Subtraction

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

Subtract

An n-bit subtraction gate.

Implements \(U|a\rangle|b\rangle \rightarrow |a\rangle|a-b\rangle\) using \(4n - 4\) T gates.

This construction uses the relation a - b = ~(~a + b) to turn the operation into addition. This relation is used in Compilation of Fault-Tolerant Quantum Heuristics for Combinatorial Optimization to turn addition into subtraction conditioned on a qubit.

Parameters

• a_dtype: Quantum datatype used to represent the integer a.

• b_dtype: Quantum datatype used to represent the integer b. Must be large enough to hold the result in the output register of a - b, or else it simply drops the most significant bits. If not specified, b_dtype is set to a_dtype.

Registers

• a: A a_dtype.bitsize-sized input register (register a above).

• b: A b_dtype.bitsize-sized input/output register (register b above).

References

• Compilation of Fault-Tolerant Quantum Heuristics for Combinatorial Optimization. Page 9.

from qualtran.bloqs.arithmetic import Subtract

Example Instances

n = sympy.Symbol('n')
sub_symb = Subtract(QInt(bitsize=n))

sub_small = Subtract(QInt(bitsize=4))

sub_large = Subtract(QInt(bitsize=64))

sub_diff_size_regs = Subtract(QInt(bitsize=4), QInt(bitsize=16))

n = sympy.Symbol('n')
sub_symp_decomposition = Subtract(QInt(bitsize=n)).decompose_bloq()

Graphical Signature

from qualtran.drawing import show_bloqs
show_bloqs([sub_symb, sub_small, sub_large, sub_diff_size_regs, sub_symp_decomposition],
           ['`sub_symb`', '`sub_small`', '`sub_large`', '`sub_diff_size_regs`', '`sub_symp_decomposition`'])

Call Graph

from qualtran.resource_counting.generalizers import ignore_split_join
sub_symb_g, sub_symb_sigma = sub_symb.call_graph(max_depth=1, generalizer=ignore_split_join)
show_call_graph(sub_symb_g)
show_counts_sigma(sub_symb_sigma)

Counts totals:

• Add: 1

• XGate⨂n: 3

SubtractFrom

A version of Subtract that subtracts the first register from the second in place.

Implements \(U|a angle|b angle ightarrow |a angle|b - a angle\), essentially equivalent to the statement b -= a.

Parameters

• dtype: Quantum datatype used to represent the integers a, b, and b - a.

Registers

• a: A dtype.bitsize-sized input register (register a above).

• b: A dtype.bitsize-sized input/output register (register b above).

from qualtran.bloqs.arithmetic import SubtractFrom

Example Instances

n = sympy.Symbol('n')
sub_from_symb = SubtractFrom(QInt(bitsize=n))

sub_from_small = SubtractFrom(QInt(bitsize=4))

sub_from_large = SubtractFrom(QInt(bitsize=64))

Graphical Signature

from qualtran.drawing import show_bloqs
show_bloqs([sub_from_symb, sub_from_small, sub_from_large],
           ['`sub_from_symb`', '`sub_from_small`', '`sub_from_large`'])

Call Graph

from qualtran.resource_counting.generalizers import ignore_split_join
sub_from_symb_g, sub_from_symb_sigma = sub_from_symb.call_graph(max_depth=1, generalizer=ignore_split_join)
show_call_graph(sub_from_symb_g)
show_counts_sigma(sub_from_symb_sigma)

Counts totals:

• Add: 1

• BitwiseNot: 2