Generic Select

Bloqs for applying SELECT unitary for LCU of Pauli Strings.

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

SelectPauliLCU

A SELECT bloq for selecting and applying operators from an array of PauliStrings.

\[ \mathrm{SELECT} = \sum_{l}|l \rangle \langle l| \otimes U_l \]

Where \(U_l\) is a member of the Pauli group.

This bloq uses the unary iteration scheme to apply select_unitaries[selection] to target controlled on the single-bit control register.

Parameters

• selection_bitsize: The size of the indexing select register. This should be at least log2(len(select_unitaries))

• target_bitsize: The size of the target register.

• select_unitaries: List of DensePauliStrings to apply to the target register. Each dense pauli string must contain target_bitsize terms.

• control_val: Optional control value. If specified, a singly controlled gate is constructed.

from qualtran.bloqs.multiplexers.select_pauli_lcu import SelectPauliLCU

Example Instances

target_bitsize = 4
us = ['XIXI', 'YIYI', 'ZZZZ', 'ZXYZ']
us = [cirq.DensePauliString(u) for u in us]
selection_bitsize = int(np.ceil(np.log2(len(us))))
select_pauli_lcu = SelectPauliLCU(selection_bitsize, target_bitsize, select_unitaries=us)

Graphical Signature

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

Call Graph

from qualtran.resource_counting.generalizers import ignore_split_join
select_pauli_lcu_g, select_pauli_lcu_sigma = select_pauli_lcu.call_graph(max_depth=1, generalizer=ignore_split_join)
show_call_graph(select_pauli_lcu_g)
show_counts_sigma(select_pauli_lcu_sigma)

Counts totals:

• And: 2

• And†: 2

• CNOT: 2

• C[cirq.+XX]: 1

• C[cirq.+YY]: 1

• C[cirq.+ZXYZ]: 1

• C[cirq.+ZZZZ]: 1

• XGate: 2