diff --git a/doc/source/api-reference/qibo.rst b/doc/source/api-reference/qibo.rst
index 53cf772628..8e4d156269 100644
--- a/doc/source/api-reference/qibo.rst
+++ b/doc/source/api-reference/qibo.rst
@@ -1964,6 +1964,12 @@ Matrix exponentiation
 .. autofunction:: qibo.quantum_info.matrix_exponentiation
 
 
+Matrix power
+""""""""""""
+
+.. autofunction:: qibo.quantum_info.matrix_power
+
+
 Quantum Networks
 ^^^^^^^^^^^^^^^^
 
diff --git a/poetry.lock b/poetry.lock
index 53bd97e80e..a995eca8f6 100644
--- a/poetry.lock
+++ b/poetry.lock
@@ -1,4 +1,4 @@
-# This file is automatically @generated by Poetry 1.7.0 and should not be changed by hand.
+# This file is automatically @generated by Poetry 1.8.3 and should not be changed by hand.
 
 [[package]]
 name = "absl-py"
@@ -1403,19 +1403,19 @@ files = [
 
 [[package]]
 name = "filelock"
-version = "3.15.4"
+version = "3.16.1"
 description = "A platform independent file lock."
 optional = false
 python-versions = ">=3.8"
 files = [
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-    {file = "filelock-3.15.4.tar.gz", hash = "sha256:2207938cbc1844345cb01a5a95524dae30f0ce089eba5b00378295a17e3e90cb"},
+    {file = "filelock-3.16.1-py3-none-any.whl", hash = "sha256:2082e5703d51fbf98ea75855d9d5527e33d8ff23099bec374a134febee6946b0"},
+    {file = "filelock-3.16.1.tar.gz", hash = "sha256:c249fbfcd5db47e5e2d6d62198e565475ee65e4831e2561c8e313fa7eb961435"},
 ]
 
 [package.extras]
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-testing = ["covdefaults (>=2.3)", "coverage (>=7.3.2)", "diff-cover (>=8.0.1)", "pytest (>=7.4.3)", "pytest-asyncio (>=0.21)", "pytest-cov (>=4.1)", "pytest-mock (>=3.12)", "pytest-timeout (>=2.2)", "virtualenv (>=20.26.2)"]
-typing = ["typing-extensions (>=4.8)"]
+docs = ["furo (>=2024.8.6)", "sphinx (>=8.0.2)", "sphinx-autodoc-typehints (>=2.4.1)"]
+testing = ["covdefaults (>=2.3)", "coverage (>=7.6.1)", "diff-cover (>=9.2)", "pytest (>=8.3.3)", "pytest-asyncio (>=0.24)", "pytest-cov (>=5)", "pytest-mock (>=3.14)", "pytest-timeout (>=2.3.1)", "virtualenv (>=20.26.4)"]
+typing = ["typing-extensions (>=4.12.2)"]
 
 [[package]]
 name = "flatbuffers"
@@ -1648,69 +1648,77 @@ grpc = ["grpcio (>=1.44.0,<2.0.0.dev0)"]
 
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 [package.extras]
@@ -1897,15 +1905,18 @@ socks = ["socksio (==1.*)"]
 
 [[package]]
 name = "idna"
-version = "3.8"
+version = "3.10"
 description = "Internationalized Domain Names in Applications (IDNA)"
 optional = false
 python-versions = ">=3.6"
 files = [
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 ]
 
+[package.extras]
+all = ["flake8 (>=7.1.1)", "mypy (>=1.11.2)", "pytest (>=8.3.2)", "ruff (>=0.6.2)"]
+
 [[package]]
 name = "imagesize"
 version = "1.4.1"
@@ -1919,32 +1930,36 @@ files = [
 
 [[package]]
 name = "importlib-metadata"
-version = "8.4.0"
+version = "8.5.0"
 description = "Read metadata from Python packages"
 optional = false
 python-versions = ">=3.8"
 files = [
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 ]
 
 [package.dependencies]
-zipp = ">=0.5"
+zipp = ">=3.20"
 
 [package.extras]
+check = ["pytest-checkdocs (>=2.4)", "pytest-ruff (>=0.2.1)"]
+cover = ["pytest-cov"]
 doc = ["furo", "jaraco.packaging (>=9.3)", "jaraco.tidelift (>=1.4)", "rst.linker (>=1.9)", "sphinx (>=3.5)", "sphinx-lint"]
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 perf = ["ipython"]
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+type = ["pytest-mypy"]
 
 [[package]]
 name = "importlib-resources"
-version = "6.4.4"
+version = "6.4.5"
 description = "Read resources from Python packages"
 optional = false
 python-versions = ">=3.8"
 files = [
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 ]
 
 [package.dependencies]
@@ -2167,13 +2182,13 @@ format-nongpl = ["fqdn", "idna", "isoduration", "jsonpointer (>1.13)", "rfc3339-
 
 [[package]]
 name = "jupyter-client"
-version = "8.6.2"
+version = "8.6.3"
 description = "Jupyter protocol implementation and client libraries"
 optional = false
 python-versions = ">=3.8"
 files = [
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 ]
 
 [package.dependencies]
@@ -2407,6 +2422,7 @@ description = "Clang Python Bindings, mirrored from the official LLVM repo: http
 optional = false
 python-versions = "*"
 files = [
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@@ -2709,28 +2725,28 @@ tbb = "==2021.*"
 
 [[package]]
 name = "ml-dtypes"
-version = "0.4.0"
+version = "0.4.1"
 description = ""
 optional = false
 python-versions = ">=3.9"
 files = [
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 [package.dependencies]
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@@ -3585,19 +3609,19 @@ xmp = ["defusedxml"]
 
 [[package]]
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 python-versions = ">=3.8"
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 [[package]]
 name = "pluggy"
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 [[package]]
@@ -3751,24 +3775,24 @@ tests = ["pytest"]
 
 [[package]]
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 python-versions = ">=3.8"
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 ]
 
 [[package]]
 name = "pyasn1-modules"
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 description = "A collection of ASN.1-based protocols modules"
 optional = false
 python-versions = ">=3.8"
 files = [
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 ]
 
 [package.dependencies]
@@ -4180,13 +4204,13 @@ files = [
 
 [[package]]
 name = "pytz"
-version = "2024.1"
+version = "2024.2"
 description = "World timezone definitions, modern and historical"
 optional = false
 python-versions = "*"
 files = [
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 ]
 
 [[package]]
@@ -4429,7 +4453,7 @@ develop = false
 [package.dependencies]
 numba = ">=0.59.0"
 psutil = "^5.9.5"
-qibo = "^0.2.10"
+qibo = {git = "https://github.com/qiboteam/qibo.git", branch = "matrix_power"}
 scipy = "^1.10.1"
 
 [package.extras]
@@ -4440,7 +4464,7 @@ cuquantum = ["cuquantum-python-cu12 (>=23.10.0,<24.0.0)"]
 type = "git"
 url = "https://github.com/qiboteam/qibojit.git"
 reference = "HEAD"
-resolved_reference = "0d9bbd2f0f3545293cdb2ac039680b8dbceaf55e"
+resolved_reference = "5dd522f84bdd2a66d67b41df990beb3135b3a9f5"
 
 [[package]]
 name = "qibotn"
@@ -4495,30 +4519,32 @@ tests = ["coverage", "pytest", "pytest-cov"]
 
 [[package]]
 name = "qulacs"
-version = "0.6.4.1"
+version = "0.6.10"
 description = "Quantum circuit simulator for research"
 optional = false
 python-versions = "*"
 files = [
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 [[package]]
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 ]
 
 [package.dependencies]
@@ -4774,11 +4800,11 @@ threadpoolctl = ">=3.1.0"
 [package.extras]
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+    {file = "SQLAlchemy-2.0.35-py3-none-any.whl", hash = "sha256:2ab3f0336c0387662ce6221ad30ab3a5e6499aab01b9790879b6578fd9b8faa1"},
+    {file = "sqlalchemy-2.0.35.tar.gz", hash = "sha256:e11d7ea4d24f0a262bccf9a7cd6284c976c5369dac21db237cff59586045ab9f"},
 ]
 
 [package.dependencies]
@@ -5719,13 +5745,13 @@ files = [
 
 [[package]]
 name = "urllib3"
-version = "2.2.2"
+version = "2.2.3"
 description = "HTTP library with thread-safe connection pooling, file post, and more."
 optional = false
 python-versions = ">=3.8"
 files = [
-    {file = "urllib3-2.2.2-py3-none-any.whl", hash = "sha256:a448b2f64d686155468037e1ace9f2d2199776e17f0a46610480d311f73e3472"},
-    {file = "urllib3-2.2.2.tar.gz", hash = "sha256:dd505485549a7a552833da5e6063639d0d177c04f23bc3864e41e5dc5f612168"},
+    {file = "urllib3-2.2.3-py3-none-any.whl", hash = "sha256:ca899ca043dcb1bafa3e262d73aa25c465bfb49e0bd9dd5d59f1d0acba2f8fac"},
+    {file = "urllib3-2.2.3.tar.gz", hash = "sha256:e7d814a81dad81e6caf2ec9fdedb284ecc9c73076b62654547cc64ccdcae26e9"},
 ]
 
 [package.extras]
@@ -5896,13 +5922,13 @@ files = [
 
 [[package]]
 name = "zipp"
-version = "3.20.1"
+version = "3.20.2"
 description = "Backport of pathlib-compatible object wrapper for zip files"
 optional = false
 python-versions = ">=3.8"
 files = [
-    {file = "zipp-3.20.1-py3-none-any.whl", hash = "sha256:9960cd8967c8f85a56f920d5d507274e74f9ff813a0ab8889a5b5be2daf44064"},
-    {file = "zipp-3.20.1.tar.gz", hash = "sha256:c22b14cc4763c5a5b04134207736c107db42e9d3ef2d9779d465f5f1bcba572b"},
+    {file = "zipp-3.20.2-py3-none-any.whl", hash = "sha256:a817ac80d6cf4b23bf7f2828b7cabf326f15a001bea8b1f9b49631780ba28350"},
+    {file = "zipp-3.20.2.tar.gz", hash = "sha256:bc9eb26f4506fda01b81bcde0ca78103b6e62f991b381fec825435c836edbc29"},
 ]
 
 [package.extras]
diff --git a/src/qibo/backends/abstract.py b/src/qibo/backends/abstract.py
index b26ed32a6d..468fa89008 100644
--- a/src/qibo/backends/abstract.py
+++ b/src/qibo/backends/abstract.py
@@ -1,4 +1,5 @@
 import abc
+from typing import Union
 
 from qibo.config import raise_error
 
@@ -355,6 +356,21 @@ def calculate_matrix_exp(
         """
         raise_error(NotImplementedError)
 
+    @abc.abstractmethod
+    def calculate_matrix_power(
+        self, matrix, power: Union[float, int]
+    ):  # pragma: no cover
+        """Calculate the (fractional) ``power`` :math:`\\alpha` of ``matrix`` :math:`A`,
+        i.e. :math:`A^{\\alpha}`.
+
+        .. note::
+            For the ``pytorch`` backend, this method relies on a copy of the original tensor.
+            This may break the gradient flow. For the GPU backends (i.e. ``cupy`` and
+            ``cuquantum``), this method falls back to CPU whenever ``power`` is not
+            an integer.
+        """
+        raise_error(NotImplementedError)
+
     @abc.abstractmethod
     def calculate_hamiltonian_matrix_product(
         self, matrix1, matrix2
diff --git a/src/qibo/backends/numpy.py b/src/qibo/backends/numpy.py
index d1bf8a6bf2..fe1441b7c6 100644
--- a/src/qibo/backends/numpy.py
+++ b/src/qibo/backends/numpy.py
@@ -1,9 +1,10 @@
 import collections
 import math
+from typing import Union
 
 import numpy as np
 from scipy import sparse
-from scipy.linalg import block_diag
+from scipy.linalg import block_diag, fractional_matrix_power
 
 from qibo import __version__
 from qibo.backends import einsum_utils
@@ -768,6 +769,14 @@ def calculate_matrix_exp(self, a, matrix, eigenvectors=None, eigenvalues=None):
         ud = self.np.transpose(np.conj(eigenvectors))
         return self.np.matmul(eigenvectors, self.np.matmul(expd, ud))
 
+    def calculate_matrix_power(self, matrix, power: Union[float, int]):
+        if not isinstance(power, (float, int)):
+            raise_error(
+                TypeError,
+                f"``power`` must be either float or int, but it is type {type(power)}.",
+            )
+        return fractional_matrix_power(matrix, power)
+
     # TODO: remove this method
     def calculate_hamiltonian_matrix_product(self, matrix1, matrix2):
         return matrix1 @ matrix2
diff --git a/src/qibo/backends/pytorch.py b/src/qibo/backends/pytorch.py
index d7612f8e49..22fbbc5640 100644
--- a/src/qibo/backends/pytorch.py
+++ b/src/qibo/backends/pytorch.py
@@ -199,6 +199,11 @@ def calculate_matrix_exp(self, a, matrix, eigenvectors=None, eigenvalues=None):
         ud = self.np.conj(eigenvectors).T
         return self.np.matmul(eigenvectors, self.np.matmul(expd, ud))
 
+    def calculate_matrix_power(self, matrix, power):
+        copied = self.to_numpy(self.np.copy(matrix))
+        copied = super().calculate_matrix_power(copied, power)
+        return self.cast(copied, dtype=copied.dtype)
+
     def _test_regressions(self, name):
         if name == "test_measurementresult_apply_bitflips":
             return [
diff --git a/src/qibo/quantum_info/entropies.py b/src/qibo/quantum_info/entropies.py
index ef0f5edd80..31972c4ff5 100644
--- a/src/qibo/quantum_info/entropies.py
+++ b/src/qibo/quantum_info/entropies.py
@@ -3,12 +3,10 @@
 from typing import Union
 
 import numpy as np
-from scipy.linalg import fractional_matrix_power
 
 from qibo.backends import _check_backend
-from qibo.backends.pytorch import PyTorchBackend
 from qibo.config import PRECISION_TOL, raise_error
-from qibo.quantum_info.linalg_operations import partial_trace
+from qibo.quantum_info.linalg_operations import matrix_power, partial_trace
 from qibo.quantum_info.metrics import _check_hermitian, purity
 
 
@@ -724,7 +722,7 @@ def renyi_entropy(state, alpha: Union[float, int], base: float = 2, backend=None
             / np.log2(base)
         )
 
-    log = backend.np.log2(backend.np.trace(_matrix_power(state, alpha, backend)))
+    log = backend.np.log2(backend.np.trace(matrix_power(state, alpha, backend)))
 
     return (1 / (1 - alpha)) * log / np.log2(base)
 
@@ -823,8 +821,8 @@ def relative_renyi_entropy(
         return relative_von_neumann_entropy(state, target, base, backend=backend)
 
     if alpha == np.inf:
-        new_state = _matrix_power(state, 0.5, backend)
-        new_target = _matrix_power(target, 0.5, backend)
+        new_state = matrix_power(state, 0.5, backend)
+        new_target = matrix_power(target, 0.5, backend)
 
         log = backend.np.log2(
             backend.calculate_norm_density_matrix(new_state @ new_target, order=1)
@@ -832,8 +830,8 @@ def relative_renyi_entropy(
 
         return -2 * log / np.log2(base)
 
-    log = _matrix_power(state, alpha, backend)
-    log = log @ _matrix_power(target, 1 - alpha, backend)
+    log = matrix_power(state, alpha, backend)
+    log = log @ matrix_power(target, 1 - alpha, backend)
     log = backend.np.log2(backend.np.trace(log))
 
     return (1 / (alpha - 1)) * log / np.log2(base)
@@ -891,7 +889,7 @@ def tsallis_entropy(state, alpha: float, base: float = 2, backend=None):
         return von_neumann_entropy(state, base=base, backend=backend)
 
     return (1 / (1 - alpha)) * (
-        backend.np.trace(_matrix_power(state, alpha, backend)) - 1
+        backend.np.trace(matrix_power(state, alpha, backend)) - 1
     )
 
 
@@ -953,19 +951,3 @@ def entanglement_entropy(
     )
 
     return entropy_entanglement
-
-
-def _matrix_power(matrix, alpha, backend):
-    """Calculates ``matrix ** alpha`` according to backend."""
-    if backend.__class__.__name__ in [
-        "CupyBackend",
-        "CuQuantumBackend",
-    ]:  # pragma: no cover
-        new_matrix = backend.to_numpy(matrix)
-    else:
-        new_matrix = backend.np.copy(matrix)
-
-    if len(new_matrix.shape) == 1:
-        new_matrix = backend.np.outer(new_matrix, backend.np.conj(new_matrix))
-
-    return backend.cast(fractional_matrix_power(backend.to_numpy(new_matrix), alpha))
diff --git a/src/qibo/quantum_info/linalg_operations.py b/src/qibo/quantum_info/linalg_operations.py
index ae87ba4e12..6fc48e6e74 100644
--- a/src/qibo/quantum_info/linalg_operations.py
+++ b/src/qibo/quantum_info/linalg_operations.py
@@ -196,3 +196,21 @@ def matrix_exponentiation(
     backend = _check_backend(backend)
 
     return backend.calculate_matrix_exp(phase, matrix, eigenvectors, eigenvalues)
+
+
+def matrix_power(matrix, power: Union[float, int], backend=None):
+    """Given a ``matrix`` :math:`A` and power :math:`\\alpha`, calculate :math:`A^{\\alpha}`.
+
+    Args:
+        matrix (ndarray): matrix whose power to calculate.
+        power (float or int): power to raise ``matrix`` to.
+        backend (:class:`qibo.backends.abstract.Backend`, optional): backend
+            to be used in the execution. If ``None``, it uses
+            :class:`qibo.backends.GlobalBackend`. Defaults to ``None``.
+
+    Returns:
+        ndarray: matrix power :math:`A^{\\alpha}`.
+    """
+    backend = _check_backend(backend)
+
+    return backend.calculate_matrix_power(matrix, power)
diff --git a/tests/test_quantum_info_entropies.py b/tests/test_quantum_info_entropies.py
index a0644a17c4..b383effed6 100644
--- a/tests/test_quantum_info_entropies.py
+++ b/tests/test_quantum_info_entropies.py
@@ -1,10 +1,8 @@
 import numpy as np
 import pytest
-from scipy.linalg import sqrtm
 
 from qibo.config import PRECISION_TOL
 from qibo.quantum_info.entropies import (
-    _matrix_power,
     classical_mutual_information,
     classical_relative_entropy,
     classical_relative_renyi_entropy,
@@ -19,6 +17,7 @@
     tsallis_entropy,
     von_neumann_entropy,
 )
+from qibo.quantum_info.linalg_operations import matrix_power
 from qibo.quantum_info.random_ensembles import (
     random_density_matrix,
     random_statevector,
@@ -646,8 +645,18 @@ def test_relative_renyi_entropy(backend, alpha, base, state_flag, target_flag):
             if alpha == 1.0:
                 log = relative_von_neumann_entropy(state, target, base, backend=backend)
             elif alpha == np.inf:
-                new_state = _matrix_power(state, 0.5, backend)
-                new_target = _matrix_power(target, 0.5, backend)
+                state_outer = (
+                    backend.np.outer(state, backend.np.conj(state.T))
+                    if state_flag
+                    else state
+                )
+                target_outer = (
+                    backend.np.outer(target, backend.np.conj(target.T))
+                    if target_flag
+                    else target
+                )
+                new_state = matrix_power(state_outer, 0.5, backend)
+                new_target = matrix_power(target_outer, 0.5, backend)
 
                 log = backend.np.log2(
                     backend.calculate_norm_density_matrix(
@@ -663,8 +672,8 @@ def test_relative_renyi_entropy(backend, alpha, base, state_flag, target_flag):
                 if len(target.shape) == 1:
                     target = backend.np.outer(target, backend.np.conj(target))
 
-                log = _matrix_power(state, alpha, backend)
-                log = log @ _matrix_power(target, 1 - alpha, backend)
+                log = matrix_power(state, alpha, backend)
+                log = log @ matrix_power(target, 1 - alpha, backend)
                 log = backend.np.log2(backend.np.trace(log))
 
                 log = (1 / (alpha - 1)) * log / np.log2(base)
@@ -710,7 +719,7 @@ def test_tsallis_entropy(backend, alpha, base):
         target = von_neumann_entropy(state, base=base, backend=backend)
     else:
         target = (1 / (1 - alpha)) * (
-            backend.np.trace(_matrix_power(state, alpha, backend)) - 1
+            backend.np.trace(matrix_power(state, alpha, backend)) - 1
         )
 
     backend.assert_allclose(
diff --git a/tests/test_quantum_info_operations.py b/tests/test_quantum_info_operations.py
index 057b69e6ea..3d97f1f63a 100644
--- a/tests/test_quantum_info_operations.py
+++ b/tests/test_quantum_info_operations.py
@@ -5,8 +5,10 @@
 from qibo.quantum_info.linalg_operations import (
     anticommutator,
     commutator,
+    matrix_power,
     partial_trace,
 )
+from qibo.quantum_info.metrics import purity
 from qibo.quantum_info.random_ensembles import random_density_matrix, random_statevector
 
 
@@ -109,3 +111,22 @@ def test_partial_trace(backend, density_matrix):
     Id = backend.identity_density_matrix(1, normalize=True)
 
     backend.assert_allclose(traced, Id)
+
+
+@pytest.mark.parametrize("power", [2, 2.0, "2"])
+def test_matrix_power(backend, power):
+    nqubits = 2
+    dims = 2**nqubits
+
+    state = random_density_matrix(dims, backend=backend)
+
+    if isinstance(power, str):
+        with pytest.raises(TypeError):
+            test = matrix_power(state, power, backend)
+    else:
+        power = matrix_power(state, power, backend)
+
+        backend.assert_allclose(
+            float(backend.np.real(backend.np.trace(power))),
+            purity(state, backend=backend),
+        )