GlobalPhase: use exponent, and implement controlled (ZPowGate) (#1117)

* Global Phase * use `exponent` instead of `coefficient` for `GlobalPhase` * regenerate notebook * fix neg-ctrl gphase, add unitary test * docstring + types * approx equal for gphase * fix generalizer --------- Co-authored-by: Matthew Harrigan <[email protected]> Co-authored-by: Tanuj Khattar <[email protected]>
quantumlib · Jul 11, 2024 · 37d523c · 37d523c
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diff --git a/qualtran/_infra/controlled_test.py b/qualtran/_infra/controlled_test.py
@@ -380,7 +380,7 @@ def test_controlled_tensor_without_decompose():
 
 
 def test_controlled_global_phase_tensor():
-    bloq = GlobalPhase(1.0j).controlled()
+    bloq = GlobalPhase.from_coefficient(1.0j).controlled()
     should_be = np.diag([1, 1.0j])
     np.testing.assert_allclose(bloq.tensor_contract(), should_be)
 

diff --git a/qualtran/bloqs/basic_gates/global_phase.ipynb b/qualtran/bloqs/basic_gates/global_phase.ipynb
@@ -36,10 +36,17 @@
    },
    "source": [
     "## `GlobalPhase`\n",
-    "Global phase operation of $z$ (where $|z| = 1$).\n",
+    "Applies a global phase to the circuit as a whole.\n",
+    "\n",
+    "The unitary effect is to multiply the state vector by the complex scalar\n",
+    "$e^{i pi t}$ for `exponent` $t$.\n",
+    "\n",
+    "The global phase of a state or circuit does not affect any observable quantity, but\n",
+    "keeping track of it can be a useful bookkeeping mechanism for testing circuit identities.\n",
+    "The global phase becomes important if the gate becomes controlled.\n",
     "\n",
     "#### Parameters\n",
-    " - `coefficient`: a unit complex number $z$ representing the global phase\n",
+    " - `exponent`: the exponent $t$ of the global phase $e^{i pi t}$ to apply.\n",
     " - `eps`: precision\n"
    ]
   },
@@ -74,7 +81,7 @@
    },
    "outputs": [],
    "source": [
-    "global_phase = GlobalPhase(1j)"
+    "global_phase = GlobalPhase(exponent=0.5)"
    ]
   },
   {
@@ -125,6 +132,46 @@
     "show_call_graph(global_phase_g)\n",
     "show_counts_sigma(global_phase_sigma)"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c183275c-cc9c-477d-888c-d8b850f67a2e",
+   "metadata": {},
+   "source": [
+    "### Tensors and Controlled\n",
+    "\n",
+    "The \"tensor\" of the global phase gate is just a number."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "d053b20b-3d61-487a-b962-e2368d834c40",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "global_phase.tensor_contract()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b737b871-9c61-4d54-860a-d9928f18808b",
+   "metadata": {},
+   "source": [
+    "When a global phase is controlled, it is equivalent to a ZPowGate"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "d873856e-a687-4b73-acdc-9188dd13a60e",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "cgp = global_phase.controlled()\n",
+    "print(repr(cgp))\n",
+    "print(cgp.tensor_contract())"
+   ]
   }
  ],
  "metadata": {
@@ -143,7 +190,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.11.7"
+   "version": "3.11.8"
   }
  },
  "nbformat": 4,

diff --git a/qualtran/bloqs/basic_gates/global_phase.py b/qualtran/bloqs/basic_gates/global_phase.py
@@ -11,45 +11,73 @@
 #  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 #  See the License for the specific language governing permissions and
 #  limitations under the License.
-
-from typing import Dict, List, TYPE_CHECKING
+from functools import cached_property
+from typing import Dict, Iterable, List, Optional, Sequence, Tuple, TYPE_CHECKING
 
 import attrs
 import cirq
-from attrs import frozen
-
-from qualtran import bloq_example, BloqDocSpec, ConnectionT, DecomposeTypeError
+from attrs import field, frozen
+
+from qualtran import (
+    AddControlledT,
+    Bloq,
+    bloq_example,
+    BloqBuilder,
+    BloqDocSpec,
+    CompositeBloq,
+    ConnectionT,
+    CtrlSpec,
+    DecomposeTypeError,
+    SoquetT,
+)
+from qualtran.bloqs.basic_gates.rotation import ZPowGate
 from qualtran.cirq_interop import CirqGateAsBloqBase
 from qualtran.cirq_interop.t_complexity_protocol import TComplexity
-from qualtran.symbolics import sconj, SymbolicComplex
+from qualtran.symbolics import pi, sarg, sexp, SymbolicComplex, SymbolicFloat
 
 if TYPE_CHECKING:
     import quimb.tensor as qtn
 
-    from qualtran import CompositeBloq
-
 
 @frozen
 class GlobalPhase(CirqGateAsBloqBase):
-    """Global phase operation of $z$ (where $|z| = 1$).
+    r"""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.
 
     Args:
-        coefficient: a unit complex number $z$ representing the global phase
+        exponent: the exponent $t$ of the global phase $e^{i pi t}$ to apply.
         eps: precision
     """
 
-    coefficient: 'SymbolicComplex'
-    eps: float = 1e-11
+    exponent: SymbolicFloat = field(kw_only=True)
+    eps: SymbolicFloat = 1e-11
+
+    @cached_property
+    def coefficient(self) -> SymbolicComplex:
+        return sexp(self.exponent * pi(self.exponent) * 1j)
+
+    @classmethod
+    def from_coefficient(
+        cls, coefficient: SymbolicComplex, *, eps: SymbolicFloat = 1e-11
+    ) -> 'GlobalPhase':
+        """Applies a global phase of `coefficient`."""
+        return cls(exponent=sarg(coefficient) / pi(coefficient), eps=eps)
 
     @property
     def cirq_gate(self) -> cirq.Gate:
-        return cirq.GlobalPhaseGate(self.coefficient, self.eps)
+        return cirq.GlobalPhaseGate(self.coefficient)
 
     def decompose_bloq(self) -> 'CompositeBloq':
         raise DecomposeTypeError(f"{self} is atomic")
 
     def adjoint(self) -> 'GlobalPhase':
-        return attrs.evolve(self, coefficient=sconj(self.coefficient))
+        return attrs.evolve(self, exponent=-self.exponent)
 
     def my_tensors(
         self, incoming: Dict[str, 'ConnectionT'], outgoing: Dict[str, 'ConnectionT']
@@ -58,6 +86,29 @@ def my_tensors(
 
         return [qtn.Tensor(data=self.coefficient, inds=[], tags=[str(self)])]
 
+    def get_ctrl_system(
+        self, ctrl_spec: Optional['CtrlSpec'] = None
+    ) -> Tuple['Bloq', 'AddControlledT']:
+
+        # Delegate to superclass logic for more than one control.
+        if not (ctrl_spec is None or ctrl_spec == CtrlSpec() or ctrl_spec == CtrlSpec(cvs=0)):
+            return super().get_ctrl_system(ctrl_spec=ctrl_spec)
+
+        # Otherwise, it's a ZPowGate
+        if ctrl_spec == CtrlSpec(cvs=0):
+            bloq = ZPowGate(exponent=-self.exponent, global_shift=-1, eps=self.eps)
+        else:
+            bloq = ZPowGate(exponent=self.exponent, eps=self.eps)
+
+        def _add_ctrled(
+            bb: 'BloqBuilder', ctrl_soqs: Sequence['SoquetT'], in_soqs: Dict[str, 'SoquetT']
+        ) -> Tuple[Iterable['SoquetT'], Iterable['SoquetT']]:
+            (ctrl,) = ctrl_soqs
+            ctrl = bb.add(bloq, q=ctrl)
+            return [ctrl], []
+
+        return bloq, _add_ctrled
+
     def pretty_name(self) -> str:
         return 'GPhase'
 
@@ -70,12 +121,8 @@ def _t_complexity_(self) -> 'TComplexity':
 
 @bloq_example
 def _global_phase() -> GlobalPhase:
-    global_phase = GlobalPhase(1j)
+    global_phase = GlobalPhase(exponent=0.5)
     return global_phase
 
 
-_GLOBAL_PHASE_DOC = BloqDocSpec(
-    bloq_cls=GlobalPhase,
-    import_line='from qualtran.bloqs.basic_gates import GlobalPhase',
-    examples=[_global_phase],
-)
+_GLOBAL_PHASE_DOC = BloqDocSpec(bloq_cls=GlobalPhase, examples=[_global_phase])
diff --git a/qualtran/bloqs/basic_gates/global_phase_test.py b/qualtran/bloqs/basic_gates/global_phase_test.py
@@ -14,22 +14,48 @@
 
 import cirq
 import numpy as np
+import pytest
 
+from qualtran import CtrlSpec
 from qualtran.bloqs.basic_gates.global_phase import _global_phase, GlobalPhase
+from qualtran.cirq_interop import cirq_gate_to_bloq
 from qualtran.cirq_interop.t_complexity_protocol import TComplexity
 
 
 def test_unitary():
     random_state = np.random.RandomState(2)
 
-    for alpha in random_state.random(size=20):
+    for alpha in random_state.random(size=10):
         coefficient = np.exp(2j * np.pi * alpha)
-        bloq = GlobalPhase(coefficient)
+        bloq = GlobalPhase(exponent=2 * alpha)
         np.testing.assert_allclose(cirq.unitary(bloq), coefficient)
 
 
+@pytest.mark.parametrize("cv", [0, 1])
+def test_controlled(cv: int):
+    ctrl_spec = CtrlSpec(cvs=cv)
+    random_state = np.random.RandomState(2)
+    for alpha in random_state.random(size=10):
+        coefficient = np.exp(2j * np.pi * alpha)
+        bloq = GlobalPhase(exponent=2 * alpha).controlled(ctrl_spec=ctrl_spec)
+        np.testing.assert_allclose(
+            cirq.unitary(cirq.GlobalPhaseGate(coefficient).controlled(control_values=[cv])),
+            bloq.tensor_contract(),
+        )
+
+
+def test_cirq_interop():
+    bloq = GlobalPhase.from_coefficient(1.0j)
+    gate = cirq.GlobalPhaseGate(1.0j)
+
+    circuit = bloq.as_composite_bloq().to_cirq_circuit()
+    assert cirq.approx_eq(circuit, cirq.Circuit(gate.on()), atol=1e-16)
+
+    assert cirq_gate_to_bloq(gate) == bloq
+
+
 def test_t_complexity():
-    assert GlobalPhase(1j).t_complexity() == TComplexity()
+    assert GlobalPhase(exponent=0.5).t_complexity() == TComplexity()
 
 
 def test_global_phase(bloq_autotester):

diff --git a/qualtran/bloqs/basic_gates/rotation.py b/qualtran/bloqs/basic_gates/rotation.py
@@ -77,14 +77,16 @@ class ZPowGate(CirqGateAsBloqBase):
     """
 
     exponent: SymbolicFloat = 1.0
-    global_shift: float = 0.0
-    eps: float = 1e-11
+    global_shift: SymbolicFloat = 0.0
+    eps: SymbolicFloat = 1e-11
 
     def decompose_bloq(self) -> 'CompositeBloq':
         raise DecomposeTypeError(f"{self} is atomic")
 
     @cached_property
     def cirq_gate(self) -> cirq.Gate:
+        if isinstance(self.global_shift, sympy.Expr):
+            raise TypeError(f"cirq.ZPowGate does not support symbolic {self.global_shift=}")
         return cirq.ZPowGate(exponent=self.exponent, global_shift=self.global_shift)
 
     def __pow__(self, power):

diff --git a/qualtran/bloqs/basic_gates/su2_rotation.py b/qualtran/bloqs/basic_gates/su2_rotation.py
@@ -23,7 +23,7 @@
 from qualtran.bloqs.basic_gates import GlobalPhase, Ry, ZPowGate
 from qualtran.cirq_interop.t_complexity_protocol import TComplexity
 from qualtran.drawing import Text, TextBox
-from qualtran.symbolics import is_symbolic, SymbolicFloat
+from qualtran.symbolics import is_symbolic, pi, SymbolicFloat
 
 if TYPE_CHECKING:
     import quimb.tensor as qtn
@@ -125,13 +125,17 @@ def _unitary_(self):
         return self.rotation_matrix
 
     def build_composite_bloq(self, bb: 'BloqBuilder', q: 'SoquetT') -> Dict[str, 'SoquetT']:
-        pi = sympy.pi if self.is_symbolic() else np.pi
-        exp = sympy.exp if self.is_symbolic() else np.exp
-
-        bb.add(GlobalPhase(coefficient=-exp(1j * self.global_shift), eps=self.eps / 4))
-        q = bb.add(ZPowGate(exponent=1 - self.lambd / pi, global_shift=-1, eps=self.eps / 4), q=q)
+        bb.add(
+            GlobalPhase(exponent=1 + self.global_shift / pi(self.global_shift), eps=self.eps / 4)
+        )
+        q = bb.add(
+            ZPowGate(exponent=1 - self.lambd / pi(self.lambd), global_shift=-1, eps=self.eps / 4),
+            q=q,
+        )
         q = bb.add(Ry(angle=2 * self.theta, eps=self.eps / 4), q=q)
-        q = bb.add(ZPowGate(exponent=-self.phi / pi, global_shift=-1, eps=self.eps / 4), q=q)
+        q = bb.add(
+            ZPowGate(exponent=-self.phi / pi(self.phi), global_shift=-1, eps=self.eps / 4), q=q
+        )
         return {'q': q}
 
     def adjoint(self) -> 'SU2RotationGate':

diff --git a/qualtran/bloqs/basic_gates/su2_rotation_test.py b/qualtran/bloqs/basic_gates/su2_rotation_test.py
@@ -99,7 +99,7 @@ def test_call_graph():
     gate = SU2RotationGate(theta, phi, lambd, alpha, eps)
     _, sigma = gate.call_graph()
     assert sigma == {
-        GlobalPhase(-sympy.exp(1j * alpha), eps / 4): 1,
+        GlobalPhase(exponent=1 + alpha / pi, eps=eps / 4): 1,
         ZPowGate(-phi / pi, -1, eps / 4): 1,
         ZPowGate(-lambd / pi + 1, -1, eps / 4): 1,
         Ry(2 * theta, eps / 4): 1,

diff --git a/qualtran/bloqs/phase_estimation/lp_resource_state.py b/qualtran/bloqs/phase_estimation/lp_resource_state.py
@@ -159,7 +159,7 @@ def decompose_from_registers(
 
         # Reset ancilla to |0> state.
         yield [XGate().on(flag), XGate().on(anc)]
-        yield GlobalPhase(1j).on()
+        yield GlobalPhase(exponent=0.5).on()
         context.qubit_manager.qfree([flag, anc])
 
     def build_call_graph(self, ssa: 'SympySymbolAllocator') -> Set['BloqCountT']:
@@ -173,7 +173,7 @@ def build_call_graph(self, ssa: 'SympySymbolAllocator') -> Set['BloqCountT']:
             (Ry(angle=flag_angle), 3),
             (MultiControlPauli(cvs, target_gate=cirq.Z), 1),
             (XGate(), 4),
-            (GlobalPhase(1j), 1),
+            (GlobalPhase(exponent=0.5), 1),
             (CZPowGate(), 1),
         }
 

diff --git a/qualtran/bloqs/reflections/reflection_using_prepare.py b/qualtran/bloqs/reflections/reflection_using_prepare.py
@@ -20,14 +20,13 @@
 import numpy as np
 from numpy.typing import NDArray
 
-from qualtran import bloq_example, BloqDocSpec, QBit, Register, Signature
+from qualtran import Bloq, bloq_example, BloqDocSpec, CtrlSpec, QBit, Register, Signature
 from qualtran._infra.gate_with_registers import (
     merge_qubits,
     SpecializedSingleQubitControlledGate,
     total_bits,
 )
 from qualtran.bloqs.basic_gates.global_phase import GlobalPhase
-from qualtran.bloqs.basic_gates.rotation import ZPowGate
 from qualtran.bloqs.basic_gates.x_basis import XGate
 from qualtran.bloqs.mcmt.multi_control_multi_target_pauli import MultiControlPauli
 from qualtran.resource_counting.generalizers import ignore_split_join
@@ -176,12 +175,10 @@ def build_call_graph(self, ssa: 'SympySymbolAllocator') -> Set['BloqCountT']:
         if self.control_val is None:
             costs.add((XGate(), 2))
         if self.global_phase != 1:
-            if self.control_val is None:
-                costs.add((GlobalPhase(self.global_phase, self.eps), 1))
-            else:
-                costs.add(
-                    (ZPowGate(exponent=float(np.angle(self.global_phase)) / np.pi, eps=self.eps), 1)
-                )
+            phase_op: Bloq = GlobalPhase.from_coefficient(self.global_phase, eps=self.eps)
+            if self.control_val is not None:
+                phase_op = phase_op.controlled(ctrl_spec=CtrlSpec(cvs=self.control_val))
+            costs.add((phase_op, 1))
         return costs