diff --git a/crates/circuit/src/classical/expr/expr.rs b/crates/circuit/src/classical/expr/expr.rs
index 2c8cc947f410..cb2ccf78a55a 100644
--- a/crates/circuit/src/classical/expr/expr.rs
+++ b/crates/circuit/src/classical/expr/expr.rs
@@ -10,6 +10,8 @@
 // copyright notice, and modified files need to carry a notice indicating
 // that they have been altered from the originals.
 
+use std::error::Error;
+
 use crate::classical::expr::{Binary, Cast, Index, Stretch, Unary, Value, Var};
 use crate::classical::types::Type;
 use pyo3::prelude::*;
@@ -140,16 +142,18 @@ impl Expr {
     }
 
     /// Visits all nodes by mutable reference, in a post-order traversal.
-    pub fn visit_mut<F>(&mut self, mut visitor: F) -> PyResult<()>
+    pub fn visit_mut<F, E>(&mut self, mut visitor: F) -> Result<(), E>
     where
-        F: FnMut(ExprRefMut) -> PyResult<()>,
+        F: FnMut(ExprRefMut) -> Result<(), E>,
+        E: Error,
     {
         self.visit_mut_impl(&mut visitor)
     }
 
-    fn visit_mut_impl<F>(&mut self, visitor: &mut F) -> PyResult<()>
+    fn visit_mut_impl<F, E>(&mut self, visitor: &mut F) -> Result<(), E>
     where
-        F: FnMut(ExprRefMut) -> PyResult<()>,
+        F: FnMut(ExprRefMut) -> Result<(), E>,
+        E: Error,
     {
         match self {
             Expr::Unary(u) => u.operand.visit_mut_impl(visitor)?,
@@ -481,7 +485,7 @@ mod tests {
     use crate::classical::types::Type;
     use crate::duration::Duration;
     use num_bigint::BigUint;
-    use pyo3::PyResult;
+    use pyo3::{PyErr, PyResult};
     use uuid::Uuid;
 
     #[test]
@@ -704,7 +708,7 @@ mod tests {
 
         expr.visit_mut(|x| {
             assert!(order.next().unwrap()(&x));
-            Ok(())
+            Ok::<_, PyErr>(())
         })?;
 
         assert!(order.next().is_none());
@@ -740,7 +744,7 @@ mod tests {
         expr.visit_mut(|x| match x {
             ExprRefMut::Var(Var::Standalone { name, .. }) => {
                 *name = "updated".to_string();
-                Ok(())
+                Ok::<_, PyErr>(())
             }
             _ => Ok(()),
         })?;
diff --git a/crates/circuit/src/variable_mapper.rs b/crates/circuit/src/variable_mapper.rs
index 3228b5ba120b..c0bd89519623 100644
--- a/crates/circuit/src/variable_mapper.rs
+++ b/crates/circuit/src/variable_mapper.rs
@@ -16,9 +16,8 @@ use crate::operations::{Condition, SwitchTarget};
 use hashbrown::{HashMap, HashSet};
 use num_bigint::BigUint;
 use num_traits::Num;
-use pyo3::PyResult;
-use pyo3::prelude::*;
 use std::cell::RefCell;
+use std::error::Error;
 
 pub(crate) struct VariableMapper {
     target_cregs: Vec<ClassicalRegister>,
@@ -59,14 +58,15 @@ impl VariableMapper {
     /// [DAGCircuit::compose]; nowhere else does this, and in general this would require *far*
     /// more complex classical rewriting than Qiskit needs to worry about in the full expression
     /// era.
-    pub fn map_condition<F>(
+    pub fn map_condition<F, E>(
         &self,
         condition: &Condition,
         allow_reorder: bool,
         mut add_register: F,
-    ) -> PyResult<Condition>
+    ) -> Result<Condition, E>
     where
-        F: FnMut(&ClassicalRegister) -> PyResult<()>,
+        F: FnMut(&ClassicalRegister) -> Result<(), E>,
+        E: Error,
     {
         Ok(match condition {
             Condition::Bit(target, value) => {
@@ -99,7 +99,7 @@ impl VariableMapper {
                         mapped_bits_set == register_set
                     })
                     .cloned()
-                    .map(Ok::<_, PyErr>)
+                    .map(Ok::<_, E>)
                     .unwrap_or_else(|| {
                         let mapped_theirs =
                             ClassicalRegister::new_alias(None, mapped_bits_order.clone());
@@ -138,13 +138,14 @@ impl VariableMapper {
 
     /// Map the real-time variables in a `target` of a `SwitchCaseOp` to the new
     /// circuit.
-    pub fn map_target<F>(
+    pub fn map_target<F, E>(
         &self,
         target: &SwitchTarget,
         mut add_register: F,
-    ) -> PyResult<SwitchTarget>
+    ) -> Result<SwitchTarget, E>
     where
-        F: FnMut(&ClassicalRegister) -> PyResult<()>,
+        F: FnMut(&ClassicalRegister) -> Result<(), E>,
+        E: Error,
     {
         Ok(match target {
             SwitchTarget::Bit(bit) => SwitchTarget::Bit(self.bit_map.get(bit).cloned().unwrap()),
@@ -156,9 +157,10 @@ impl VariableMapper {
     }
 
     /// Map the variables in an [expr::Expr] node to the new circuit.
-    pub fn map_expr<F>(&self, expr: &expr::Expr, mut add_register: F) -> PyResult<expr::Expr>
+    pub fn map_expr<F, E>(&self, expr: &expr::Expr, mut add_register: F) -> Result<expr::Expr, E>
     where
-        F: FnMut(&ClassicalRegister) -> PyResult<()>,
+        F: FnMut(&ClassicalRegister) -> Result<(), E>,
+        E: Error,
     {
         let mut mapped = expr.clone();
         mapped.visit_mut(|e| match e {
@@ -194,13 +196,14 @@ impl VariableMapper {
 
     /// Map the target's registers to suitable equivalents in the destination, adding an
     /// extra one if there's no exact match."""
-    fn map_register<F>(
+    fn map_register<F, E>(
         &self,
         theirs: &ClassicalRegister,
         mut add_register: F,
-    ) -> PyResult<ClassicalRegister>
+    ) -> Result<ClassicalRegister, E>
     where
-        F: FnMut(&ClassicalRegister) -> PyResult<()>,
+        F: FnMut(&ClassicalRegister) -> Result<(), E>,
+        E: Error,
     {
         if let Some(mapped_theirs) = self.register_map.borrow().get(theirs.name()) {
             return Ok(mapped_theirs.clone());
@@ -215,7 +218,7 @@ impl VariableMapper {
                 mapped_bits == register
             })
             .cloned()
-            .map(Ok::<_, PyErr>)
+            .map(Ok::<_, E>)
             .unwrap_or_else(|| {
                 let mapped_theirs = ClassicalRegister::new_alias(None, mapped_bits.clone());
                 add_register(&mapped_theirs)?;