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Apply to Lth Target

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

ApplyGateToLthQubit

A controlled SELECT operation for single-qubit gates.

\[ \mathrm{SELECT} = \sum_{l}|l \rangle \langle l| \otimes [G(l)]_l \]

Where \(G\) is a function that maps an index to a single-qubit gate.

This gate uses the unary iteration scheme to apply nth_gate(selection) to the selection-th qubit of target all controlled by the control register.

Parameters

• selection_regs: Indexing select signature of type Tuple[Register, …]. It also contains information about the iteration length of each selection register.

• nth_gate: A function mapping the composite selection index to a single-qubit gate.

• control_regs: Control signature for constructing a controlled version of the gate.

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_gate_to_lth_target import ApplyGateToLthQubit

Example Instances

from qualtran import BQUInt, Register

def _z_to_odd(n: int):
    if n % 2 == 1:
        return cirq.Z
    return cirq.I

apply_z_to_odd = ApplyGateToLthQubit(
    Register('selection', BQUInt(3, 4)),
    nth_gate=_z_to_odd,
    control_regs=Signature.build(control=2),
)

Graphical Signature

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

Decomposition

import qualtran.cirq_interop.testing as cq_testing
from qualtran.cirq_interop.jupyter_tools import display_gate_and_compilation

g = cq_testing.GateHelper(
    apply_z_to_odd
)

display_gate_and_compilation(g)

Call Graph

from qualtran.resource_counting.generalizers import ignore_split_join
apply_z_to_odd_g, apply_z_to_odd_sigma = apply_z_to_odd.call_graph(max_depth=1, generalizer=ignore_split_join)
show_call_graph(apply_z_to_odd_g)
show_counts_sigma(apply_z_to_odd_sigma)

Counts totals:

• And: 1

• And: 3

• And†: 4

• CNOT: 3

• CZ: 2

• I: 2