Polynomials over GF(\(2^m\)) - Addition

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

GF2PolyAdd

In place quantum-quantum addition of two polynomials defined over GF(\(2^m\)).

The bloq implements in place addition of quantum registers \(|f(x)\rangle\) and \(|g(x)\rangle\) storing coefficients of two degree-n polynomials defined over GF(\(2^m\)). Addition in GF(\(2^m\)) simply reduces to a component wise XOR, which can be implemented via CNOT gates.

\[ |f(x)\rangle |g(x)\rangle \rightarrow |f(x)\rangle |f(x) + g(x)\rangle \]

Parameters

• qgf_poly: An instance of QGFPoly type that defines the data type for quantum register \(|f(x)\rangle\) storing coefficients of a degree-n polynomial defined over GF(\(2^m\)).

Registers

• f_x: THRU register that stores coefficients of first polynomial defined over \(GF(2^m)\).

• g_x: THRU register that stores coefficients of second polynomial defined over \(GF(2^m)\).

from qualtran.bloqs.gf_poly_arithmetic import GF2PolyAdd

Example Instances

from qualtran import QGF, QGFPoly

qgf_poly = QGFPoly(4, QGF(2, 3))
gf2_poly_4_8_add = GF2PolyAdd(qgf_poly)

import sympy

from qualtran import QGF, QGFPoly

n, m = sympy.symbols('n, m', positive=True, integers=True)
qgf_poly = QGFPoly(n, QGF(2, m))
gf2_poly_add_symbolic = GF2PolyAdd(qgf_poly)

Graphical Signature

from qualtran.drawing import show_bloqs
show_bloqs([gf2_poly_4_8_add, gf2_poly_add_symbolic],
           ['`gf2_poly_4_8_add`', '`gf2_poly_add_symbolic`'])

Call Graph

from qualtran.resource_counting.generalizers import ignore_split_join
gf2_poly_4_8_add_g, gf2_poly_4_8_add_sigma = gf2_poly_4_8_add.call_graph(max_depth=1, generalizer=ignore_split_join)
show_call_graph(gf2_poly_4_8_add_g)
show_counts_sigma(gf2_poly_4_8_add_sigma)

Counts totals:

• GF2Addition: 5