diff --git a/qiskit_experiments/framework/cache_method.py b/qiskit_experiments/framework/cache_method.py
new file mode 100644
index 0000000000..e2dc58650f
--- /dev/null
+++ b/qiskit_experiments/framework/cache_method.py
@@ -0,0 +1,124 @@
+# This code is part of Qiskit.
+#
+# (C) Copyright IBM 2022.
+#
+# 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.
+"""
+Method decorator for caching regular methods in class instances.
+"""
+
+from typing import Union, Dict, Callable
+import functools
+
+
+def cache_method(cache: Union[Dict, str] = "_cache", cache_args: bool = True) -> Callable:
+    """Decorator for caching regular methods in classes.
+
+    .. note::
+
+        When specifying a cache an existing dictionary value will be
+        used as is. A string value will be used to check for an existing
+        dict under that attribute name in the class instance.
+        If the attribute is not present a new cache dict will be created
+        and stored in that class instance.
+
+    Args:
+        cache: A dictionary or attribute name string to use as cache.
+        cache_args: If True include method arg and kwarg values when
+                    matching cached values. These values must be hashable.
+
+    Returns:
+        The decorator for caching methods.
+    """
+    cache_fn = _cache_function(cache)
+    cache_key_fn = _cache_key_function(cache_args)
+
+    def cache_method_decorator(method: Callable) -> Callable:
+        """Decorator for caching method.
+
+        Args:
+            method: A method to cache.
+
+        Returns:
+            The wrapped cached method.
+        """
+
+        @functools.wraps(method)
+        def _cached_method(self, *args, **kwargs):
+            meth_cache = cache_fn(self, method)
+            key = cache_key_fn(*args, **kwargs)
+            if key in meth_cache:
+                return meth_cache[key]
+            result = method(self, *args, **kwargs)
+            meth_cache[key] = result
+            return result
+
+        return _cached_method
+
+    return cache_method_decorator
+
+
+def _cache_key_function(cache_args: bool) -> Callable:
+    """Return function for generating cache keys.
+
+    Args:
+        cache_args: If True include method arg and kwarg values when
+                    caching the method. If False all calls to the instances
+                    method will return the same cached value regardless of
+                    any arg or kwarg values.
+
+    Returns:
+        The functions for generating cache keys.
+    """
+    if not cache_args:
+
+        def _cache_key(*args, **kwargs):
+            # pylint: disable = unused-argument
+            return tuple()
+
+    else:
+
+        def _cache_key(*args, **kwargs):
+            return args + tuple(list(kwargs.items()))
+
+    return _cache_key
+
+
+def _cache_function(cache: Union[Dict, str]) -> Callable:
+    """Return function for initializing and accessing cache dict.
+
+    Args:
+        cache: The dictionary or cache attribute name to use. If a dict it
+               will be used directly, if a str a cache dict will be created
+               under that attribute name if one is not already present.
+
+    Returns:
+        The function for accessing the cache dict.
+    """
+    if isinstance(cache, str):
+
+        def _cache_fn(instance, method):
+            if not hasattr(instance, cache):
+                setattr(instance, cache, {})
+            instance_cache = getattr(instance, cache)
+            name = method.__name__
+            if name not in instance_cache:
+                instance_cache[name] = {}
+            return instance_cache[name]
+
+    else:
+
+        def _cache_fn(instance, method):
+            # pylint: disable = unused-argument
+            name = method.__name__
+            if name not in cache:
+                cache[name] = {}
+            return cache[name]
+
+    return _cache_fn
diff --git a/qiskit_experiments/library/tomography/basis/local_basis.py b/qiskit_experiments/library/tomography/basis/local_basis.py
index 7c39e46c5c..9356182441 100644
--- a/qiskit_experiments/library/tomography/basis/local_basis.py
+++ b/qiskit_experiments/library/tomography/basis/local_basis.py
@@ -12,13 +12,13 @@
 """
 Circuit basis for tomography preparation and measurement circuits
 """
-import functools
 from typing import Sequence, Optional, Tuple, Union, List, Dict
 import numpy as np
 from qiskit.circuit import QuantumCircuit, Instruction
 from qiskit.quantum_info import DensityMatrix, Statevector, Operator, SuperOp
 from qiskit.quantum_info.operators.channel.quantum_channel import QuantumChannel
 from qiskit.exceptions import QiskitError
+from qiskit_experiments.framework.cache_method import cache_method
 from .base_basis import PreparationBasis, MeasurementBasis
 
 # Typing object for POVM args of measurement basis
@@ -351,7 +351,7 @@ def matrix(self, index: Sequence[int], outcome: int, qubits: Optional[Sequence[i
             # a qubit not in the specified kwargs.
             raise ValueError(f"Invalid qubits for basis {self.name}") from ex
 
-    @functools.lru_cache(None)
+    @cache_method()
     def _outcome_indices(self, outcome: int, qubits: Tuple[int, ...]) -> Tuple[int, ...]:
         """Convert an outcome integer to a tuple of single-qubit outcomes"""
         num_outcomes = self._qubit_num_outcomes.get(qubits[0], self._default_num_outcomes)
diff --git a/releasenotes/notes/cache-method-3824562833460741.yaml b/releasenotes/notes/cache-method-3824562833460741.yaml
new file mode 100644
index 0000000000..e4b99fb7f6
--- /dev/null
+++ b/releasenotes/notes/cache-method-3824562833460741.yaml
@@ -0,0 +1,5 @@
+---
+developer:
+  - |
+    Adds a ``cache_method`` decorator for caching methods in classes. This
+    can be imported from ``qiskit_experiments.framework.cache_method``.
diff --git a/test/framework/test_cache_method.py b/test/framework/test_cache_method.py
new file mode 100644
index 0000000000..42e44832bf
--- /dev/null
+++ b/test/framework/test_cache_method.py
@@ -0,0 +1,138 @@
+# This code is part of Qiskit.
+#
+# (C) Copyright IBM 2022.
+#
+# 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.
+
+"""Tests cache_method decorator."""
+
+from test.base import QiskitExperimentsTestCase
+from qiskit_experiments.framework.cache_method import cache_method
+
+
+class TestCacheMethod(QiskitExperimentsTestCase):
+    """Test for cache_method decorator"""
+
+    def test_cache_args(self):
+        """Test cache_args=True"""
+
+        class CachedClass:
+            """Class with cached method"""
+
+            def __init__(self):
+                self.method_calls = 0
+
+            @cache_method(cache_args=True)
+            def method(self, *args, **kwargs):
+                """Test method for caching"""
+                self.method_calls += 1
+                return args, kwargs
+
+        obj = CachedClass()
+        size = 10
+        cached_vals = [obj.method(i, i) for i in range(size)]
+        for i, val in enumerate(cached_vals):
+            self.assertEqual(obj.method(i, i), val, msg="method didn't return cached value")
+        self.assertEqual(obj.method_calls, size, msg="Cached method was not evaluated once per arg")
+
+    def test_cache_args_kwargs(self):
+        """Test cache_args=True with args and kwargs"""
+
+        class CachedClass:
+            """Class with cached method"""
+
+            def __init__(self):
+                self.method_calls = 0
+
+            @cache_method(cache_args=True)
+            def method(self, *args, **kwargs):
+                """Test method for caching"""
+                self.method_calls += 1
+                return args, kwargs
+
+        obj = CachedClass()
+        args = (1, 2, 3)
+        names = ["a", "b", "c", "d"]
+        cached_vals = [obj.method(*args, name=name) for name in names]
+        for name, val in zip(names, cached_vals):
+            self.assertEqual(
+                obj.method(*args, name=name), val, msg="method didn't return cached value"
+            )
+        self.assertEqual(
+            obj.method_calls, len(names), msg="Cached method was not evaluated once per arg"
+        )
+
+    def test_cache_args_false(self):
+        """Test cache_args=False"""
+
+        class CachedClass:
+            """Class with cached method"""
+
+            def __init__(self):
+                self.method_calls = 0
+
+            @cache_method(cache_args=False)
+            def method(self, *args, **kwargs):
+                """Test method for caching"""
+                self.method_calls += 1
+                return args, kwargs
+
+        obj = CachedClass()
+        ret = obj.method(1999)
+        for i in range(10):
+            self.assertEqual(obj.method(i), ret, msg="method didn't return cached value")
+        self.assertEqual(obj.method_calls, 1, msg="Cached method was not evaluated once")
+
+    def test_non_hashable_raises(self):
+        """Test non hashable args raise"""
+
+        class CachedClass:
+            """Class with cached method"""
+
+            @cache_method()
+            def method(self, *args, **kwargs):
+                """Test method for caching"""
+                return args, kwargs
+
+        obj = CachedClass()
+        self.assertRaises(TypeError, obj.method, [1, 2, 3])
+        self.assertRaises(TypeError, obj.method, kwarg=[1, 2, 3])
+
+    def test_cache_name(self):
+        """Test decorator with a custom cache name"""
+
+        class CachedClass:
+            """Class with cached method"""
+
+            @cache_method(cache="memory")
+            def method(self, *args, **kwargs):
+                """Test method for caching"""
+                return args, kwargs
+
+        obj = CachedClass()
+        obj.method(1, 2, 3)
+        self.assertTrue(hasattr(obj, "memory"))
+        self.assertIn("method", getattr(obj, "memory", {}))
+
+    def test_cache_dict(self):
+        """Test decorate with custom cache value"""
+
+        external_cache = {}
+
+        class CachedClass:
+            """Class with cached method"""
+
+            @cache_method(cache=external_cache)
+            def method(self, *args, **kwargs):
+                """Test method for caching"""
+                return args, kwargs
+
+        obj = CachedClass()
+        obj.method(1, 2, 3)
+        self.assertIn("method", external_cache)