Add efficient gate power methods (#9318)

* add efficient gate power methods

* fix imports

* override some more methods

* use scipy.linalg.fractional_matrix_power

* use assertIsInstance and add isinstance check

* lint

Co-authored-by: mergify[bot] <37929162+mergify[bot]@users.noreply.github.com>

qiskit/circuit/library/standard_gates/i.py

@@ -55,3 +55,7 @@ def inverse(self):
     def __array__(self, dtype=None):
         """Return a numpy.array for the identity gate."""
         return numpy.array([[1, 0], [0, 1]], dtype=dtype)
+
+    def power(self, exponent: float):
+        """Raise gate to a power."""
+        return IGate()

qiskit/circuit/library/standard_gates/iswap.py

@@ -13,10 +13,14 @@
 """iSWAP gate."""
 
 from typing import Optional
+
 import numpy as np
+
 from qiskit.circuit.gate import Gate
 from qiskit.circuit.quantumregister import QuantumRegister
 
+from .xx_plus_yy import XXPlusYYGate
+
 
 class iSwapGate(Gate):
     r"""iSWAP gate.
@@ -96,6 +100,7 @@ def _define(self):
         """
         # pylint: disable=cyclic-import
         from qiskit.circuit.quantumcircuit import QuantumCircuit
+
         from .h import HGate
         from .s import SGate
         from .x import CXGate
@@ -118,3 +123,7 @@ def _define(self):
     def __array__(self, dtype=None):
         """Return a numpy.array for the iSWAP gate."""
         return np.array([[1, 0, 0, 0], [0, 0, 1j, 0], [0, 1j, 0, 0], [0, 0, 0, 1]], dtype=dtype)
+
+    def power(self, exponent: float):
+        """Raise gate to a power."""
+        return XXPlusYYGate(-np.pi * exponent)

qiskit/circuit/library/standard_gates/p.py

@@ -125,6 +125,11 @@ def __array__(self, dtype=None):
         lam = float(self.params[0])
         return numpy.array([[1, 0], [0, exp(1j * lam)]], dtype=dtype)
 
+    def power(self, exponent: float):
+        """Raise gate to a power."""
+        (theta,) = self.params
+        return PhaseGate(exponent * theta)
+
 
 class CPhaseGate(ControlledGate):
     r"""Controlled-Phase gate.
@@ -244,6 +249,11 @@ def __array__(self, dtype=None):
             )
         return numpy.array([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, eith, 0], [0, 0, 0, 1]], dtype=dtype)
 
+    def power(self, exponent: float):
+        """Raise gate to a power."""
+        (theta,) = self.params
+        return CPhaseGate(exponent * theta)
+
 
 class MCPhaseGate(ControlledGate):
     r"""Multi-controlled-Phase gate.

qiskit/circuit/library/standard_gates/r.py

@@ -88,3 +88,8 @@ def __array__(self, dtype=None):
         exp_m = exp(-1j * phi)
         exp_p = exp(1j * phi)
         return numpy.array([[cos, -1j * exp_m * sin], [-1j * exp_p * sin, cos]], dtype=dtype)
+
+    def power(self, exponent: float):
+        """Raise gate to a power."""
+        theta, phi = self.params
+        return RGate(exponent * theta, phi)

qiskit/circuit/library/standard_gates/rx.py

@@ -106,6 +106,11 @@ def __array__(self, dtype=None):
         sin = math.sin(self.params[0] / 2)
         return numpy.array([[cos, -1j * sin], [-1j * sin, cos]], dtype=dtype)
 
+    def power(self, exponent: float):
+        """Raise gate to a power."""
+        (theta,) = self.params
+        return RXGate(exponent * theta)
+
 
 class CRXGate(ControlledGate):
     r"""Controlled-RX gate.

qiskit/circuit/library/standard_gates/rxx.py

@@ -119,3 +119,8 @@ def __array__(self, dtype=None):
             [[cos, 0, 0, -isin], [0, cos, -isin, 0], [0, -isin, cos, 0], [-isin, 0, 0, cos]],
             dtype=dtype,
         )
+
+    def power(self, exponent: float):
+        """Raise gate to a power."""
+        (theta,) = self.params
+        return RXXGate(exponent * theta)

qiskit/circuit/library/standard_gates/ry.py

@@ -105,6 +105,11 @@ def __array__(self, dtype=None):
         sin = math.sin(self.params[0] / 2)
         return numpy.array([[cos, -sin], [sin, cos]], dtype=dtype)
 
+    def power(self, exponent: float):
+        """Raise gate to a power."""
+        (theta,) = self.params
+        return RYGate(exponent * theta)
+
 
 class CRYGate(ControlledGate):
     r"""Controlled-RY gate.

qiskit/circuit/library/standard_gates/ryy.py

@@ -119,3 +119,8 @@ def __array__(self, dtype=None):
             [[cos, 0, 0, isin], [0, cos, -isin, 0], [0, -isin, cos, 0], [isin, 0, 0, cos]],
             dtype=dtype,
         )
+
+    def power(self, exponent: float):
+        """Raise gate to a power."""
+        (theta,) = self.params
+        return RYYGate(exponent * theta)

qiskit/circuit/library/standard_gates/rz.py

@@ -117,6 +117,11 @@ def __array__(self, dtype=None):
         ilam2 = 0.5j * float(self.params[0])
         return np.array([[exp(-ilam2), 0], [0, exp(ilam2)]], dtype=dtype)
 
+    def power(self, exponent: float):
+        """Raise gate to a power."""
+        (theta,) = self.params
+        return RZGate(exponent * theta)
+
 
 class CRZGate(ControlledGate):
     r"""Controlled-RZ gate.

qiskit/circuit/library/standard_gates/rzx.py

@@ -165,3 +165,8 @@ def __array__(self, dtype=None):
             [[cos, 0, -isin, 0], [0, cos, 0, isin], [-isin, 0, cos, 0], [0, isin, 0, cos]],
             dtype=dtype,
         )
+
+    def power(self, exponent: float):
+        """Raise gate to a power."""
+        (theta,) = self.params
+        return RZXGate(exponent * theta)

qiskit/circuit/library/standard_gates/rzz.py

@@ -132,3 +132,8 @@ def __array__(self, dtype=None):
             ],
             dtype=dtype,
         )
+
+    def power(self, exponent: float):
+        """Raise gate to a power."""
+        (theta,) = self.params
+        return RZZGate(exponent * theta)

qiskit/circuit/library/standard_gates/s.py

@@ -13,11 +13,14 @@
 """The S, Sdg, CS and CSdg gates."""
 
 from typing import Optional, Union
+
 import numpy
-from qiskit.qasm import pi
+
 from qiskit.circuit.controlledgate import ControlledGate
 from qiskit.circuit.gate import Gate
+from qiskit.circuit.library.standard_gates.p import CPhaseGate, PhaseGate
 from qiskit.circuit.quantumregister import QuantumRegister
+from qiskit.qasm import pi
 
 
 class SGate(Gate):
@@ -60,6 +63,7 @@ def _define(self):
         """
         # pylint: disable=cyclic-import
         from qiskit.circuit.quantumcircuit import QuantumCircuit
+
         from .u1 import U1Gate
 
         q = QuantumRegister(1, "q")
@@ -78,6 +82,10 @@ def __array__(self, dtype=None):
         """Return a numpy.array for the S gate."""
         return numpy.array([[1, 0], [0, 1j]], dtype=dtype)
 
+    def power(self, exponent: float):
+        """Raise gate to a power."""
+        return PhaseGate(0.5 * numpy.pi * exponent)
+
 
 class SdgGate(Gate):
     r"""Single qubit S-adjoint gate (~Z**0.5).
@@ -119,6 +127,7 @@ def _define(self):
         """
         # pylint: disable=cyclic-import
         from qiskit.circuit.quantumcircuit import QuantumCircuit
+
         from .u1 import U1Gate
 
         q = QuantumRegister(1, "q")
@@ -137,6 +146,10 @@ def __array__(self, dtype=None):
         """Return a numpy.array for the Sdg gate."""
         return numpy.array([[1, 0], [0, -1j]], dtype=dtype)
 
+    def power(self, exponent: float):
+        """Raise gate to a power."""
+        return PhaseGate(-0.5 * numpy.pi * exponent)
+
 
 class CSGate(ControlledGate):
     r"""Controlled-S gate.
@@ -194,9 +207,6 @@ def _define(self):
         """
         gate cs a,b { h b; cp(pi/2) a,b; h b; }
         """
-        # pylint: disable=cyclic-import
-        from .p import CPhaseGate
-
         self.definition = CPhaseGate(theta=pi / 2).definition
 
     def inverse(self):
@@ -210,6 +220,10 @@ def __array__(self, dtype=None):
             return numpy.asarray(mat, dtype=dtype)
         return mat
 
+    def power(self, exponent: float):
+        """Raise gate to a power."""
+        return CPhaseGate(0.5 * numpy.pi * exponent)
+
 
 class CSdgGate(ControlledGate):
     r"""Controlled-S^\dagger gate.
@@ -273,9 +287,6 @@ def _define(self):
         """
         gate csdg a,b { h b; cp(-pi/2) a,b; h b; }
         """
-        # pylint: disable=cyclic-import
-        from .p import CPhaseGate
-
         self.definition = CPhaseGate(theta=-pi / 2).definition
 
     def inverse(self):
@@ -288,3 +299,7 @@ def __array__(self, dtype=None):
         if dtype is not None:
             return numpy.asarray(mat, dtype=dtype)
         return mat
+
+    def power(self, exponent: float):
+        """Raise gate to a power."""
+        return CPhaseGate(-0.5 * numpy.pi * exponent)

qiskit/circuit/library/standard_gates/t.py

@@ -13,10 +13,13 @@
 """T and Tdg gate."""
 import math
 from typing import Optional
+
 import numpy
-from qiskit.qasm import pi
+
 from qiskit.circuit.gate import Gate
+from qiskit.circuit.library.standard_gates.p import PhaseGate
 from qiskit.circuit.quantumregister import QuantumRegister
+from qiskit.qasm import pi
 
 
 class TGate(Gate):
@@ -60,6 +63,7 @@ def _define(self):
         """
         # pylint: disable=cyclic-import
         from qiskit.circuit.quantumcircuit import QuantumCircuit
+
         from .u1 import U1Gate
 
         q = QuantumRegister(1, "q")
@@ -78,6 +82,10 @@ def __array__(self, dtype=None):
         """Return a numpy.array for the T gate."""
         return numpy.array([[1, 0], [0, (1 + 1j) / numpy.sqrt(2)]], dtype=dtype)
 
+    def power(self, exponent: float):
+        """Raise gate to a power."""
+        return PhaseGate(0.25 * numpy.pi * exponent)
+
 
 class TdgGate(Gate):
     r"""Single qubit T-adjoint gate (~Z**0.25).
@@ -119,6 +127,7 @@ def _define(self):
         """
         # pylint: disable=cyclic-import
         from qiskit.circuit.quantumcircuit import QuantumCircuit
+
         from .u1 import U1Gate
 
         q = QuantumRegister(1, "q")
@@ -136,3 +145,7 @@ def inverse(self):
     def __array__(self, dtype=None):
         """Return a numpy.array for the inverse T gate."""
         return numpy.array([[1, 0], [0, (1 - 1j) / math.sqrt(2)]], dtype=dtype)
+
+    def power(self, exponent: float):
+        """Raise gate to a power."""
+        return PhaseGate(-0.25 * numpy.pi * exponent)

qiskit/circuit/library/standard_gates/xx_minus_yy.py

@@ -169,3 +169,8 @@ def __array__(self, dtype=complex):
             ],
             dtype=dtype,
         )
+
+    def power(self, exponent: float):
+        """Raise gate to a power."""
+        theta, beta = self.params
+        return XXMinusYYGate(exponent * theta, beta)

qiskit/circuit/library/standard_gates/xx_plus_yy.py

@@ -170,3 +170,8 @@ def __array__(self, dtype=complex):
             ],
             dtype=dtype,
         )
+
+    def power(self, exponent: float):
+        """Raise gate to a power."""
+        theta, beta = self.params
+        return XXPlusYYGate(exponent * theta, beta)

qiskit/circuit/library/standard_gates/z.py

@@ -13,12 +13,16 @@
 """Z, CZ and CCZ gates."""
 
 from typing import Optional, Union
+
 import numpy
-from qiskit.qasm import pi
+
+from qiskit.circuit._utils import _compute_control_matrix
 from qiskit.circuit.controlledgate import ControlledGate
 from qiskit.circuit.gate import Gate
 from qiskit.circuit.quantumregister import QuantumRegister
-from qiskit.circuit._utils import _compute_control_matrix
+from qiskit.qasm import pi
+
+from .p import PhaseGate
 
 
 class ZGate(Gate):
@@ -74,6 +78,7 @@ def __init__(self, label: Optional[str] = None):
     def _define(self):
         # pylint: disable=cyclic-import
         from qiskit.circuit.quantumcircuit import QuantumCircuit
+
         from .u1 import U1Gate
 
         q = QuantumRegister(1, "q")
@@ -117,6 +122,10 @@ def __array__(self, dtype=None):
         """Return a numpy.array for the Z gate."""
         return numpy.array([[1, 0], [0, -1]], dtype=dtype)
 
+    def power(self, exponent: float):
+        """Raise gate to a power."""
+        return PhaseGate(numpy.pi * exponent)
+
 
 class CZGate(ControlledGate):
     r"""Controlled-Z gate.
@@ -163,6 +172,7 @@ def _define(self):
         """
         # pylint: disable=cyclic-import
         from qiskit.circuit.quantumcircuit import QuantumCircuit
+
         from .h import HGate
         from .x import CXGate
 
@@ -241,6 +251,7 @@ def _define(self):
         """
         # pylint: disable=cyclic-import
         from qiskit.circuit.quantumcircuit import QuantumCircuit
+
         from .h import HGate
         from .x import CCXGate
 

releasenotes/notes/efficient-gate-power-effa21e3ee4581ee.yaml

@@ -0,0 +1,25 @@
+---
+features:
+  - |
+    Overrides some gate power methods to make them more efficient and less lossy:
+    - Powering a :class:`~.CPhaseGate` gives a :class:`~.CPhaseGate`.
+    - Powering a :class:`~.CSGate` gives a :class:`~.CPhaseGate`.
+    - Powering a :class:`~.CSdgGate` gives a :class:`~.CPhaseGate`.
+    - Powering an :class:`~.IGate` gives an :class:`~.IGate`.
+    - Powering a :class:`~.PhaseGate` gives a :class:`~.PhaseGate`.
+    - Powering an :class:`~.RGate` gives an :class:`~.RGate`.
+    - Powering an :class:`~.RXGate` gives an :class:`~.RXGate`.
+    - Powering an :class:`~.RXXGate` gives an :class:`~.RXXGate`.
+    - Powering an :class:`~.RYGate` gives an :class:`~.RYGate`.
+    - Powering an :class:`~.RYYGate` gives an :class:`~.RYYGate`.
+    - Powering an :class:`~.RZGate` gives an :class:`~.RZGate`.
+    - Powering an :class:`~.RZXGate` gives an :class:`~.RZXGate`.
+    - Powering an :class:`~.RZZGate` gives an :class:`~.RZZGate`.
+    - Powering a :class:`~.SdgGate` gives a :class:`~.PhaseGate`.
+    - Powering an :class:`~.SGate` gives a :class:`~.PhaseGate`.
+    - Powering a :class:`~.TdgGate` gives a :class:`~.PhaseGate`.
+    - Powering a :class:`~.TGate` gives a :class:`~.PhaseGate`.
+    - Powering an :class:`~.XXMinusYYGate` gives an :class:`~.XXMinusYYGate`.
+    - Powering an :class:`~.XXPlusYYGate` gives an :class:`~.XXPlusYYGate`.
+    - Powering a :class:`~.ZGate` gives a :class:`~.PhaseGate`.
+    - Powering an :class:`~.iSwapGate` gives an :class:`~.XXPlusYYGate`.