diff --git a/backend/src/plonk/keygen.rs b/backend/src/plonk/keygen.rs
index 0af7d704..4c61e459 100644
--- a/backend/src/plonk/keygen.rs
+++ b/backend/src/plonk/keygen.rs
@@ -18,7 +18,7 @@ use crate::{
         EvaluationDomain,
     },
 };
-use halo2_middleware::circuit::{Advice, Any, Challenge, CompiledCircuitV2, Fixed, Instance};
+use halo2_middleware::circuit::{Advice, Any, CompiledCircuitV2, Fixed, Instance};
 use halo2_middleware::plonk::Assigned;
 
 pub(crate) fn create_domain<C, ConcreteCircuit>(
diff --git a/common/src/circuit.rs b/common/src/circuit.rs
index 59826767..5b50a3d1 100644
--- a/common/src/circuit.rs
+++ b/common/src/circuit.rs
@@ -4,8 +4,11 @@ use std::{fmt, marker::PhantomData};
 
 use halo2_middleware::ff::Field;
 
-use crate::plonk::{circuit::Column, Error, Selector, TableColumn};
-use halo2_middleware::circuit::{Advice, Any, Challenge, Fixed, Instance};
+use crate::plonk::{
+    circuit::{Challenge, Column},
+    Error, Selector, TableColumn,
+};
+use halo2_middleware::circuit::{Advice, Any, Fixed, Instance};
 use halo2_middleware::plonk::Assigned;
 
 mod value;
diff --git a/common/src/circuit/floor_planner/single_pass.rs b/common/src/circuit/floor_planner/single_pass.rs
index 8a1b9db4..18a04582 100644
--- a/common/src/circuit/floor_planner/single_pass.rs
+++ b/common/src/circuit/floor_planner/single_pass.rs
@@ -11,9 +11,9 @@ use crate::{
         table_layouter::{compute_table_lengths, SimpleTableLayouter},
         Cell, Column, Layouter, Region, RegionIndex, RegionStart, Table, Value,
     },
-    plonk::{Assignment, Circuit, Error, FloorPlanner, Selector, TableColumn},
+    plonk::{circuit::Challenge, Assignment, Circuit, Error, FloorPlanner, Selector, TableColumn},
 };
-use halo2_middleware::circuit::{Advice, Any, Challenge, Fixed, Instance};
+use halo2_middleware::circuit::{Advice, Any, Fixed, Instance};
 use halo2_middleware::plonk::Assigned;
 
 /// A simple [`FloorPlanner`] that performs minimal optimizations.
diff --git a/common/src/circuit/floor_planner/v1.rs b/common/src/circuit/floor_planner/v1.rs
index 1557fe2d..820af78c 100644
--- a/common/src/circuit/floor_planner/v1.rs
+++ b/common/src/circuit/floor_planner/v1.rs
@@ -8,9 +8,9 @@ use crate::{
         table_layouter::{compute_table_lengths, SimpleTableLayouter},
         Cell, Column, Layouter, Region, RegionIndex, RegionStart, Table, Value,
     },
-    plonk::{Assignment, Circuit, Error, FloorPlanner, Selector, TableColumn},
+    plonk::{circuit::Challenge, Assignment, Circuit, Error, FloorPlanner, Selector, TableColumn},
 };
-use halo2_middleware::circuit::{Advice, Any, Challenge, Fixed, Instance};
+use halo2_middleware::circuit::{Advice, Any, Fixed, Instance};
 use halo2_middleware::plonk::Assigned;
 
 pub mod strategy;
diff --git a/common/src/plonk/circuit.rs b/common/src/plonk/circuit.rs
index 6e11a99b..0150468d 100644
--- a/common/src/plonk/circuit.rs
+++ b/common/src/plonk/circuit.rs
@@ -4,7 +4,7 @@ use crate::circuit::{Layouter, Region, Value};
 use core::cmp::max;
 use core::ops::{Add, Mul};
 use halo2_middleware::circuit::{
-    Advice, AdviceQueryMid, Any, Challenge, ColumnMid, ColumnType, ConstraintSystemV2Backend,
+    Advice, AdviceQueryMid, Any, ChallengeMid, ColumnMid, ColumnType, ConstraintSystemV2Backend,
     ExpressionMid, Fixed, FixedQueryMid, GateV2Backend, Instance, InstanceQueryMid,
 };
 use halo2_middleware::ff::Field;
@@ -56,7 +56,26 @@ impl<C: ColumnType> Column<C> {
 
     /// Return expression from column at a relative position
     pub fn query_cell<F: Field>(&self, at: Rotation) -> Expression<F> {
-        self.column_type.query_cell(self.index, at)
+        let expr_mid = self.column_type.query_cell::<F>(self.index, at);
+        match expr_mid {
+            ExpressionMid::Advice(q) => Expression::Advice(AdviceQuery {
+                index: None,
+                column_index: q.column_index,
+                rotation: q.rotation,
+                phase: sealed::Phase(q.phase),
+            }),
+            ExpressionMid::Fixed(q) => Expression::Fixed(FixedQuery {
+                index: None,
+                column_index: q.column_index,
+                rotation: q.rotation,
+            }),
+            ExpressionMid::Instance(q) => Expression::Instance(InstanceQuery {
+                index: None,
+                column_index: q.column_index,
+                rotation: q.rotation,
+            }),
+            _ => unreachable!(),
+        }
     }
 
     /// Return expression from column at the current row
@@ -426,6 +445,48 @@ impl TableColumn {
     }
 }
 
+/// A challenge squeezed from transcript after advice columns at the phase have been committed.
+#[derive(Clone, Copy, Debug, Eq, PartialEq, Hash)]
+pub struct Challenge {
+    pub index: usize,
+    pub phase: u8,
+}
+
+impl Challenge {
+    /// Index of this challenge.
+    pub fn index(&self) -> usize {
+        self.index
+    }
+
+    /// Phase of this challenge.
+    pub fn phase(&self) -> u8 {
+        self.phase
+    }
+
+    /// Return Expression
+    pub fn expr<F: Field>(&self) -> Expression<F> {
+        Expression::Challenge(*self)
+    }
+}
+
+impl Into<ChallengeMid> for Challenge {
+    fn into(self) -> ChallengeMid {
+        ChallengeMid {
+            index: self.index,
+            phase: self.phase,
+        }
+    }
+}
+
+impl From<ChallengeMid> for Challenge {
+    fn from(c: ChallengeMid) -> Self {
+        Self {
+            index: c.index,
+            phase: c.phase,
+        }
+    }
+}
+
 /// This trait allows a [`Circuit`] to direct some backend to assign a witness
 /// for a constraint system.
 pub trait Assignment<F: Field> {
@@ -669,7 +730,7 @@ impl<F> Into<ExpressionMid<F>> for Expression<F> {
                 column_index,
                 rotation,
             }),
-            Expression::Challenge(c) => ExpressionMid::Challenge(c),
+            Expression::Challenge(c) => ExpressionMid::Challenge(c.into()),
             Expression::Negated(e) => ExpressionMid::Negated(Box::new((*e).into())),
             Expression::Sum(lhs, rhs) => {
                 ExpressionMid::Sum(Box::new((*lhs).into()), Box::new((*rhs).into()))
@@ -1477,7 +1538,7 @@ impl QueriesMap {
                     rotation: query.rotation,
                 })
             }
-            ExpressionMid::Challenge(c) => Expression::Challenge(*c),
+            ExpressionMid::Challenge(c) => Expression::Challenge(c.clone().into()),
             ExpressionMid::Negated(e) => Expression::Negated(Box::new(self.as_expression(e))),
             ExpressionMid::Sum(lhs, rhs) => Expression::Sum(
                 Box::new(self.as_expression(lhs)),
diff --git a/common/src/plonk/keygen.rs b/common/src/plonk/keygen.rs
index cd7a835b..77507589 100644
--- a/common/src/plonk/keygen.rs
+++ b/common/src/plonk/keygen.rs
@@ -3,11 +3,11 @@ use std::ops::Range;
 use halo2_middleware::ff::Field;
 
 use super::{
-    circuit::{Assignment, Column, Selector},
+    circuit::{Assignment, Challenge, Column, Selector},
     permutation, Error, LagrangeCoeff, Polynomial,
 };
 use crate::circuit::Value;
-use halo2_middleware::circuit::{Advice, Any, Challenge, Fixed, Instance};
+use halo2_middleware::circuit::{Advice, Any, Fixed, Instance};
 use halo2_middleware::plonk::Assigned;
 
 /// Assembly to be used in circuit synthesis.
diff --git a/frontend/src/circuit.rs b/frontend/src/circuit.rs
index 9483b0ea..582ec394 100644
--- a/frontend/src/circuit.rs
+++ b/frontend/src/circuit.rs
@@ -1,16 +1,14 @@
 //! Traits and structs for implementing circuit components.
 
 use halo2_common::plonk::{
-    circuit::Column,
+    circuit::{Challenge, Column},
     permutation,
     sealed::{self, SealedPhase},
     Assignment, Circuit, ConstraintSystem, Error, FirstPhase, FloorPlanner, SecondPhase, Selector,
     ThirdPhase,
 };
 use halo2_common::poly::{batch_invert_assigned, Polynomial};
-use halo2_middleware::circuit::{
-    Advice, Any, Challenge, CompiledCircuitV2, Fixed, Instance, PreprocessingV2,
-};
+use halo2_middleware::circuit::{Advice, Any, CompiledCircuitV2, Fixed, Instance, PreprocessingV2};
 use halo2_middleware::ff::Field;
 use halo2_middleware::plonk::Assigned;
 use std::collections::BTreeSet;
diff --git a/frontend/src/circuit/floor_planner/single_pass.rs b/frontend/src/circuit/floor_planner/single_pass.rs
index ec2aa18e..39d0a6a0 100644
--- a/frontend/src/circuit/floor_planner/single_pass.rs
+++ b/frontend/src/circuit/floor_planner/single_pass.rs
@@ -5,8 +5,8 @@ mod tests {
 
     use super::SimpleFloorPlanner;
     use crate::dev::MockProver;
-    use halo2_common::plonk::{Circuit, ConstraintSystem, Error};
-    use halo2_middleware::circuit::{Advice, Column};
+    use halo2_common::plonk::{circuit::Column, Circuit, ConstraintSystem, Error};
+    use halo2_middleware::circuit::Advice;
 
     #[test]
     fn not_enough_columns_for_constants() {
diff --git a/frontend/src/circuit/floor_planner/v1.rs b/frontend/src/circuit/floor_planner/v1.rs
index 6a78b58e..591cab81 100644
--- a/frontend/src/circuit/floor_planner/v1.rs
+++ b/frontend/src/circuit/floor_planner/v1.rs
@@ -7,8 +7,8 @@ mod tests {
     use halo2curves::pasta::vesta;
 
     use crate::dev::MockProver;
-    use halo2_common::plonk::{Circuit, ConstraintSystem, Error};
-    use halo2_middleware::circuit::{Advice, Column};
+    use halo2_common::plonk::{circuit::Column, Circuit, ConstraintSystem, Error};
+    use halo2_middleware::circuit::Advice;
 
     #[test]
     fn not_enough_columns_for_constants() {
diff --git a/frontend/src/circuit/floor_planner/v1/strategy.rs b/frontend/src/circuit/floor_planner/v1/strategy.rs
index 7b05709d..29d8f431 100644
--- a/frontend/src/circuit/floor_planner/v1/strategy.rs
+++ b/frontend/src/circuit/floor_planner/v1/strategy.rs
@@ -2,7 +2,8 @@
 fn test_slot_in() {
     use crate::circuit::layouter::RegionShape;
     use halo2_common::circuit::floor_planner::v1::strategy::slot_in;
-    use halo2_middleware::circuit::{Any, Column};
+    use halo2_common::plonk::circuit::Column;
+    use halo2_middleware::circuit::Any;
 
     let regions = vec![
         RegionShape {
diff --git a/frontend/src/dev.rs b/frontend/src/dev.rs
index 6707a99f..23d56c3f 100644
--- a/frontend/src/dev.rs
+++ b/frontend/src/dev.rs
@@ -12,14 +12,14 @@ use halo2_middleware::ff::FromUniformBytes;
 use halo2_common::{
     circuit,
     plonk::{
-        circuit::Column,
+        circuit::{Challenge, Column},
         permutation,
         sealed::{self, SealedPhase},
         Assignment, Circuit, ConstraintSystem, Error, Expression, FirstPhase, FloorPlanner, Phase,
         Selector,
     },
 };
-use halo2_middleware::circuit::{Advice, Any, Challenge, ColumnMid, Fixed, Instance};
+use halo2_middleware::circuit::{Advice, Any, ColumnMid, Fixed, Instance};
 use halo2_middleware::plonk::Assigned;
 
 use halo2_common::multicore::{
@@ -1252,9 +1252,9 @@ mod tests {
     use super::{FailureLocation, MockProver, VerifyFailure};
     use crate::circuit::{Layouter, SimpleFloorPlanner, Value};
     use halo2_common::plonk::{
-        Circuit, ConstraintSystem, Error, Expression, Selector, TableColumn,
+        circuit::Column, Circuit, ConstraintSystem, Error, Expression, Selector, TableColumn,
     };
-    use halo2_middleware::circuit::{Advice, Any, Column, Fixed, Instance};
+    use halo2_middleware::circuit::{Advice, Any, Fixed, Instance};
     use halo2_middleware::poly::Rotation;
 
     #[test]
diff --git a/frontend/src/dev/cost.rs b/frontend/src/dev/cost.rs
index 36c0f686..9452975c 100644
--- a/frontend/src/dev/cost.rs
+++ b/frontend/src/dev/cost.rs
@@ -15,10 +15,11 @@ use halo2_middleware::poly::Rotation;
 use halo2_common::{
     circuit::{layouter::RegionColumn, Value},
     plonk::{
-        circuit::Column, Assignment, Circuit, ConstraintSystem, Error, FloorPlanner, Selector,
+        circuit::{Challenge, Column},
+        Assignment, Circuit, ConstraintSystem, Error, FloorPlanner, Selector,
     },
 };
-use halo2_middleware::circuit::{Advice, Any, Challenge, Fixed, Instance};
+use halo2_middleware::circuit::{Advice, Any, Fixed, Instance};
 use halo2_middleware::plonk::Assigned;
 
 /// Measures a circuit to determine its costs, and explain what contributes to them.
diff --git a/frontend/src/dev/tfp.rs b/frontend/src/dev/tfp.rs
index 72c3ea27..8729d33a 100644
--- a/frontend/src/dev/tfp.rs
+++ b/frontend/src/dev/tfp.rs
@@ -8,9 +8,10 @@ use halo2_common::circuit::{
     AssignedCell, Cell, Layouter, Region, Table, Value,
 };
 use halo2_common::plonk::{
-    circuit::Column, Assignment, Circuit, ConstraintSystem, Error, FloorPlanner, Selector,
+    circuit::{Challenge, Column},
+    Assignment, Circuit, ConstraintSystem, Error, FloorPlanner, Selector,
 };
-use halo2_middleware::circuit::{Advice, Any, Challenge, Fixed, Instance};
+use halo2_middleware::circuit::{Advice, Any, Fixed, Instance};
 use halo2_middleware::plonk::Assigned;
 
 /// A helper type that augments a [`FloorPlanner`] with [`tracing`] spans and events.
diff --git a/halo2_proofs/src/plonk.rs b/halo2_proofs/src/plonk.rs
index bc477308..6fbaf263 100644
--- a/halo2_proofs/src/plonk.rs
+++ b/halo2_proofs/src/plonk.rs
@@ -11,8 +11,9 @@ pub use verifier::verify_proof;
 
 pub use halo2_backend::plonk::{ProvingKey, VerifyingKey};
 pub use halo2_common::plonk::{
-    circuit::Column, Circuit, ConstraintSystem, Error, Expression, FirstPhase, SecondPhase,
-    Selector, TableColumn, ThirdPhase,
+    circuit::{Challenge, Column},
+    Circuit, ConstraintSystem, Error, Expression, FirstPhase, SecondPhase, Selector, TableColumn,
+    ThirdPhase,
 };
-pub use halo2_middleware::circuit::{Advice, Challenge, Fixed, Instance};
+pub use halo2_middleware::circuit::{Advice, Fixed, Instance};
 pub use halo2_middleware::plonk::Assigned;
diff --git a/halo2_proofs/tests/frontend_backend_split.rs b/halo2_proofs/tests/frontend_backend_split.rs
index fb97416e..c647fa2e 100644
--- a/halo2_proofs/tests/frontend_backend_split.rs
+++ b/halo2_proofs/tests/frontend_backend_split.rs
@@ -13,8 +13,8 @@ use halo2_backend::plonk::{
 use halo2_common::{
     circuit::{AssignedCell, Layouter, Region, SimpleFloorPlanner, Value},
     plonk::{
-        circuit::Column, Circuit, ConstraintSystem, Error, Expression, FirstPhase, SecondPhase,
-        Selector,
+        circuit::{Challenge, Column},
+        Circuit, ConstraintSystem, Error, Expression, FirstPhase, SecondPhase, Selector,
     },
     transcript::{
         Blake2bRead, Blake2bWrite, Challenge255, TranscriptReadBuffer, TranscriptWriterBuffer,
@@ -25,7 +25,7 @@ use halo2_frontend::{
     dev::MockProver,
 };
 use halo2_middleware::{
-    circuit::{Advice, Challenge, Fixed, Instance},
+    circuit::{Advice, Fixed, Instance},
     ff::Field,
     poly::Rotation,
 };
diff --git a/middleware/src/circuit.rs b/middleware/src/circuit.rs
index 918b307b..004e86d4 100644
--- a/middleware/src/circuit.rs
+++ b/middleware/src/circuit.rs
@@ -35,12 +35,12 @@ pub struct InstanceQueryMid {
 
 /// A challenge squeezed from transcript after advice columns at the phase have been committed.
 #[derive(Clone, Copy, Debug, Eq, PartialEq, Hash)]
-pub struct Challenge {
+pub struct ChallengeMid {
     pub index: usize,
     pub phase: u8,
 }
 
-impl Challenge {
+impl ChallengeMid {
     /// Index of this challenge.
     pub fn index(&self) -> usize {
         self.index
@@ -51,10 +51,10 @@ impl Challenge {
         self.phase
     }
 
-    /// Return Expression
-    pub fn expr<F: Field>(&self) -> ExpressionMid<F> {
-        ExpressionMid::Challenge(*self)
-    }
+    // /// Return Expression
+    // pub fn expr<F: Field>(&self) -> ExpressionMid<F> {
+    //     ExpressionMid::Challenge(*self)
+    // }
 }
 
 /// Low-degree expression representing an identity that must hold over the committed columns.
@@ -69,7 +69,7 @@ pub enum ExpressionMid<F> {
     /// This is an instance (external) column queried at a certain relative location
     Instance(InstanceQueryMid),
     /// This is a challenge
-    Challenge(Challenge),
+    Challenge(ChallengeMid),
     /// This is a negated polynomial
     Negated(Box<ExpressionMid<F>>),
     /// This is the sum of two polynomials
@@ -166,6 +166,12 @@ pub struct CompiledCircuitV2<F: Field> {
     pub cs: ConstraintSystemV2Backend<F>,
 }
 
+// TODO: The query_cell method is only used in the frontend, which uses Expression.  By having this
+// trait implemented here we can only return ExpressionMid, which requires conversion to Expression
+// when used.  On the other hand, it's difficult to move ColumnType to the frontend because this
+// trait is implemented for Any which is used in the backend.  It would be great to find a way to
+// move all the `query_cell` implementations to the frontend and have them return `Expression`,
+// while keeping `Any` in the middleware.
 /// A column type
 pub trait ColumnType:
     'static + Sized + Copy + std::fmt::Debug + PartialEq + Eq + Into<Any>