Global Phase

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

GlobalPhase

Applies a global phase to the circuit as a whole.

The unitary effect is to multiply the state vector by the complex scalar \(e^{i pi t}\) for exponent \(t\).

The global phase of a state or circuit does not affect any observable quantity, but keeping track of it can be a useful bookkeeping mechanism for testing circuit identities. The global phase becomes important if the gate becomes controlled.

Parameters

• exponent: the exponent \(t\) of the global phase \(e^{i pi t}\) to apply.

• eps: precision

from qualtran.bloqs.basic_gates import GlobalPhase

Example Instances

global_phase = GlobalPhase(exponent=0.5)

Graphical Signature

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

Call Graph

from qualtran.resource_counting.generalizers import ignore_split_join
global_phase_g, global_phase_sigma = global_phase.call_graph(max_depth=1, generalizer=ignore_split_join)
show_call_graph(global_phase_g)
show_counts_sigma(global_phase_sigma)

Counts totals:

• GPhase((6.123233995736766e-17+1j)): 1

Tensors and Controlled

The “tensor” of the global phase gate is just a number.

global_phase.tensor_contract()

/usr/local/google/home/mpharrigan/qualtran/conda-311/lib/python3.11/site-packages/cotengra/hyperoptimizers/hyper.py:57: UserWarning: Couldn't find `optuna`, `cmaes`, `baytune (btb)`, `chocolate`, or `nevergrad` so will use completely random sampling in place of hyper-optimization.
  warnings.warn(
/usr/local/google/home/mpharrigan/qualtran/conda-311/lib/python3.11/site-packages/cotengra/hyperoptimizers/hyper.py:76: UserWarning: Couldn't find `optuna`, `cmaes`, `baytune (btb)`, `chocolate`, or `nevergrad` so will use completely random sampling in place of hyper-optimization.
  warnings.warn(

(6.123233995736766e-17+1j)

When a global phase is controlled, it is equivalent to a ZPowGate

cgp = global_phase.controlled()
print(repr(cgp))
print(cgp.tensor_contract())

ZPowGate(exponent=0.5, global_shift=0.0, eps=1e-11)
[[1.+0.j 0.+0.j]
 [0.+0.j 0.+1.j]]