diff --git a/crates/pecos-qsim/src/pauli_prop.rs b/crates/pecos-qsim/src/pauli_prop.rs
new file mode 100644
index 00000000..d9928ddb
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+++ b/crates/pecos-qsim/src/pauli_prop.rs
@@ -0,0 +1,223 @@
+// Copyright 2024 The PECOS Developers
+//
+// 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
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, 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.
+#![allow(unused_variables)]
+
+use super::clifford_simulator::CliffordSimulator;
+use crate::quantum_simulator::QuantumSimulator;
+use core::marker::PhantomData;
+use pecos_core::{IndexableElement, Set, VecSet};
+
+// TODO: Allow for the use of sets of elements of types other than usize
+
+#[expect(clippy::module_name_repetitions)]
+pub type StdPauliProp = PauliProp<VecSet<usize>, usize>;
+
+#[derive(Clone, Debug)]
+pub struct PauliProp<T, E>
+where
+    T: for<'a> Set<'a, Element = E>,
+    E: IndexableElement,
+{
+    num_qubits: usize,
+    xs: T,
+    zs: T,
+    _marker: PhantomData<E>,
+}
+
+impl<T, E> QuantumSimulator for PauliProp<T, E>
+where
+    E: IndexableElement,
+    T: for<'a> Set<'a, Element = E>,
+{
+    #[inline]
+    #[must_use]
+    fn new(num_qubits: usize) -> PauliProp<T, E> {
+        Self {
+            num_qubits,
+            xs: T::new(),
+            zs: T::new(),
+            _marker: PhantomData,
+        }
+    }
+
+    #[inline]
+    fn num_qubits(&self) -> usize {
+        self.num_qubits
+    }
+
+    #[inline]
+    fn reset(&mut self) -> &mut Self {
+        todo!()
+    }
+}
+
+impl<T, E> PauliProp<T, E>
+where
+    T: for<'a> Set<'a, Element = E>,
+    E: IndexableElement,
+{
+    #[inline]
+    pub fn insert_x(&mut self, item: E) {
+        self.xs.insert(item);
+    }
+
+    #[inline]
+    pub fn insert_z(&mut self, item: E) {
+        self.zs.insert(item);
+    }
+
+    #[inline]
+    pub fn insert_y(&mut self, item: E) {
+        self.insert_x(item);
+        self.insert_z(item);
+    }
+
+    #[inline]
+    #[expect(clippy::similar_names)]
+    pub fn h_v2(&mut self, q: E) {
+        let in_xs = self.xs.contains(&q);
+        let in_zs = self.zs.contains(&q);
+
+        if in_xs && !in_zs {
+            self.xs.remove(&q);
+            self.zs.insert(q);
+        } else if !in_xs && in_zs {
+            self.zs.remove(&q);
+            self.xs.insert(q);
+        } else if in_xs && in_zs {
+            return;
+        }
+    }
+}
+
+impl<T, E> CliffordSimulator<E> for PauliProp<T, E>
+where
+    T: for<'a> Set<'a, Element = E>,
+    E: IndexableElement,
+{
+    #[inline]
+    fn px(&mut self, q: E) -> (bool, bool) {
+        todo!()
+    }
+
+    #[inline]
+    fn pnx(&mut self, q: E) -> (bool, bool) {
+        todo!()
+    }
+
+    #[inline]
+    fn py(&mut self, q: E) -> (bool, bool) {
+        todo!()
+    }
+
+    #[inline]
+    fn pny(&mut self, q: E) -> (bool, bool) {
+        todo!()
+    }
+
+    #[inline]
+    fn pz(&mut self, q: E) -> (bool, bool) {
+        self.xs.remove(&q);
+        self.zs.remove(&q);
+        (true, true) // TODO: fix...
+    }
+
+    #[inline]
+    fn pnz(&mut self, q: E) -> (bool, bool) {
+        todo!()
+    }
+
+    #[inline]
+    fn mx(&mut self, q: E) -> (bool, bool) {
+        todo!()
+    }
+
+    #[inline]
+    fn mnx(&mut self, q: E) -> (bool, bool) {
+        todo!()
+    }
+
+    #[inline]
+    fn my(&mut self, q: E) -> (bool, bool) {
+        todo!()
+    }
+
+    #[inline]
+    fn mny(&mut self, q: E) -> (bool, bool) {
+        todo!()
+    }
+
+    /// Output true if there is an X on the qubit.
+    #[inline]
+    fn mz(&mut self, q: E) -> (bool, bool) {
+        (self.xs.contains(&q), true) // TODO: Is deterministic a useful value... maybe, maybe not... fix
+    }
+
+    #[inline]
+    fn mnz(&mut self, q: E) -> (bool, bool) {
+        todo!()
+    }
+
+    #[inline]
+    fn identity(&mut self, _q: E) {}
+
+    #[inline]
+    fn x(&mut self, q: E) {
+        todo!()
+    }
+
+    #[inline]
+    fn y(&mut self, q: E) {
+        todo!()
+    }
+
+    #[inline]
+    fn z(&mut self, q: E) {
+        todo!()
+    }
+
+    /// X -> Y, Z -> Z, Y -> -X
+    #[inline]
+    fn sz(&mut self, q: E) {
+        if self.xs.contains(&q) {
+            self.zs.symmetric_difference_item_update(&q);
+        }
+    }
+
+    /// X -> Z, Z -> X, Y -> -Y
+    #[inline]
+    #[expect(clippy::similar_names)]
+    fn h(&mut self, q: E) {
+        let in_xs = self.xs.contains(&q);
+        let in_zs = self.zs.contains(&q);
+
+        if in_xs && in_zs {
+        } else if in_xs {
+            self.xs.remove(&q);
+            self.zs.insert(q);
+        } else if in_zs {
+            self.zs.remove(&q);
+            self.xs.insert(q);
+        }
+    }
+
+    /// XI -> XX, ZI -> ZI, IX -> IX, IZ -> ZZ
+    #[inline]
+    fn cx(&mut self, q1: E, q2: E) {
+        if self.xs.contains(&q1) {
+            self.xs.symmetric_difference_item_update(&q2);
+        }
+        if self.zs.contains(&q2) {
+            self.zs.symmetric_difference_item_update(&q1);
+        }
+    }
+}