Add two-qubit unitary decomposition for (inverse) sqrt-iSWAP (#4213)

- Add the method cirq.two_qubit_matrix_to_sqrt_iswap_operations() to optimally decompose with SQRT_ISWAP or SQRT_ISWAP_INV gates.
- Add cirq.SQRT_ISWAP and cirq.SQRT_ISWAP_INV (aliases for cirq.ISWAP**0.5 and cirq.ISWAP**-0.5).

Author: cduck

cirq-core/cirq/__init__.py

@@ -271,6 +271,8 @@
     SingleQubitCliffordGate,
     SingleQubitGate,
     SingleQubitPauliStringGateOperation,
+    SQRT_ISWAP,
+    SQRT_ISWAP_INV,
     SWAP,
     SwapPowGate,
     T,
@@ -326,6 +328,7 @@
     SynchronizeTerminalMeasurements,
     two_qubit_matrix_to_operations,
     two_qubit_matrix_to_diagonal_and_operations,
+    two_qubit_matrix_to_sqrt_iswap_operations,
     three_qubit_matrix_to_operations,
 )
 

cirq-core/cirq/ops/__init__.py

@@ -241,6 +241,8 @@
     ISWAP,
     ISwapPowGate,
     riswap,
+    SQRT_ISWAP,
+    SQRT_ISWAP_INV,
     SWAP,
     SwapPowGate,
 )

cirq-core/cirq/ops/swap_gates.py

@@ -16,9 +16,12 @@
 This module creates Gate instances for the following gates:
     SWAP: the swap gate.
     ISWAP: a swap gate with a phase on the swapped subspace.
+    SQRT_ISWAP: square root of the ISWAP gate.
+    SQRT_ISWAP_INV: inverse square root of the ISWAP gate.
 
 Each of these are implemented as EigenGates, which means that they can be
-raised to a power (i.e. cirq.ISWAP**0.5). See the definition in EigenGate.
+raised to a power (i.e. SQRT_ISWAP_INV=cirq.ISWAP**-0.5). See the definition in
+EigenGate.
 """
 
 from typing import Optional, Tuple, TYPE_CHECKING, List, Sequence
@@ -332,3 +335,33 @@ def riswap(rads: value.TParamVal) -> ISwapPowGate:
     ```
     """,
 )
+
+SQRT_ISWAP = ISwapPowGate(exponent=0.5)
+document(
+    SQRT_ISWAP,
+    """The square root of iswap gate.
+
+    Matrix:
+    ```
+        [[1, 0,    0,    0],
+         [0, 1/√2, i/√2, 0],
+         [0, i/√2, 1/√2, 0],
+         [0, 0,    0,    1]]
+    ```
+    """,
+)
+
+SQRT_ISWAP_INV = ISwapPowGate(exponent=-0.5)
+document(
+    SQRT_ISWAP_INV,
+    """The inverse square root of iswap gate.
+
+    Matrix:
+    ```
+        [[1, 0,     0,     0],
+         [0, 1/√2,  -i/√2, 0],
+         [0, -i/√2, 1/√2,  0],
+         [0, 0,     0,     1]]
+    ```
+    """,
+)

cirq-core/cirq/ops/swap_gates_test.py

@@ -109,6 +109,34 @@ def test_iswap_unitary():
     # yapf: enable
 
 
+def test_sqrt_iswap_unitary():
+    # yapf: disable
+    cirq.testing.assert_allclose_up_to_global_phase(
+        cirq.unitary(cirq.SQRT_ISWAP),
+        # Reference for the sqrt-iSWAP gate's matrix:
+        # https://arxiv.org/abs/2105.06074
+        np.array([[1, 0,         0,         0],
+                  [0, 1/2**0.5,  1j/2**0.5, 0],
+                  [0, 1j/2**0.5, 1/2**0.5,  0],
+                  [0, 0,         0,         1]]),
+        atol=1e-8)
+    # yapf: enable
+
+
+def test_sqrt_iswap_inv_unitary():
+    # yapf: disable
+    cirq.testing.assert_allclose_up_to_global_phase(
+        cirq.unitary(cirq.SQRT_ISWAP_INV),
+        # Reference for the inv-sqrt-iSWAP gate's matrix:
+        # https://arxiv.org/abs/2105.06074
+        np.array([[1, 0,          0,          0],
+                  [0, 1/2**0.5,   -1j/2**0.5, 0],
+                  [0, -1j/2**0.5, 1/2**0.5,   0],
+                  [0, 0,          0,          1]]),
+        atol=1e-8)
+    # yapf: enable
+
+
 def test_repr():
     assert repr(cirq.SWAP) == 'cirq.SWAP'
     assert repr(cirq.SWAP ** 0.5) == '(cirq.SWAP**0.5)'

cirq-core/cirq/optimizers/__init__.py

@@ -90,6 +90,9 @@
     two_qubit_matrix_to_operations,
     two_qubit_matrix_to_diagonal_and_operations,
 )
+from cirq.optimizers.two_qubit_to_sqrt_iswap import (
+    two_qubit_matrix_to_sqrt_iswap_operations,
+)
 
 from cirq.optimizers.two_qubit_to_fsim import (
     decompose_two_qubit_interaction_into_four_fsim_gates,

cirq-core/cirq/optimizers/two_qubit_decompositions.py

@@ -14,7 +14,7 @@
 
 """Utility methods related to optimizing quantum circuits."""
 
-from typing import Iterable, List, Tuple, Optional, cast, TYPE_CHECKING
+from typing import Iterable, List, Sequence, Tuple, Optional, cast, TYPE_CHECKING
 
 import numpy as np
 
@@ -161,7 +161,7 @@ def _xx_yy_zz_interaction_via_full_czs(
     yield ops.H(q1)
 
 
-def _cleanup_operations(operations: List[ops.Operation]):
+def _cleanup_operations(operations: Sequence[ops.Operation]):
     circuit = circuits.Circuit(operations)
     merge_single_qubit_gates.merge_single_qubit_gates_into_phased_x_z(circuit)
     eject_phased_paulis.EjectPhasedPaulis().optimize_circuit(circuit)