GF(\(2^m\)) Add Constant

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

GF2AddK

In place addition of a constant \(k\) for elements in GF(\(2^m\)).

The bloq implements in place addition of a classical constant \(k\) and a quantum register \(|x\rangle\) storing elements from GF(\(2^m\)). Addition in GF(\(2^m\)) simply reduces to a component wise XOR, which can be implemented via X gates.

\[ |x\rangle \rightarrow |x + k\rangle \]

Parameters

• bitsize: The degree \(m\) of the galois field GF(\(2^m\)). Also corresponds to the number of qubits in the input register x.

• k: Integer representation of constant over GF(\(2^m\)) that should be added to the input register x.

Registers

• x: Input THRU register of size \(m\) that stores elements from \(GF(2^m)\).

from qualtran.bloqs.gf_arithmetic import GF2AddK

Example Instances

gf16_add_k = GF2AddK(4, 1)

import sympy

m, k = sympy.symbols('m, k', positive=True, integers=True)
gf2_add_k_symbolic = GF2AddK(m, k)

Graphical Signature

from qualtran.drawing import show_bloqs
show_bloqs([gf16_add_k, gf2_add_k_symbolic],
           ['`gf16_add_k`', '`gf2_add_k_symbolic`'])

Call Graph

from qualtran.resource_counting.generalizers import ignore_split_join
gf16_add_k_g, gf16_add_k_sigma = gf16_add_k.call_graph(max_depth=1, generalizer=ignore_split_join)
show_call_graph(gf16_add_k_g)
show_counts_sigma(gf16_add_k_sigma)

Counts totals:

• XGate: 1