diff --git a/src/stim/stabilizers/tableau.pybind.cc b/src/stim/stabilizers/tableau.pybind.cc
index da568248..ea562c65 100644
--- a/src/stim/stabilizers/tableau.pybind.cc
+++ b/src/stim/stabilizers/tableau.pybind.cc
@@ -2130,16 +2130,8 @@ void stim_pybind::pybind_tableau_methods(pybind11::module &m, pybind11::class_<T
             }
 
             std::vector<std::complex<float>> v;
-            double weight = 0;
             for (const auto &obj : state_vector) {
                 v.push_back(pybind11::cast<std::complex<float>>(obj));
-                weight += std::norm(v.back());
-            }
-            if (weight != 1.0 && weight > 0.0) {
-                std::complex<float> scale = (float)sqrt(1.0 / weight);
-                for (auto &amplitude : v) {
-                    amplitude *= scale;
-                }
             }
 
             return circuit_to_tableau<MAX_BITWORD_WIDTH>(
@@ -2155,7 +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.
+                    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 a346ab12..ec91bb2b 100644
--- a/src/stim/stabilizers/tableau_pybind_test.py
+++ b/src/stim/stabilizers/tableau_pybind_test.py
@@ -1,3 +1,5 @@
+# Copyright 2021 Google LLC
+#
 # Licensed under the Apache License, Version 2.0 (the "License");
 # you may not use this file except in compliance with the License.
 # You may obtain a copy of the License at
@@ -54,6 +56,7 @@ def test_from_named_gate():
     with pytest.raises(IndexError, match="not unitary"):
         stim.Tableau.from_named_gate("X_ERROR")
 
+
 def test_from_state_vector():
     t = stim.Tableau.from_state_vector([
         0.5**0.5,
@@ -67,14 +70,6 @@ def test_from_state_vector():
     assert t.z_output(0) == stim.PauliString("XX")
     assert t.z_output(1) == stim.PauliString("ZZ")
 
-    unnormalized = stim.Tableau.from_state_vector([
-        1,
-        0,
-        0,
-        1
-    ], endian='little')
-    assert unnormalized == t
-
 
 def test_identity():
     t = stim.Tableau(3)
diff --git a/src/stim/util_top/circuit_vs_amplitudes.cc b/src/stim/util_top/circuit_vs_amplitudes.cc
index 75bfeba9..18aa9152 100644
--- a/src/stim/util_top/circuit_vs_amplitudes.cc
+++ b/src/stim/util_top/circuit_vs_amplitudes.cc
@@ -40,17 +40,17 @@ 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;
+    /*
+        double weight = 0;
+        for (const auto &c : sim.state) {
+            weight += std::norm(c);
+        }
+        if (weight == 0.0) {
+            throw std::invalid_argument("The given state vector has zero length.");
+        }
+        */
 
     Circuit recorded;
     auto apply = [&](GateType gate_type, uint32_t target) {
@@ -73,7 +73,7 @@ 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..f841d16e 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. Must be non-zero and will be
+///     normalized if necessary.
 ///     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(