diff --git a/crates/circuit/src/bit.rs b/crates/circuit/src/bit.rs
index e5535741559..65c7252ede8 100644
--- a/crates/circuit/src/bit.rs
+++ b/crates/circuit/src/bit.rs
@@ -1,16 +1,17 @@
 use std::hash::{DefaultHasher, Hash, Hasher};
 
-use pyo3::prelude::*;
+use pyo3::{prelude::*, types::PyDict};
 
 use crate::{
+    circuit_data::CircuitError,
     interner::Interned,
     register::{Register, RegisterAsKey},
 };
 
 /// Object representing a Python bit, that allows us to keep backwards compatibility
 /// with the previous structure.
-#[pyclass(name = "Bit")]
-#[derive(Debug, Clone, Copy, PartialEq, Eq, PartialOrd, Ord, Hash)]
+#[pyclass(name = "Bit", module = "qiskit._accelerate.bit", subclass)]
+#[derive(Debug, Clone, PartialEq, Eq, PartialOrd, Ord, Hash)]
 pub struct PyBit {
     register: Option<RegisterAsKey>, // Register identifier
     index: Option<u32>,              // Index within Register
@@ -20,10 +21,13 @@ pub struct PyBit {
 impl PyBit {
     #[new]
     #[pyo3(signature=(register=None, index=None))]
-    pub fn new(register: Option<RegisterAsKey>, index: Option<u32>) -> Self {
-        Self {
-            register,
-            index,
+    pub fn new(register: Option<RegisterAsKey>, index: Option<u32>) -> PyResult<Self> {
+        match (&register, index) {
+            (None, None) => Ok(Self { register, index }),
+            (Some(_), Some(_)) => Ok(Self { register, index }),
+            _ => Err(CircuitError::new_err(
+                "You should provide both an index and a register, not just one of them.",
+            )),
         }
     }
 
@@ -38,17 +42,103 @@ impl PyBit {
         slf.is(&other)
     }
 
-    fn __hash__(slf: Bound<'_, Self>) -> PyResult<isize> {
-        let borrowed = slf.borrow();
+    fn __hash__(&self, py: Python<'_>) -> PyResult<isize> {
+        if let (Some(reg), Some(idx)) = (self.register.as_ref(), self.index) {
+            return (reg.reduce(), idx).to_object(py).bind(py).hash();
+        }
+
+        // If registers are unavailable, hash by pointer value.
         let mut hasher = DefaultHasher::new();
-        borrowed.hash(&mut hasher);
+        let pointer_val = self as *const Self;
+        pointer_val.hash(&mut hasher);
         Ok(hasher.finish() as isize)
     }
+
+    fn __copy__(slf: Bound<Self>) -> Bound<Self> {
+        slf
+    }
+
+    #[pyo3(signature = (_memo=None))]
+    fn __deepcopy__<'py>(
+        slf: Bound<'py, Self>,
+        _memo: Option<Bound<'py, PyDict>>,
+    ) -> PyResult<Bound<'py, PyBit>> {
+        let borrowed: PyRef<Self> = slf.borrow();
+        if borrowed.index.is_none() && borrowed.register.is_none() {
+            return Ok(slf);
+        }
+        let copy = slf
+            .get_type()
+            .call_method1("__new__", (slf.get_type(),))?
+            .downcast_into::<PyBit>()?;
+        let mut copy_mut = copy.borrow_mut();
+        copy_mut.register = borrowed.register.clone();
+        copy_mut.index = borrowed.index;
+        Ok(copy)
+    }
+
+    fn __getstate__(slf: PyRef<'_, Self>) -> (Option<(String, u32)>, Option<u32>) {
+        (
+            slf.register.as_ref().map(|reg| {
+                let (name, num_qubits) = reg.reduce();
+                (name.to_string(), num_qubits)
+            }),
+            slf.index.as_ref().copied(),
+        )
+    }
+
+    fn __setstate__(mut slf: PyRefMut<'_, Self>, state: (Option<(String, u32)>, Option<u32>)) {
+        slf.register = state
+            .0
+            .map(|(name, num_qubits)| RegisterAsKey::new(name.as_str(), num_qubits));
+        slf.index = state.1;
+    }
 }
 
+macro_rules! create_py_bit {
+    ($name:ident, $pyname:literal, $module:literal) => {
+        #[pyclass(name=$pyname, extends=PyBit, subclass, module=$module)]
+        #[derive(Debug, Clone, Hash, PartialEq, Eq, PartialOrd, Ord)]
+        pub struct $name();
+
+        #[pymethods]
+        impl $name {
+            #[new]
+            #[pyo3(signature = (register=None, index=None))]
+            pub fn py_new(
+                register: Option<RegisterAsKey>,
+                index: Option<u32>,
+            ) -> PyResult<(Self, PyBit)> {
+                Ok((Self(), PyBit::new(register, index)?))
+            }
+        }
+    };
+}
+
+// Create python instances
+create_py_bit! {PyQubit, "Qubit", "qiskit._accelerate.bit"}
+create_py_bit! {PyClbit, "Clbit", "qiskit._accelerate.bit"}
+
 /// Keeps information about where a qubit is located within the circuit.
 #[derive(Debug, Clone)]
 pub struct BitInfo<T: Register + Hash + Eq> {
     register_idx: Interned<T>,
     index: u32,
 }
+
+impl<T: Register + Hash + Eq> BitInfo<T> {
+    pub fn new(register_idx: Interned<T>, index: u32) -> Self {
+        Self {
+            register_idx,
+            index,
+        }
+    }
+
+    pub fn register_index(&self) -> Interned<T> {
+        self.register_idx
+    }
+
+    pub fn index(&self) -> u32 {
+        self.index
+    }
+}
diff --git a/crates/circuit/src/lib.rs b/crates/circuit/src/lib.rs
index 0486cf75a15..619cd3ec885 100644
--- a/crates/circuit/src/lib.rs
+++ b/crates/circuit/src/lib.rs
@@ -125,6 +125,9 @@ impl From<Clbit> for BitType {
 }
 
 pub fn circuit(m: &Bound<PyModule>) -> PyResult<()> {
+    m.add_class::<bit::PyBit>()?;
+    m.add_class::<bit::PyClbit>()?;
+    m.add_class::<bit::PyQubit>()?;
     m.add_class::<circuit_data::CircuitData>()?;
     m.add_class::<circuit_instruction::CircuitInstruction>()?;
     m.add_class::<dag_circuit::DAGCircuit>()?;
diff --git a/crates/circuit/src/register.rs b/crates/circuit/src/register.rs
index 3e3a826fdb0..6d383df036b 100644
--- a/crates/circuit/src/register.rs
+++ b/crates/circuit/src/register.rs
@@ -1,36 +1,40 @@
 use indexmap::IndexSet;
 use pyo3::{intern, types::PyAnyMethods, FromPyObject};
-use std::hash::{DefaultHasher, Hash, Hasher};
+use std::{
+    hash::{Hash, Hasher},
+    sync::Mutex,
+};
 
 use crate::{
     interner::{Interned, Interner},
     Clbit, Qubit,
 };
 
+static REGISTER_INSTANCE_COUNTER: Mutex<u32> = Mutex::new(0);
+static PREFIX: &str = "reg";
+
 /// This represents the hash value of a Register according to the register's
 /// name and number of qubits.
-#[derive(Debug, Clone, Copy, PartialEq, Eq, PartialOrd, Ord, Hash)]
-pub struct RegisterAsKey(u64);
+#[derive(Debug, Clone, PartialEq, Eq, PartialOrd, Ord, Hash)]
+pub struct RegisterAsKey(String, u32);
 
 impl RegisterAsKey {
-    pub fn new(name: Option<&str>, num_qubits: u32) -> Self {
-        let mut hasher = DefaultHasher::default();
-        (name, num_qubits).hash(&mut hasher);
-        Self(hasher.finish())
+    pub fn new(name: &str, num_qubits: u32) -> Self {
+        Self(name.to_string(), num_qubits)
+    }
+
+    pub fn reduce(&self) -> (&str, u32) {
+        (self.0.as_str(), self.1)
     }
 }
 
 impl<'py> FromPyObject<'py> for RegisterAsKey {
     fn extract_bound(ob: &pyo3::Bound<'py, pyo3::PyAny>) -> pyo3::PyResult<Self> {
         let (name, num_qubits) = (
-            ob.getattr(intern!(ob.py(), "name"))?
-                .extract::<Option<String>>()?,
-            ob.getattr(intern!(ob.py(), "num_qubits"))?.extract()?,
+            ob.getattr(intern!(ob.py(), "name"))?.extract()?,
+            ob.len()? as u32,
         );
-        Ok(RegisterAsKey::new(
-            name.as_deref(),
-            num_qubits,
-        ))
+        Ok(RegisterAsKey(name, num_qubits))
     }
 }
 /// Described the desired behavior of a Register.
@@ -53,11 +57,23 @@ macro_rules! create_register {
         #[derive(Debug, Clone, Eq)]
         pub struct $name {
             register: IndexSet<<$name as Register>::Bit>,
-            name: Option<String>,
+            name: String,
         }
 
         impl $name {
             pub fn new(size: usize, name: Option<String>) -> Self {
+                let name = if let Some(name) = name {
+                    name
+                } else {
+                    let count = if let Ok(ref mut count) = REGISTER_INSTANCE_COUNTER.try_lock() {
+                        let curr = **count;
+                        **count += 1;
+                        curr
+                    } else {
+                        panic!("Could not access register counter.")
+                    };
+                    format!("{}{}", PREFIX, count)
+                };
                 Self {
                     register: (0..size).map(|bit| <$bit>::new(bit)).collect(),
                     name,
@@ -87,7 +103,7 @@ macro_rules! create_register {
 
         impl Hash for $name {
             fn hash<H: Hasher>(&self, state: &mut H) {
-                (self.name.as_ref(), self.len()).hash(state);
+                (self.name.as_str(), self.len()).hash(state);
             }
         }