Controlled Add-or-Subtract

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

ControlledAddOrSubtract

Adds or subtracts in-place into the target, based on a control bit.

Applies the transformation

\[\begin{split} |1\rangle |a\rangle |b\rangle \mapsto |1\rangle |a\rangle |b + a\rangle \\ |0\rangle |a\rangle |b\rangle \mapsto |0\rangle |a\rangle |b - a\rangle \end{split}\]

Given two numbers a, b and a control bit ctrl, this bloq computes:

• the sum b + a when ctrl=1,

• the difference b - a when ctrl=0,

and stores the result in the second register (b).

This uses an uncontrolled Add surrounded by controlled BitwiseNots, and only the Add requires T gates, which has half the T-cost of a controlled Add.

Parameters

• a_dtype: dtype of the lhs a

• b_dtype: dtype of the rhs b. If it is not big enough to store the result, the most significant bits are dropped on overflow.

• add_when_ctrl_is_on: If True (default), add when ctrl=1 and subtract when ctrl=0. If False, do the opposite: subtract when ctrl=0 and add when ctrl=1.

Registers

• ctrl: a single control bit

• a: an integer value.

• b: an integer value.

References

• Compilation of Fault-Tolerant Quantum Heuristics for Combinatorial Optimization. Sanders et al. Section II-A-1, Algorithm 1.

from qualtran.bloqs.arithmetic.controlled_add_or_subtract import ControlledAddOrSubtract

Example Instances

ctrl_add_or_sub_unsigned = ControlledAddOrSubtract(QUInt(8), QUInt(8))

ctrl_add_or_sub_signed = ControlledAddOrSubtract(QInt(8), QInt(8))

import sympy

n = sympy.Symbol("n")
ctrl_add_or_sub_signed_symb = ControlledAddOrSubtract(QInt(n), QInt(n))

Graphical Signature

from qualtran.drawing import show_bloqs
show_bloqs([ctrl_add_or_sub_signed_symb, ctrl_add_or_sub_unsigned, ctrl_add_or_sub_signed],
           ['`ctrl_add_or_sub_signed_symb`', '`ctrl_add_or_sub_unsigned`', '`ctrl_add_or_sub_signed`'])

Call Graph

from qualtran.resource_counting.generalizers import ignore_split_join
ctrl_add_or_sub_signed_symb_g, ctrl_add_or_sub_signed_symb_sigma = ctrl_add_or_sub_signed_symb.call_graph(max_depth=1, generalizer=ignore_split_join)
show_call_graph(ctrl_add_or_sub_signed_symb_g)
show_counts_sigma(ctrl_add_or_sub_signed_symb_sigma)

Counts totals:

• Add: 1

• C[BitwiseNot]: 2

• XGate: 2