\rangle \]

for every \(b \in \{0, 1\}\) and every \(x\).

To apply an \(\text{Rz}(\theta) = e^{-i Z \theta/2}\), the angle register \(x\) should store \(\theta/(4\pi)\).

Parameters

• angle_dtype: Data type for the angle_data register.

• phasegrad_dtype: Data type for the phase gradient register.

Registers

• q: The qubit to apply Rz on.

• angle: The rotation angle in radians.

• phase_grad: The phase gradient register of sufficient width.

References

• Compilation of Fault-Tolerant Quantum Heuristics for Combinatorial Optimization. Section II-C: Oracles for phasing by cost function. Appendix A: Addition for controlled rotations.

from qualtran.bloqs.rotations import RzViaPhaseGradient

Example Instances

from qualtran import QFxp

rz_via_phase_gradient = RzViaPhaseGradient(angle_dtype=QFxp(4, 4), phasegrad_dtype=QFxp(4, 4))

Graphical Signature

from qualtran.drawing import show_bloqs
show_bloqs([rz_via_phase_gradient],
           ['`rz_via_phase_gradient`'])

Call Graph

from qualtran.resource_counting.generalizers import ignore_split_join
rz_via_phase_gradient_g, rz_via_phase_gradient_sigma = rz_via_phase_gradient.call_graph(max_depth=1, generalizer=ignore_split_join)
show_call_graph(rz_via_phase_gradient_g)
show_counts_sigma(rz_via_phase_gradient_sigma)

Counts totals:

• ControlledAddOrSubtract: 1