diff --git a/doc/python_api_reference_vDev.md b/doc/python_api_reference_vDev.md
index 784cb9e9..106ac282 100644
--- a/doc/python_api_reference_vDev.md
+++ b/doc/python_api_reference_vDev.md
@@ -11665,7 +11665,7 @@ def from_state_vector(
     Args:
         state_vector: A list of complex amplitudes specifying a superposition. The
             vector must correspond to a state that is reachable using Clifford
-            operations, and must be normalized (i.e. it must be a unit vector).
+            operations, and can be unnormalized.
         endian:
             "little": state vector is in little endian order, where higher index
                 qubits correspond to larger changes in the state index.
diff --git a/doc/stim.pyi b/doc/stim.pyi
index c629b71e..c6279d9e 100644
--- a/doc/stim.pyi
+++ b/doc/stim.pyi
@@ -9169,7 +9169,7 @@ class Tableau:
         Args:
             state_vector: A list of complex amplitudes specifying a superposition. The
                 vector must correspond to a state that is reachable using Clifford
-                operations, and must be normalized (i.e. it must be a unit vector).
+                operations, and can be unnormalized.
             endian:
                 "little": state vector is in little endian order, where higher index
                     qubits correspond to larger changes in the state index.
diff --git a/glue/python/src/stim/__init__.pyi b/glue/python/src/stim/__init__.pyi
index c629b71e..c6279d9e 100644
--- a/glue/python/src/stim/__init__.pyi
+++ b/glue/python/src/stim/__init__.pyi
@@ -9169,7 +9169,7 @@ class Tableau:
         Args:
             state_vector: A list of complex amplitudes specifying a superposition. The
                 vector must correspond to a state that is reachable using Clifford
-                operations, and must be normalized (i.e. it must be a unit vector).
+                operations, and can be unnormalized.
             endian:
                 "little": state vector is in little endian order, where higher index
                     qubits correspond to larger changes in the state index.
diff --git a/src/stim/stabilizers/tableau.pybind.cc b/src/stim/stabilizers/tableau.pybind.cc
index e3dcd32e..ea562c65 100644
--- a/src/stim/stabilizers/tableau.pybind.cc
+++ b/src/stim/stabilizers/tableau.pybind.cc
@@ -2147,7 +2147,7 @@ void stim_pybind::pybind_tableau_methods(pybind11::module &m, pybind11::class_<T
             Args:
                 state_vector: A list of complex amplitudes specifying a superposition. The
                     vector must correspond to a state that is reachable using Clifford
-                    operations, and must be normalized (i.e. it must be a unit vector).
+                    operations, and can be unnormalized.
                 endian:
                     "little": state vector is in little endian order, where higher index
                         qubits correspond to larger changes in the state index.
diff --git a/src/stim/stabilizers/tableau_pybind_test.py b/src/stim/stabilizers/tableau_pybind_test.py
index 6ea803ff..a5dcdfe3 100644
--- a/src/stim/stabilizers/tableau_pybind_test.py
+++ b/src/stim/stabilizers/tableau_pybind_test.py
@@ -11,6 +11,7 @@
 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 # See the License for the specific language governing permissions and
 # limitations under the License.
+import random
 import re
 
 import numpy as np
@@ -57,6 +58,14 @@ def test_from_named_gate():
         stim.Tableau.from_named_gate("X_ERROR")
 
 
+def test_from_state_vector_fuzz():
+    for n in range(1, 7):
+        t = stim.Tableau.random(n)
+        v = t.to_state_vector() * (random.random() + 1j*random.random())
+        t2 = stim.Tableau.from_state_vector(v, endian='little')
+        np.testing.assert_array_equal(t.to_stabilizers(canonicalize=True), t2.to_stabilizers(canonicalize=True))
+
+
 def test_identity():
     t = stim.Tableau(3)
     assert len(t) == 3
diff --git a/src/stim/util_top/circuit_vs_amplitudes.cc b/src/stim/util_top/circuit_vs_amplitudes.cc
index 75bfeba9..124c3357 100644
--- a/src/stim/util_top/circuit_vs_amplitudes.cc
+++ b/src/stim/util_top/circuit_vs_amplitudes.cc
@@ -40,15 +40,6 @@ Circuit stim::stabilizer_state_vector_to_circuit(
     }
 
     uint8_t num_qubits = floor_lg2(state_vector.size());
-    double weight = 0;
-    for (const auto &c : state_vector) {
-        weight += std::norm(c);
-    }
-    if (abs(weight - 1) > 0.125) {
-        throw std::invalid_argument(
-            "The given state vector wasn't a unit vector. It had a length of " + std::to_string(weight) + ".");
-    }
-
     VectorSimulator sim(num_qubits);
     sim.state = state_vector;
 
@@ -73,7 +64,7 @@ Circuit stim::stabilizer_state_vector_to_circuit(
             {});
     };
 
-    // Move biggest amplitude to start of state vector..
+    // Move biggest amplitude to start of state vector.
     size_t pivot = biggest_index(state_vector);
     for (size_t q = 0; q < num_qubits; q++) {
         if ((pivot >> q) & 1) {
diff --git a/src/stim/util_top/circuit_vs_amplitudes.h b/src/stim/util_top/circuit_vs_amplitudes.h
index be7d59d8..f9b38148 100644
--- a/src/stim/util_top/circuit_vs_amplitudes.h
+++ b/src/stim/util_top/circuit_vs_amplitudes.h
@@ -8,7 +8,8 @@ namespace stim {
 /// Synthesizes a circuit to generate the given state vector.
 ///
 /// Args:
-///     stabilizer_state_vector: The vector of amplitudes to produce using a circuit.
+///     stabilizer_state_vector: The vector of amplitudes to produce using a circuit. Does not need to be a unit vector,
+///     but must be non-zero.
 ///     little_endian: Whether the vector is using little endian or big endian ordering.
 ///     inverted_circuit: If false, returns a circuit that sends |000...0> to the state vector.
 ///         If true, returns a circuit that sends the state vector to |000...0> instead of a cir.
diff --git a/src/stim/util_top/circuit_vs_amplitudes.test.cc b/src/stim/util_top/circuit_vs_amplitudes.test.cc
index cd45c7f3..db60267c 100644
--- a/src/stim/util_top/circuit_vs_amplitudes.test.cc
+++ b/src/stim/util_top/circuit_vs_amplitudes.test.cc
@@ -8,10 +8,12 @@
 using namespace stim;
 
 TEST(conversions, stabilizer_state_vector_to_circuit_basic) {
+    ASSERT_THROW(stabilizer_state_vector_to_circuit({}, false), std::invalid_argument);
+
     ASSERT_THROW(
         stabilizer_state_vector_to_circuit(
             {
-                {0.5},
+                {0},
             },
             false),
         std::invalid_argument);
@@ -175,6 +177,35 @@ TEST(conversions, stabilizer_state_vector_to_circuit_fuzz_round_trip) {
     }
 }
 
+TEST(conversions, stabilizer_state_vector_to_circuit_unnormalized_fuzz_round_trip) {
+    auto rng = INDEPENDENT_TEST_RNG();
+    auto little_endian = true;
+
+    for (size_t i = 0; i < 100; i++) {
+        // Pick a random stabilizer state.
+        size_t n = i % 5;
+        TableauSimulator<64> sim(INDEPENDENT_TEST_RNG(), n);
+        sim.inv_state = Tableau<64>::random(n, rng);
+        auto desired_vec = sim.to_state_vector(little_endian);
+
+        // Unnormalize by multiplying by a random non-zero factor.
+        auto scaled_vec = desired_vec;
+        std::uniform_real_distribution<float> dist(-1000.0, +1000.0);
+        std::complex<float> scale = {dist(rng), dist(rng)};
+        while (std::norm(scale) < 0.01) {
+            scale = {dist(rng), dist(rng)};
+        }
+        for (auto &c : scaled_vec) {
+            c *= scale;
+        }
+
+        // Round trip through a circuit.
+        auto circuit = stabilizer_state_vector_to_circuit(scaled_vec, little_endian);
+        auto actual_vec = circuit_to_output_state_vector(circuit, little_endian);
+        ASSERT_EQ(actual_vec, desired_vec) << " scale=" << scale;
+    }
+}
+
 TEST(conversions, circuit_to_output_state_vector) {
     ASSERT_EQ(circuit_to_output_state_vector(Circuit(""), false), (std::vector<std::complex<float>>{{1}}));
     ASSERT_EQ(