Apply Lth Bloq

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

ApplyLthBloq

A SELECT operation that executes one of a list of bloqs \(U_l\) based on a quantum index:

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

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

Parameters

• ops: NDArray of bloqs. Each bloq must have identical registers that are all THRU.

• selection_regs: List of selection registers, defaults to N-D selection index based on ops.

• control_val: If provided, a singly controlled gate is constructed.

Registers

• selection: The indices of the bloq in ops to execute.

• control: The control bit if specified above.

• [user_spec]: The output registers of the bloqs in ops.

References

• Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity. Babbush et al. (2018). Section III.A. and Figure 7.

from qualtran.bloqs.multiplexers.apply_lth_bloq import ApplyLthBloq

Example Instances

from qualtran.bloqs.basic_gates import Hadamard, TGate, XGate, ZGate

ops = np.array((TGate(), Hadamard(), ZGate(), XGate()))
apply_lth_bloq = ApplyLthBloq(ops, control_val=1)

Graphical Signature

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

Call Graph

from qualtran.resource_counting.generalizers import ignore_split_join
apply_lth_bloq_g, apply_lth_bloq_sigma = apply_lth_bloq.call_graph(max_depth=1, generalizer=ignore_split_join)
show_call_graph(apply_lth_bloq_g)
show_counts_sigma(apply_lth_bloq_sigma)

Counts totals:

• And: 3

• And†: 3

• CHadamard: 1

• CNOT: 4

• CZ: 1

• C[T]: 1