Implement the relative phase Toffoli gates

qiskit/extensions/standard/__init__.py

@@ -18,6 +18,8 @@
 from .iden import IdGate
 from .ms import MSGate
 from .r import RGate
+from .rccx import RCCXGate
+from .rcccx import RCCCXGate
 from .rx import RXGate, CrxGate
 from .rxx import RXXGate
 from .ry import RYGate, CryGate

qiskit/extensions/standard/multi_control_toffoli_gate.py

@@ -22,8 +22,6 @@
 from qiskit.circuit import QuantumCircuit, QuantumRegister, Qubit
 
 from qiskit import QiskitError
-# pylint: disable=unused-import
-from .relative_phase_toffoli import rccx
 
 logger = logging.getLogger(__name__)
 

qiskit/extensions/standard/rcccx.py

@@ -0,0 +1,116 @@
+# -*- coding: utf-8 -*-
+
+# This code is part of Qiskit.
+#
+# (C) Copyright IBM 2019.
+#
+# This code is licensed under the Apache License, Version 2.0. You may
+# obtain a copy of this license in the LICENSE.txt file in the root directory
+# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
+#
+# Any modifications or derivative works of this code must retain this
+# copyright notice, and modified files need to carry a notice indicating
+# that they have been altered from the originals.
+
+"""The simplified 3-controlled Toffoli gate."""
+
+import numpy
+
+from qiskit.circuit import QuantumCircuit, Gate, QuantumRegister
+from qiskit.extensions.standard.u1 import U1Gate
+from qiskit.extensions.standard.u2 import U2Gate
+from qiskit.extensions.standard.x import CnotGate
+from qiskit.qasm import pi
+
+
+class RCCCXGate(Gate):
+    """The simplified 3-controlled Toffoli gate.
+
+    The simplified Toffoli gate implements the Toffoli gate up to relative phases.
+    Note, that the simplified Toffoli is not equivalent to the Toffoli. But can be used in places
+    where the Toffoli gate is uncomputed again.
+
+    This concrete implementation is from https://arxiv.org/abs/1508.03273, the complete circuit
+    of Fig. 4.
+    """
+
+    def __init__(self):
+        """Create a new PCCCX gate."""
+        super().__init__('rcccx', 4, [])
+
+    def _define(self):
+        """
+        gate rcccx a,b,c,d
+        { u2(0,pi) d;
+          u1(pi/4) d;
+          cx c,d;
+          u1(-pi/4) d;
+          u2(0,pi) d;
+          cx a,d;
+          u1(pi/4) d;
+          cx b,d;
+          u1(-pi/4) d;
+          cx a,d;
+          u1(pi/4) d;
+          cx b,d;
+          u1(-pi/4) d;
+          u2(0,pi) d;
+          u1(pi/4) d;
+          cx c,d;
+          u1(-pi/4) d;
+          u2(0,pi) d;
+        }
+        """
+        definition = []
+        q = QuantumRegister(4, 'q')
+
+        rule = [
+            (U2Gate(0, pi), [q[3]], []),  # H gate
+            (U1Gate(pi / 4), [q[3]], []),  # T gate
+            (CnotGate(), [q[2], q[3]], []),
+            (U1Gate(-pi / 4), [q[3]], []),  # inverse T gate
+            (U2Gate(0, pi), [q[3]], []),
+            (CnotGate(), [q[0], q[3]], []),
+            (U1Gate(pi / 4), [q[3]], []),
+            (CnotGate(), [q[1], q[3]], []),
+            (U1Gate(-pi / 4), [q[3]], []),
+            (CnotGate(), [q[0], q[3]], []),
+            (U1Gate(pi / 4), [q[3]], []),
+            (CnotGate(), [q[1], q[3]], []),
+            (U1Gate(-pi / 4), [q[3]], []),
+            (U2Gate(0, pi), [q[3]], []),
+            (U1Gate(pi / 4), [q[3]], []),
+            (CnotGate(), [q[2], q[3]], []),
+            (U1Gate(-pi / 4), [q[3]], []),
+            (U2Gate(0, pi), [q[3]], []),
+        ]
+        for inst in rule:
+            definition.append(inst)
+        self.definition = definition
+
+    def to_matrix(self):
+        """Return a numpy.array for the PCCCX gate."""
+        return numpy.array([[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
+                            [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
+                            [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
+                            [0, 0, 0, 1j, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
+                            [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
+                            [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
+                            [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0],
+                            [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
+                            [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0],
+                            [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0],
+                            [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0],
+                            [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1j, 0, 0, 0, 0],
+                            [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0],
+                            [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0],
+                            [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0],
+                            [0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0]], dtype=complex)
+
+
+def rcccx(self, ctl1, ctl2, ctl3, tgt):
+    """Apply the simplified, relative-phase 3-control Toffoli gate."""
+    return self.append(RCCCXGate(), [ctl1, ctl2, ctl3, tgt], [])
+
+
+QuantumCircuit.rcccx = rcccx

qiskit/extensions/standard/rccx.py

@@ -0,0 +1,91 @@
+# -*- coding: utf-8 -*-
+
+# This code is part of Qiskit.
+#
+# (C) Copyright IBM 2020.
+#
+# This code is licensed under the Apache License, Version 2.0. You may
+# obtain a copy of this license in the LICENSE.txt file in the root directory
+# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
+#
+# Any modifications or derivative works of this code must retain this
+# copyright notice, and modified files need to carry a notice indicating
+# that they have been altered from the originals.
+
+"""The simplified Toffoli gate."""
+
+import numpy
+
+from qiskit.circuit import QuantumCircuit, Gate, QuantumRegister
+from qiskit.extensions.standard.u1 import U1Gate
+from qiskit.extensions.standard.u2 import U2Gate
+from qiskit.extensions.standard.x import CnotGate
+from qiskit.qasm import pi
+
+
+class RCCXGate(Gate):
+    """The simplified Toffoli gate, also referred to as Margolus gate.
+
+    The simplified Toffoli gate implements the Toffoli gate up to relative phases.
+    This implementation requires three CX gates which is the minimal amount possible,
+    as shown in https://arxiv.org/abs/quant-ph/0312225.
+    Note, that the simplified Toffoli is not equivalent to the Toffoli. But can be used in places
+    where the Toffoli gate is uncomputed again.
+
+    This concrete implementation is from https://arxiv.org/abs/1508.03273, the dashed box
+    of Fig. 3.
+    """
+
+    def __init__(self):
+        """Create a new simplified CCX gate."""
+        super().__init__('rccx', 3, [])
+
+    def _define(self):
+        """
+        gate rccx a,b,c
+        { u2(0,pi) c;
+          u1(pi/4) c;
+          cx b, c;
+          u1(-pi/4) c;
+          cx a, c;
+          u1(pi/4) c;
+          cx b, c;
+          u1(-pi/4) c;
+          u2(0,pi) c;
+        }
+        """
+        definition = []
+        q = QuantumRegister(3, 'q')
+        rule = [
+            (U2Gate(0, pi), [q[2]], []),  # H gate
+            (U1Gate(pi / 4), [q[2]], []),  # T gate
+            (CnotGate(), [q[1], q[2]], []),
+            (U1Gate(-pi / 4), [q[2]], []),  # inverse T gate
+            (CnotGate(), [q[0], q[2]], []),
+            (U1Gate(pi / 4), [q[2]], []),
+            (CnotGate(), [q[1], q[2]], []),
+            (U1Gate(-pi / 4), [q[2]], []),  # inverse T gate
+            (U2Gate(0, pi), [q[2]], []),  # H gate
+        ]
+        for inst in rule:
+            definition.append(inst)
+        self.definition = definition
+
+    def to_matrix(self):
+        """Return a numpy.array for the simplified CCX gate."""
+        return numpy.array([[1, 0, 0, 0, 0, 0, 0, 0],
+                            [0, 1, 0, 0, 0, 0, 0, 0],
+                            [0, 0, 1, 0, 0, 0, 0, 0],
+                            [0, 0, 0, 0, 0, 0, 0, -1j],
+                            [0, 0, 0, 0, 1, 0, 0, 0],
+                            [0, 0, 0, 0, 0, -1, 0, 0],
+                            [0, 0, 0, 0, 0, 0, 1, 0],
+                            [0, 0, 0, 1j, 0, 0, 0, 0]], dtype=complex)
+
+
+def rccx(self, ctl1, ctl2, tgt):
+    """Apply the simplified, relative-phase Toffoli gate."""
+    return self.append(RCCXGate(), [ctl1, ctl2, tgt], [])
+
+
+QuantumCircuit.rccx = rccx

qiskit/qasm/libs/qelib1.inc

@@ -140,3 +140,38 @@ gate rzz(theta) a,b
   u1(theta) b;
   cx a,b;
 }
+// relative-phase CCX
+gate rccx a,b,c
+{
+  u2(0,pi) c;
+  u1(pi/4) c;
+  cx b, c;
+  u1(-pi/4) c;
+  cx a, c;
+  u1(pi/4) c;
+  cx b, c;
+  u1(-pi/4) c;
+  u2(0,pi) c;
+}
+// relative-phase CCCX
+gate rcccx a,b,c,d
+{
+  u2(0,pi) d;
+  u1(pi/4) d;
+  cx c,d;
+  u1(-pi/4) d;
+  u2(0,pi) d;
+  cx a,d;
+  u1(pi/4) d;
+  cx b,d;
+  u1(-pi/4) d;
+  cx a,d;
+  u1(pi/4) d;
+  cx b,d;
+  u1(-pi/4) d;
+  u2(0,pi) d;
+  u1(pi/4) d;
+  cx c,d;
+  u1(-pi/4) d;
+  u2(0,pi) d;
+}