From aa312366200f6ec42845e7cdd5b5afc8ebfb254b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=C3=89lie=20Gouzien?= <elie.gouzien@alice-bob.com>
Date: Fri, 30 Aug 2024 20:32:29 +0200
Subject: [PATCH] Fix the number of routing qubits in the factories.

---
 src/estimates.rs | 13 ++++++++-----
 src/factories.rs | 12 +++++++++---
 2 files changed, 17 insertions(+), 8 deletions(-)

diff --git a/src/estimates.rs b/src/estimates.rs
index 545279e..b584714 100644
--- a/src/estimates.rs
+++ b/src/estimates.rs
@@ -25,12 +25,13 @@ impl AliceAndBobEstimates {
     #[must_use]
     /// Count the number of physical qubits, routing qubits included.
     pub fn physical_qubits(&self) -> u64 {
-        // Routing qubits must be added to ensure all-to-all connectivity
+        // "Vertical" routing qubits must be added to ensure all-to-all connectivity
         // Formula from arXiv: 2302.06639, p. 27. `logical_qubits()` include the "horizontal
-        // routing qubits".
+        // routing qubits", including the one between the computation qubits and factories.
         let additional_routing_qubits = 2
-            * ((3 * self.layout_overhead().logical_qubits()
-                + self.toffoli_factory_part().map_or(0, FactoryPart::copies) * 6)
+            * ((3
+                * (self.layout_overhead().logical_qubits()
+                    + self.toffoli_factory_part().map_or(0, FactoryPart::copies) * 5))
                 - 1);
         self.0.physical_qubits() + additional_routing_qubits
     }
@@ -111,7 +112,9 @@ impl Display for AliceAndBobEstimates {
         writeln!(
             f,
             "factories distance:  {}",
-            self.toffoli_factory_part().expect("No factory part").factory()
+            self.toffoli_factory_part()
+                .expect("No factory part")
+                .factory()
         )?;
         writeln!(f, "factory fraction:    {:.2}%", self.factory_fraction())?;
         writeln!(f, "─────────────────────────────")
diff --git a/src/factories.rs b/src/factories.rs
index f34b31b..a8bf30f 100644
--- a/src/factories.rs
+++ b/src/factories.rs
@@ -76,11 +76,17 @@ impl estimates::Factory for ToffoliFactory {
 
     /// Number of physical qubits in each factory.
     ///
-    /// Each Toffoli factory requires 4 logical qubits, see
-    /// [arXiv:2302.06639](https://arxiv.org/abs/2302.06639) (p. 27).
+    /// Each Toffoli factory requires 4 logical qubits + 1 "horizontal" routing qubit,
+    /// see [arXiv:2302.06639](https://arxiv.org/abs/2302.06639) (p. 27).
+    /// The routing qubit under the factories is associated with the compute qubits.
+    ///
+    /// Note that the formula might not be exact when factories internal distance is
+    /// different than the main code distance, but it is negligeable.
+    /// Additionnaly, note that that is might not even be a real problem as only one of the 4
+    /// factory qubit needs to be accessed through all it's physical qubits.
     fn physical_qubits(&self) -> u64 {
         let num_logical_qubits: u64 = 4;
-        let horizontal_routing_qubits = num_logical_qubits.div_ceil(4) + 1;
+        let horizontal_routing_qubits: u64 = 1;
 
         (num_logical_qubits + horizontal_routing_qubits) * (2 * self.code_distance as u64 - 1)
     }