diff --git a/src/core/backend/avx512/bit_reverse.rs b/src/core/backend/avx512/bit_reverse.rs
index 83a68d01e..f729ca590 100644
--- a/src/core/backend/avx512/bit_reverse.rs
+++ b/src/core/backend/avx512/bit_reverse.rs
@@ -166,6 +166,6 @@ mod tests {
         let mut data: BaseFieldVec = data.into_iter().collect();
 
         bit_reverse_m31(&mut data.data[..]);
-        assert_eq!(data.to_vec(), expected);
+        assert_eq!(data.to_cpu(), expected);
     }
 }
diff --git a/src/core/backend/avx512/circle.rs b/src/core/backend/avx512/circle.rs
index 8769ee128..e74d57728 100644
--- a/src/core/backend/avx512/circle.rs
+++ b/src/core/backend/avx512/circle.rs
@@ -349,7 +349,7 @@ mod tests {
             );
             let poly = evaluation.clone().interpolate();
             let evaluation2 = poly.evaluate(domain);
-            assert_eq!(evaluation.values.to_vec(), evaluation2.values.to_vec());
+            assert_eq!(evaluation.values.to_cpu(), evaluation2.values.to_cpu());
         }
     }
 
@@ -369,8 +369,8 @@ mod tests {
             let evaluation2 = poly.evaluate(domain_ext);
             let poly2 = evaluation2.interpolate();
             assert_eq!(
-                poly.extend(log_size + 3).coeffs.to_vec(),
-                poly2.coeffs.to_vec()
+                poly.extend(log_size + 3).coeffs.to_cpu(),
+                poly2.coeffs.to_cpu()
             );
         }
     }
@@ -411,7 +411,7 @@ mod tests {
                 .extend(log_size + 2)
                 .evaluate(CanonicCoset::new(log_size + 2).circle_domain());
 
-            assert_eq!(eval0.values.to_vec(), eval1.values.to_vec());
+            assert_eq!(eval0.values.to_cpu(), eval1.values.to_cpu());
         }
     }
 
diff --git a/src/core/backend/avx512/fft/ifft.rs b/src/core/backend/avx512/fft/ifft.rs
index 0a4093126..980fe5ae0 100644
--- a/src/core/backend/avx512/fft/ifft.rs
+++ b/src/core/backend/avx512/fft/ifft.rs
@@ -687,7 +687,7 @@ mod tests {
                 );
 
                 // Compare.
-                assert_eq!(values.to_vec(), expected_coeffs);
+                assert_eq!(values.to_cpu(), expected_coeffs);
             }
         }
     }
@@ -718,7 +718,7 @@ mod tests {
             );
 
             // Compare.
-            assert_eq!(values.to_vec(), expected_coeffs);
+            assert_eq!(values.to_cpu(), expected_coeffs);
         }
     }
 
diff --git a/src/core/backend/avx512/fft/rfft.rs b/src/core/backend/avx512/fft/rfft.rs
index 8c46e8f44..5349a5e7a 100644
--- a/src/core/backend/avx512/fft/rfft.rs
+++ b/src/core/backend/avx512/fft/rfft.rs
@@ -659,7 +659,7 @@ mod tests {
                 );
 
                 // Compare.
-                assert_eq!(values.to_vec(), expected_coeffs);
+                assert_eq!(values.to_cpu(), expected_coeffs);
             }
         }
     }
@@ -690,7 +690,7 @@ mod tests {
             );
 
             // Compare.
-            assert_eq!(values.to_vec(), expected_coeffs);
+            assert_eq!(values.to_cpu(), expected_coeffs);
         }
     }
 
diff --git a/src/core/backend/avx512/mod.rs b/src/core/backend/avx512/mod.rs
index 99b7c2dfa..2ada5a4c2 100644
--- a/src/core/backend/avx512/mod.rs
+++ b/src/core/backend/avx512/mod.rs
@@ -7,16 +7,13 @@ pub mod qm31;
 pub mod quotients;
 
 use bytemuck::{cast_slice, cast_slice_mut, Pod, Zeroable};
-use itertools::izip;
 use num_traits::Zero;
 
 use self::bit_reverse::bit_reverse_m31;
-use self::cm31::PackedCM31;
 pub use self::m31::{PackedBaseField, K_BLOCK_SIZE};
 use self::qm31::PackedQM31;
 use super::{Column, ColumnOps};
 use crate::core::fields::m31::BaseField;
-use crate::core::fields::qm31::SecureField;
 use crate::core::fields::secure_column::SecureColumn;
 use crate::core::fields::{FieldExpOps, FieldOps};
 use crate::core::utils;
@@ -79,7 +76,7 @@ impl Column<BaseField> for BaseFieldVec {
             length: len,
         }
     }
-    fn to_vec(&self) -> Vec<BaseField> {
+    fn to_cpu(&self) -> Vec<BaseField> {
         self.data
             .iter()
             .flat_map(|x| x.to_array())
@@ -133,21 +130,6 @@ impl FromIterator<BaseField> for BaseFieldVec {
 }
 
 impl SecureColumn<AVX512Backend> {
-    pub fn at(&self, vec_index: usize) -> PackedQM31 {
-        unsafe {
-            PackedQM31([
-                PackedCM31([
-                    *self.columns[0].data.get_unchecked(vec_index),
-                    *self.columns[1].data.get_unchecked(vec_index),
-                ]),
-                PackedCM31([
-                    *self.columns[2].data.get_unchecked(vec_index),
-                    *self.columns[3].data.get_unchecked(vec_index),
-                ]),
-            ])
-        }
-    }
-
     pub fn set(&mut self, vec_index: usize, value: PackedQM31) {
         unsafe {
             *self.columns[0].data.get_unchecked_mut(vec_index) = value.a().a();
@@ -156,17 +138,6 @@ impl SecureColumn<AVX512Backend> {
             *self.columns[3].data.get_unchecked_mut(vec_index) = value.b().b();
         }
     }
-
-    pub fn to_cpu(&self) -> Vec<SecureField> {
-        izip!(
-            self.columns[0].to_vec(),
-            self.columns[1].to_vec(),
-            self.columns[2].to_vec(),
-            self.columns[3].to_vec(),
-        )
-        .map(|(a, b, c, d)| SecureField::from_m31_array([a, b, c, d]))
-        .collect()
-    }
 }
 
 #[cfg(all(target_arch = "x86_64", target_feature = "avx512f"))]
@@ -186,7 +157,7 @@ mod tests {
         for i in 0..100 {
             let col = Col::<B, BaseField>::from_iter((0..i).map(BaseField::from));
             assert_eq!(
-                col.to_vec(),
+                col.to_cpu(),
                 (0..i).map(BaseField::from).collect::<Vec<_>>()
             );
             for j in 0..i {
@@ -202,7 +173,7 @@ mod tests {
             let mut col = Col::<B, BaseField>::from_iter((0..len).map(BaseField::from));
             B::bit_reverse_column(&mut col);
             assert_eq!(
-                col.to_vec(),
+                col.to_cpu(),
                 (0..len)
                     .map(|x| BaseField::from(utils::bit_reverse_index(x, i as u32)))
                     .collect::<Vec<_>>()
diff --git a/src/core/backend/avx512/quotients.rs b/src/core/backend/avx512/quotients.rs
index 8dbb699c7..def77a437 100644
--- a/src/core/backend/avx512/quotients.rs
+++ b/src/core/backend/avx512/quotients.rs
@@ -139,7 +139,7 @@ mod tests {
             .map(|c| {
                 CircleEvaluation::<CPUBackend, _, BitReversedOrder>::new(
                     c.domain,
-                    c.values.to_vec(),
+                    c.values.to_cpu(),
                 )
             })
             .collect::<Vec<_>>();
diff --git a/src/core/backend/cpu/mod.rs b/src/core/backend/cpu/mod.rs
index 5927165d0..589bde681 100644
--- a/src/core/backend/cpu/mod.rs
+++ b/src/core/backend/cpu/mod.rs
@@ -35,7 +35,7 @@ impl<T: Debug + Clone + Default> Column<T> for Vec<T> {
     fn zeros(len: usize) -> Self {
         vec![T::default(); len]
     }
-    fn to_vec(&self) -> Vec<T> {
+    fn to_cpu(&self) -> Vec<T> {
         self.clone()
     }
     fn len(&self) -> usize {
diff --git a/src/core/backend/mod.rs b/src/core/backend/mod.rs
index 026fbacc4..7f290386d 100644
--- a/src/core/backend/mod.rs
+++ b/src/core/backend/mod.rs
@@ -2,16 +2,18 @@ use std::fmt::Debug;
 
 pub use cpu::CPUBackend;
 
+use super::commitment_scheme::quotients::QuotientOps;
 use super::fields::m31::BaseField;
 use super::fields::qm31::SecureField;
 use super::fields::FieldOps;
+use super::fri::FriOps;
 use super::poly::circle::PolyOps;
 
 pub mod avx512;
 pub mod cpu;
 
 pub trait Backend:
-    Copy + Clone + Debug + FieldOps<BaseField> + FieldOps<SecureField> + PolyOps
+    Copy + Clone + Debug + FieldOps<BaseField> + FieldOps<SecureField> + PolyOps + QuotientOps + FriOps
 {
 }
 
@@ -27,7 +29,7 @@ pub trait Column<T>: Clone + Debug + FromIterator<T> {
     /// Creates a new column of zeros with the given length.
     fn zeros(len: usize) -> Self;
     /// Returns a cpu vector of the column.
-    fn to_vec(&self) -> Vec<T>;
+    fn to_cpu(&self) -> Vec<T>;
     /// Returns the length of the column.
     fn len(&self) -> usize;
     /// Returns true if the column is empty.
diff --git a/src/core/commitment_scheme/prover.rs b/src/core/commitment_scheme/prover.rs
index 3bf716236..502cc83f4 100644
--- a/src/core/commitment_scheme/prover.rs
+++ b/src/core/commitment_scheme/prover.rs
@@ -9,7 +9,6 @@ use std::ops::Deref;
 
 use itertools::Itertools;
 
-use super::super::backend::cpu::{CPUCircleEvaluation, CPUCirclePoly};
 use super::super::backend::CPUBackend;
 use super::super::channel::Blake2sChannel;
 use super::super::circle::CirclePoint;
@@ -28,27 +27,28 @@ use super::utils::TreeVec;
 use crate::commitment_scheme::blake2_hash::{Blake2sHash, Blake2sHasher};
 use crate::commitment_scheme::merkle_decommitment::MerkleDecommitment;
 use crate::commitment_scheme::merkle_tree::MerkleTree;
+use crate::core::backend::{Backend, Column};
 use crate::core::channel::Channel;
-use crate::core::poly::circle::SecureEvaluation;
+use crate::core::poly::circle::{CircleEvaluation, CirclePoly, SecureEvaluation};
 
 type MerkleHasher = Blake2sHasher;
 type ProofChannel = Blake2sChannel;
 
 /// The prover side of a FRI polynomial commitment scheme. See [self].
-pub struct CommitmentSchemeProver {
-    pub trees: TreeVec<CommitmentTreeProver>,
+pub struct CommitmentSchemeProver<B: Backend> {
+    pub trees: TreeVec<CommitmentTreeProver<B>>,
     pub log_blowup_factor: u32,
 }
 
-impl CommitmentSchemeProver {
+impl<B: Backend> CommitmentSchemeProver<B> {
     pub fn new(log_blowup_factor: u32) -> Self {
         CommitmentSchemeProver {
-            trees: TreeVec::<CommitmentTreeProver>::default(),
+            trees: TreeVec::default(),
             log_blowup_factor,
         }
     }
 
-    pub fn commit(&mut self, polynomials: ColumnVec<CPUCirclePoly>, channel: &mut ProofChannel) {
+    pub fn commit(&mut self, polynomials: ColumnVec<CirclePoly<B>>, channel: &mut ProofChannel) {
         let tree = CommitmentTreeProver::new(polynomials, self.log_blowup_factor, channel);
         self.trees.push(tree);
     }
@@ -57,13 +57,13 @@ impl CommitmentSchemeProver {
         self.trees.as_ref().map(|tree| tree.root())
     }
 
-    pub fn polynomials(&self) -> TreeVec<ColumnVec<&CPUCirclePoly>> {
+    pub fn polynomials(&self) -> TreeVec<ColumnVec<&CirclePoly<B>>> {
         self.trees
             .as_ref()
             .map(|tree| tree.polynomials.iter().collect())
     }
 
-    fn evaluations(&self) -> TreeVec<ColumnVec<&CPUCircleEvaluation<BaseField, BitReversedOrder>>> {
+    fn evaluations(&self) -> TreeVec<ColumnVec<&CircleEvaluation<B, BaseField, BitReversedOrder>>> {
         self.trees
             .as_ref()
             .map(|tree| tree.evaluations.iter().collect())
@@ -101,7 +101,7 @@ impl CommitmentSchemeProver {
         // SecureColumn.
         let quotients = quotients
             .into_iter()
-            .map(SecureEvaluation::to_cpu)
+            .map(SecureEvaluation::to_cpu_circle_eval)
             .collect_vec();
 
         // Run FRI commitment phase on the oods quotients.
@@ -146,16 +146,16 @@ pub struct CommitmentSchemeProof {
 
 /// Prover data for a single commitment tree in a commitment scheme. The commitment scheme allows to
 /// commit on a set of polynomials at a time. This corresponds to such a set.
-pub struct CommitmentTreeProver {
-    pub polynomials: ColumnVec<CPUCirclePoly>,
-    pub evaluations: ColumnVec<CPUCircleEvaluation<BaseField, BitReversedOrder>>,
+pub struct CommitmentTreeProver<B: Backend> {
+    pub polynomials: ColumnVec<CirclePoly<B>>,
+    pub evaluations: ColumnVec<CircleEvaluation<B, BaseField, BitReversedOrder>>,
     // TODO(AlonH): Change to mixed degree merkle and remove values clone.
     commitment: MerkleTree<BaseField, MerkleHasher>,
 }
 
-impl CommitmentTreeProver {
+impl<B: Backend> CommitmentTreeProver<B> {
     fn new(
-        polynomials: ColumnVec<CPUCirclePoly>,
+        polynomials: ColumnVec<CirclePoly<B>>,
         log_blowup_factor: u32,
         channel: &mut ProofChannel,
     ) -> Self {
@@ -167,10 +167,11 @@ impl CommitmentTreeProver {
                 )
             })
             .collect_vec();
+        // TODO(spapini): Remove to_cpu() when Merkle support different backends.
         let commitment = MerkleTree::<BaseField, MerkleHasher>::commit(
             evaluations
                 .iter()
-                .map(|eval| eval.values.clone())
+                .map(|eval| eval.values.to_cpu())
                 .collect_vec(),
         );
         channel.mix_digest(commitment.root());
@@ -194,14 +195,14 @@ impl CommitmentTreeProver {
         let values = self
             .evaluations
             .iter()
-            .map(|c| queries.iter().map(|p| c[*p]).collect())
+            .map(|c| queries.iter().map(|p| c.at(*p)).collect())
             .collect();
         let decommitment = self.commitment.generate_decommitment(queries);
         (values, decommitment)
     }
 }
 
-impl Deref for CommitmentTreeProver {
+impl<B: Backend> Deref for CommitmentTreeProver<B> {
     type Target = MerkleTree<BaseField, MerkleHasher>;
 
     fn deref(&self) -> &Self::Target {
diff --git a/src/core/commitment_scheme/quotients.rs b/src/core/commitment_scheme/quotients.rs
index e90505cb1..12ae0f9ad 100644
--- a/src/core/commitment_scheme/quotients.rs
+++ b/src/core/commitment_scheme/quotients.rs
@@ -136,7 +136,7 @@ pub fn fri_answers_for_log_size(
                     random_coeff,
                     &batched_openings,
                 )
-                .to_cpu()
+                .to_cpu_circle_eval()
             })
             .collect(),
     );
diff --git a/src/core/fields/secure_column.rs b/src/core/fields/secure_column.rs
index bc865139d..77e75d867 100644
--- a/src/core/fields/secure_column.rs
+++ b/src/core/fields/secure_column.rs
@@ -13,21 +13,12 @@ pub struct SecureColumn<B: FieldOps<BaseField>> {
     pub columns: [Col<B, BaseField>; SECURE_EXTENSION_DEGREE],
 }
 impl SecureColumn<CPUBackend> {
-    pub fn at(&self, index: usize) -> SecureField {
-        SecureField::from_m31_array(std::array::from_fn(|i| self.columns[i][index]))
-    }
-
     pub fn set(&mut self, index: usize, value: SecureField) {
         self.columns
             .iter_mut()
             .map(|c| &mut c[index])
             .assign(value.to_m31_array());
     }
-
-    // TODO(spapini): Remove when we no longer use CircleEvaluation<SecureField>.
-    pub fn to_cpu(&self) -> Vec<SecureField> {
-        (0..self.len()).map(|i| self.at(i)).collect()
-    }
 }
 impl<B: FieldOps<BaseField>> SecureColumn<B> {
     pub fn zeros(len: usize) -> Self {
@@ -43,4 +34,13 @@ impl<B: FieldOps<BaseField>> SecureColumn<B> {
     pub fn is_empty(&self) -> bool {
         self.columns[0].is_empty()
     }
+
+    pub fn at(&self, index: usize) -> SecureField {
+        SecureField::from_m31_array(std::array::from_fn(|i| self.columns[i].at(index)))
+    }
+
+    // TODO(spapini): Remove when we no longer use CircleEvaluation<SecureField>.
+    pub fn to_cpu(&self) -> Vec<SecureField> {
+        (0..self.len()).map(|i| self.at(i)).collect()
+    }
 }
diff --git a/src/core/fri.rs b/src/core/fri.rs
index 5c9642c85..f9843ed51 100644
--- a/src/core/fri.rs
+++ b/src/core/fri.rs
@@ -804,7 +804,7 @@ impl<B: FriOps, H: Hasher<NativeType = u8>> FriLayerProver<B, H> {
     fn new(evaluation: LineEvaluation<B, SecureField, BitReversedOrder>) -> Self {
         // TODO(spapini): Commit on slice.
         // TODO(spapini): Merkle tree in backend.
-        let merkle_tree = MerkleTree::commit(vec![evaluation.values.to_vec()]);
+        let merkle_tree = MerkleTree::commit(vec![evaluation.values.to_cpu()]);
         #[allow(unreachable_code)]
         FriLayerProver {
             evaluation,
diff --git a/src/core/poly/circle/evaluation.rs b/src/core/poly/circle/evaluation.rs
index 1d50559ed..5db0ffadb 100644
--- a/src/core/poly/circle/evaluation.rs
+++ b/src/core/poly/circle/evaluation.rs
@@ -34,6 +34,7 @@ impl<B: FieldOps<F>, F: ExtensionOf<BaseField>, EvalOrder> CircleEvaluation<B, F
 // Note: The concrete implementation of the poly operations is in the specific backend used.
 // For example, the CPU backend implementation is in `src/core/backend/cpu/poly.rs`.
 impl<F: ExtensionOf<BaseField>, B: FieldOps<F>> CircleEvaluation<B, F, NaturalOrder> {
+    // TODO(spapini): Remove. Is this even used.
     pub fn get_at(&self, point_index: CirclePointIndex) -> F {
         self.values
             .at(self.domain.find(point_index).expect("Not in domain"))
diff --git a/src/core/poly/circle/secure_poly.rs b/src/core/poly/circle/secure_poly.rs
index e581ef2e2..a7ee0946e 100644
--- a/src/core/poly/circle/secure_poly.rs
+++ b/src/core/poly/circle/secure_poly.rs
@@ -2,7 +2,6 @@ use std::ops::Deref;
 
 use super::CircleDomain;
 use crate::core::backend::cpu::{CPUCircleEvaluation, CPUCirclePoly};
-use crate::core::backend::CPUBackend;
 use crate::core::circle::CirclePoint;
 use crate::core::fields::m31::BaseField;
 use crate::core::fields::qm31::SecureField;
@@ -56,9 +55,9 @@ pub struct SecureEvaluation<B: FieldOps<BaseField>> {
     pub domain: CircleDomain,
     pub values: SecureColumn<B>,
 }
-impl SecureEvaluation<CPUBackend> {
+impl<B: FieldOps<BaseField>> SecureEvaluation<B> {
     // TODO(spapini): Remove when we no longer use CircleEvaluation<SecureField>.
-    pub fn to_cpu(self) -> CPUCircleEvaluation<SecureField, BitReversedOrder> {
+    pub fn to_cpu_circle_eval(self) -> CPUCircleEvaluation<SecureField, BitReversedOrder> {
         CPUCircleEvaluation::new(self.domain, self.values.to_cpu())
     }
 }
diff --git a/src/core/poly/line.rs b/src/core/poly/line.rs
index e369401a0..69cd40a6e 100644
--- a/src/core/poly/line.rs
+++ b/src/core/poly/line.rs
@@ -230,7 +230,7 @@ impl<B: FieldOps<F>, F: Field, EvalOrder> LineEvaluation<B, F, EvalOrder> {
 
     /// Clones the values into a new line evaluation in the CPU.
     pub fn to_cpu(&self) -> CPULineEvaluation<F, EvalOrder> {
-        CPULineEvaluation::new(self.domain, self.values.to_vec())
+        CPULineEvaluation::new(self.domain, self.values.to_cpu())
     }
 }