Performance improvement of SparsePauliOp.to_matrix (Qiskit#9620)

* optimize SparsePauliOp.to_matrix

* optimize dense

* proper vectorize

* update copyright year

* small opt

* update a comment

Author: t-imamichi

qiskit/quantum_info/operators/symplectic/base_pauli.py

@@ -1,6 +1,6 @@
 # This code is part of Qiskit.
 #
-# (C) Copyright IBM 2017, 2020
+# (C) Copyright IBM 2017, 2023
 #
 # 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
@@ -26,6 +26,10 @@
 from qiskit.quantum_info.operators.mixins import AdjointMixin, MultiplyMixin
 
 
+# utility for _to_matrix
+_PARITY = np.array([-1 if bin(i).count("1") % 2 else 1 for i in range(256)], dtype=complex)
+
+
 class BasePauli(BaseOperator, AdjointMixin, MultiplyMixin):
     r"""Symplectic representation of a list of N-qubit Paulis.
 
@@ -392,7 +396,7 @@ def _from_array(z, x, phase=0):
 
     @staticmethod
     def _to_matrix(z, x, phase=0, group_phase=False, sparse=False):
-        """Return the matrix matrix from symplectic representation.
+        """Return the matrix from symplectic representation.
 
         The Pauli is defined as :math:`P = (-i)^{phase + z.x} * Z^z.x^x`
         where ``array = [x, z]``.
@@ -430,7 +434,19 @@ def _to_matrix(z, x, phase=0, group_phase=False, sparse=False):
             coeff = (-1j) ** phase
         else:
             coeff = 1
-        data = np.array([coeff * (-1) ** (bin(i).count("1") % 2) for i in z_indices & indptr])
+
+        # Compute parities of `z_indices & indptr`, i.e.,
+        # np.array([(-1) ** bin(i).count("1") for i in z_indices & indptr])
+        vec_u64 = z_indices & indptr
+        mat_u8 = np.zeros((vec_u64.size, 8), dtype=np.uint8)
+        for i in range(8):
+            mat_u8[:, i] = vec_u64 & 255
+            vec_u64 >>= 8
+            if np.all(vec_u64 == 0):
+                break
+        parity = _PARITY[np.bitwise_xor.reduce(mat_u8, axis=1)]
+
+        data = coeff * parity
         if sparse:
             # Return sparse matrix
             from scipy.sparse import csr_matrix
@@ -439,8 +455,7 @@ def _to_matrix(z, x, phase=0, group_phase=False, sparse=False):
 
         # Build dense matrix using csr format
         mat = np.zeros((dim, dim), dtype=complex)
-        for i in range(dim):
-            mat[i][indices[indptr[i] : indptr[i + 1]]] = data[indptr[i] : indptr[i + 1]]
+        mat[range(dim), indices[:dim]] = data[:dim]
         return mat
 
     @staticmethod

test/python/quantum_info/operators/symplectic/test_sparse_pauli_op.py

@@ -1,6 +1,6 @@
 # This code is part of Qiskit.
 #
-# (C) Copyright IBM 2017, 2020.
+# (C) Copyright IBM 2017, 2023.
 #
 # 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
@@ -236,6 +236,20 @@ def test_to_matrix(self):
         for coeff, label in zip(coeffs, labels):
             target += coeff * pauli_mat(label)
         np.testing.assert_array_equal(spp_op.to_matrix(), target)
+        np.testing.assert_array_equal(spp_op.to_matrix(sparse=True).toarray(), target)
+
+    def test_to_matrix_large(self):
+        """Test to_matrix method with a large number of qubits."""
+        reps = 5
+        labels = ["XI" * reps, "YZ" * reps, "YY" * reps, "ZZ" * reps]
+        coeffs = [-3, 4.4j, 0.2 - 0.1j, 66.12]
+        spp_op = SparsePauliOp(labels, coeffs)
+        size = 1 << 2 * reps
+        target = np.zeros((size, size), dtype=complex)
+        for coeff, label in zip(coeffs, labels):
+            target += coeff * pauli_mat(label)
+        np.testing.assert_array_equal(spp_op.to_matrix(), target)
+        np.testing.assert_array_equal(spp_op.to_matrix(sparse=True).toarray(), target)
 
     def test_to_matrix_parameters(self):
         """Test to_matrix method for parameterized SparsePauliOp."""