diff --git a/docs/conf.py b/docs/conf.py
index 28280d731..a96bf7418 100644
--- a/docs/conf.py
+++ b/docs/conf.py
@@ -75,8 +75,4 @@
 # nbsphinx_execute = os.getenv('QISKIT_DOCS_BUILD_TUTORIALS', 'never')
 nbsphinx_execute = 'always'
 nbsphinx_widgets_path = ''
-exclude_patterns = ['_build', '**.ipynb_checkpoints']
-
-# this is tied to the temporary restriction to JAX versions <=0.4.6. See issue #190
-import os
-os.environ["JAX_JIT_PJIT_API_MERGE"] = "0"
\ No newline at end of file
+exclude_patterns = ['_build', '**.ipynb_checkpoints']
\ No newline at end of file
diff --git a/qiskit_dynamics/dispatch/backends/jax.py b/qiskit_dynamics/dispatch/backends/jax.py
index ed104b9ef..0d5d55936 100644
--- a/qiskit_dynamics/dispatch/backends/jax.py
+++ b/qiskit_dynamics/dispatch/backends/jax.py
@@ -20,24 +20,6 @@
     from jax import Array
     from jax.core import Tracer
 
-    # warning based on JAX version
-    from packaging import version
-    import warnings
-
-    if version.parse(jax.__version__) >= version.parse("0.4.4"):
-        import os
-
-        if (
-            version.parse(jax.__version__) > version.parse("0.4.6")
-            or os.environ.get("JAX_JIT_PJIT_API_MERGE", None) != "0"
-        ):
-            warnings.warn(
-                "The functionality in the perturbation module of Qiskit Dynamics requires a JAX "
-                "version <= 0.4.6, due to a bug in JAX versions > 0.4.6. For versions 0.4.4, "
-                "0.4.5, and 0.4.6, using the perturbation module functionality requires setting "
-                "os.environ['JAX_JIT_PJIT_API_MERGE'] = '0' before importing JAX or Dynamics."
-            )
-
     JAX_TYPES = (Array, Tracer)
 
     from ..dispatch import Dispatch
diff --git a/qiskit_dynamics/perturbation/dyson_magnus.py b/qiskit_dynamics/perturbation/dyson_magnus.py
index 7642bcd25..741c76fc6 100644
--- a/qiskit_dynamics/perturbation/dyson_magnus.py
+++ b/qiskit_dynamics/perturbation/dyson_magnus.py
@@ -57,7 +57,7 @@
 
 try:
     import jax.numpy as jnp
-    from jax.lax import scan, switch
+    from jax.lax import scan
     from jax import vmap
 except ImportError:
     pass
@@ -472,17 +472,15 @@ def _setup_dyson_rhs_jax(
 
     custom_matmul = _CustomMatmul(lmult_rule, index_offset=1, backend="jax")
 
-    perturbations_evaluation_order = jnp.array(perturbations_evaluation_order, dtype=int)
+    perturbations_evaluation_order = np.array(perturbations_evaluation_order, dtype=int)
 
     new_list = [generator] + perturbations
 
-    def single_eval(idx, t):
-        return switch(idx, new_list, t)
-
-    multiple_eval = vmap(single_eval, in_axes=(0, None))
+    def multiple_eval(t):
+        return jnp.array([new_list[idx](t) for idx in perturbations_evaluation_order])
 
     def dyson_rhs(t, y):
-        return custom_matmul(multiple_eval(perturbations_evaluation_order, t), y)
+        return custom_matmul(multiple_eval(t), y)
 
     return dyson_rhs
 
diff --git a/qiskit_dynamics/solvers/lanczos.py b/qiskit_dynamics/solvers/lanczos.py
index 55012c729..f10364895 100644
--- a/qiskit_dynamics/solvers/lanczos.py
+++ b/qiskit_dynamics/solvers/lanczos.py
@@ -57,7 +57,7 @@ def lanczos_basis(A: Union[csr_matrix, np.ndarray], y0: np.ndarray, k_dim: int):
 
     q_basis[[0], :] = y0.T
     projection = A @ y0
-    alpha[0] = y0.conj().T @ projection
+    alpha[0] = np.sum(y0.conj() * projection)
     projection = projection - alpha[0] * y0
     beta[0] = np.linalg.norm(projection)
 
diff --git a/releasenotes/notes/update-jax-a50ce1b7d6b47219.yaml b/releasenotes/notes/update-jax-a50ce1b7d6b47219.yaml
new file mode 100644
index 000000000..cf80785d4
--- /dev/null
+++ b/releasenotes/notes/update-jax-a50ce1b7d6b47219.yaml
@@ -0,0 +1,10 @@
+---
+issues:
+  - |
+    A JAX warning about casting complex values to real is raised when computing gradients of
+    simulations in Qiskit Dynamics. Note that this warning does not appear to signify any error
+    in numerical computation, and can be safely ignored.
+upgrade:
+  - |
+    The upper bound on JAX and Diffrax in the last version of Qiskit Dynamics has been removed.
+    Users should try to use the latest version of JAX.
\ No newline at end of file
diff --git a/setup.py b/setup.py
index 937f9d879..a8e1fcd68 100644
--- a/setup.py
+++ b/setup.py
@@ -25,8 +25,7 @@
     "arraylias"
 ]
 
-jax_extras = ['jax>=0.4.0, <= 0.4.6',
-              'jaxlib>=0.4.0, <= 0.4.6']
+jax_extras = ['jax', 'jaxlib']
 
 PACKAGES = setuptools.find_packages(exclude=['test*'])
 
diff --git a/test/dynamics/__init__.py b/test/dynamics/__init__.py
index af0a00fef..be625db2a 100644
--- a/test/dynamics/__init__.py
+++ b/test/dynamics/__init__.py
@@ -13,8 +13,3 @@
 """
 Qiskit Dynamics tests
 """
-
-# temporarily disable a change in JAX 0.4.4 that introduced a bug. Must be run before importing JAX
-import os
-
-os.environ["JAX_JIT_PJIT_API_MERGE"] = "0"
diff --git a/test/dynamics/common.py b/test/dynamics/common.py
index a369bb6e2..f3d8d343e 100644
--- a/test/dynamics/common.py
+++ b/test/dynamics/common.py
@@ -286,7 +286,8 @@ def jit_grad_wrap(self, func_to_test: Callable) -> Callable:
         Args:
             func_to_test: The function whose gradient will be graded.
         Returns:
-            JIT-compiled gradient of function."""
+            JIT-compiled gradient of function.
+        """
         wf = wrap(lambda f: jit(grad(f)), decorator=True)
         f = lambda *args: np.sum(func_to_test(*args)).real
         return wf(f)
diff --git a/test/dynamics/perturbation/test_dyson_magnus.py b/test/dynamics/perturbation/test_dyson_magnus.py
index 3d812cba4..e63cea459 100644
--- a/test/dynamics/perturbation/test_dyson_magnus.py
+++ b/test/dynamics/perturbation/test_dyson_magnus.py
@@ -718,3 +718,51 @@ def assertMultRulesEqual(self, rule1, rule2):
         for sub_rule1, sub_rule2 in zip(rule1, rule2):
             self.assertAllClose(sub_rule1[0], sub_rule2[0])
             self.assertAllClose(sub_rule1[1], sub_rule2[1])
+
+
+class TestWorkaround(QiskitDynamicsTestCase):
+    """Test whether workaround in dyson_magnus._setup_dyson_rhs_jax is no longer required.
+
+    The workaround was introduced in the same commit as this test class to avoid an error being
+    raised by a non-trivial combination of JAX transformations. The test in this class has been
+    set up to expect the original minimal reproduction of the issue to fail. Once it no longer
+    fails, the changes made to _setup_dyson_rhs_jax in this commit should be reverted.
+
+    See https://github.com/google/jax/discussions/9951#discussioncomment-2385157 for discussion of
+    issue.
+    """
+
+    def test_minimal_example(self):
+        """Test minimal reproduction of issue."""
+
+        with self.assertRaises(Exception):
+            import jax.numpy as jnp
+            from jax import grad, vmap
+            from jax.lax import switch
+            from jax.experimental.ode import odeint
+
+            # pylint: disable=unused-argument
+            def A0(t):
+                return 2.0
+
+            # pylint: disable=unused-argument
+            def A1(a, t):
+                return a**2
+
+            y0 = np.random.rand(2)
+            T = np.pi * 1.232
+
+            def test_func(a):
+                eval_list = [A0, lambda t: A1(a, t)]
+
+                def single_eval(idx, t):
+                    return switch(idx, eval_list, t)
+
+                multiple_eval = vmap(single_eval, in_axes=(0, None))
+                idx_list = jnp.array([0, 1])
+                rhs = lambda y, t: multiple_eval(idx_list, t) * y
+
+                out = odeint(rhs, y0=y0, t=jnp.array([0, T], dtype=float), atol=1e-13, rtol=1e-13)
+                return out
+
+            jit(grad(lambda a: test_func(a)[-1][1].real))(1.0)
diff --git a/test/dynamics/solvers/test_solver_classes.py b/test/dynamics/solvers/test_solver_classes.py
index f45507a6e..492d3cbdb 100644
--- a/test/dynamics/solvers/test_solver_classes.py
+++ b/test/dynamics/solvers/test_solver_classes.py
@@ -957,8 +957,8 @@ def test_two_channel_SuperOp_simulation(self, model):
             schedules=sched,
             signals=signals,
             test_tol=1e-8,
-            atol=1e-11,
-            rtol=1e-11,
+            atol=1e-12,
+            rtol=1e-12,
         )
 
     def test_4_channel_schedule(self):
diff --git a/tox.ini b/tox.ini
index c134ac558..b81ffb106 100644
--- a/tox.ini
+++ b/tox.ini
@@ -15,18 +15,16 @@ commands = stestr run {posargs}
 [testenv:jax]
 deps =
     -r{toxinidir}/requirements-dev.txt
-    jax<=0.4.6
-    jaxlib<=0.4.6
-    equinox<=0.10.3
-    diffrax<=0.3.1
+    jax
+    jaxlib
+    diffrax
 
 [testenv:lint]
 deps =
     -r{toxinidir}/requirements-dev.txt
-    jax<=0.4.6
-    jaxlib<=0.4.6
-    equinox<=0.10.3
-    diffrax<=0.3.1
+    jax
+    jaxlib
+    diffrax
 commands =
   black --check {posargs} qiskit_dynamics test
   pylint -rn -j 0 --rcfile={toxinidir}/.pylintrc qiskit_dynamics/ test/
@@ -41,8 +39,8 @@ commands = black {posargs} qiskit_dynamics test
 usedevelop = False
 deps =
     -r{toxinidir}/requirements-dev.txt
-    jax<=0.4.6
-    jaxlib<=0.4.6
+    jax
+    jaxlib
     diffrax
 commands =
   sphinx-build -j auto -W -T --keep-going {posargs} docs/ docs/_build/html