Polynomials over 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

GF2PolyAddK

In place addition of a constant polynomial defined over GF(\(2^m\)).

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

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

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(\(2^m\)).

• g_x: An instance of galois.Poly that specifies that constant polynomial g(x) defined over GF(\(2^m\)) that should be added to the input register f(x).

Registers

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

from qualtran.bloqs.gf_poly_arithmetic import GF2PolyAddK

Example Instances

from galois import Poly

from qualtran import QGF, QGFPoly

qgf_poly = QGFPoly(4, QGF(2, 3))
g_x = Poly(qgf_poly.qgf.gf_type([1, 2, 3, 4, 5]))
gf2_poly_4_8_add_k = GF2PolyAddK(qgf_poly, g_x)

import sympy
from galois import Poly

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_k_symbolic = GF2PolyAddK(qgf_poly, Poly([0, 0, 0, 0]))

Graphical Signature

from qualtran.drawing import show_bloqs
show_bloqs([gf2_poly_4_8_add_k, gf2_poly_add_k_symbolic],
           ['`gf2_poly_4_8_add_k`', '`gf2_poly_add_k_symbolic`'])

Call Graph

from qualtran.resource_counting.generalizers import ignore_split_join
gf2_poly_4_8_add_k_g, gf2_poly_4_8_add_k_sigma = gf2_poly_4_8_add_k.call_graph(max_depth=1, generalizer=ignore_split_join)
show_call_graph(gf2_poly_4_8_add_k_g)
show_counts_sigma(gf2_poly_4_8_add_k_sigma)

Counts totals:

• GF2AddK: 1

• GF2AddK: 1

• GF2AddK: 1

• GF2AddK: 1

• GF2AddK: 1

• GFPolyJoin: 1

• GFPolySplit: 1