From 592a2cc51d997de14e271a70d647c8fe621dccf8 Mon Sep 17 00:00:00 2001
From: rishi763 <55810666+rishi763@users.noreply.github.com>
Date: Sat, 22 Jun 2024 02:29:01 +0000
Subject: [PATCH 1/2] Closes #46

---
 src/fusion/fusion.rs | 43 +++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 43 insertions(+)

diff --git a/src/fusion/fusion.rs b/src/fusion/fusion.rs
index a8520ed..5574eb2 100644
--- a/src/fusion/fusion.rs
+++ b/src/fusion/fusion.rs
@@ -165,6 +165,49 @@ impl Fusion {
             .zip(self.ising_canonical_topo_charge(init_charge).iter())
             .all(|(a, b)| *b <= 0 || *a > 0)
     }
+
+    ///
+    /// Returns number of sigmas that can be in the initial topological charges of anyons to exactly a certain number of qubits for the Ising model
+    /// 
+    pub fn ising_possible_sigmas(&self, qubits:u32) -> Vec<u32>{
+        vec![2*qubits+1, 2*qubits+2]
+    }
+    ///
+    /// Returns number of taus that can be in the initial topological charges of anyons to exactly a certain number of qubits for the Fibonacci model
+    /// 
+    /// Precondition: Requires qubits <=30
+    pub fn fibonacci_possible_taus(&self, qubits:u32) -> Vec<u32> {
+
+        if qubits ==0{
+            return vec![0,1,2,3];
+        }
+
+        let mut possible_taus = Vec::new();
+
+        let mut n = 1;
+
+
+        // We have that the fibonacci recurrence gives us that tau^n = a + b * tau
+        let mut a = 0;
+        let mut b = 1;
+        
+        // Checks that b < 2^(qubits+1) meaning as otherwise fusing to tau would result in too many qubits
+        while b < 1 << (qubits+1) {
+            
+            // If b >= 2^qubits we have that this will give exactly 'qubits' qubits
+            if (1 << (qubits)) <= b{
+                possible_taus.push(n);
+            }
+
+            b=a+b;
+            a=b-a;
+
+            n+=1;
+        }
+        // Accounts for the case that we can also fuse to vaccuum
+        possible_taus.push(n);
+        possible_taus
+    }
 }
 
 /// Python Facing Methods

From e373e16452a7caae45cc2eb0a938bd7bf646f779 Mon Sep 17 00:00:00 2001
From: rishi763 <55810666+rishi763@users.noreply.github.com>
Date: Sat, 22 Jun 2024 21:55:14 +0000
Subject: [PATCH 2/2] Wrote tests and interface for #46

---
 python/tests/test_fusion.py | 12 ++++++++++++
 src/fusion/fusion.rs        |  8 ++++++++
 2 files changed, 20 insertions(+)

diff --git a/python/tests/test_fusion.py b/python/tests/test_fusion.py
index 5f6937a..f6d6320 100644
--- a/python/tests/test_fusion.py
+++ b/python/tests/test_fusion.py
@@ -67,3 +67,15 @@ def test_verify_fusion_result(state):
     assert not fusion.verify_fusion_result(TopoCharge.from_ising(IsingTopoCharge.Vacuum), AnyonModel.Ising)
     assert not fusion.verify_fusion_result(TopoCharge.from_ising(IsingTopoCharge.Psi), AnyonModel.Ising)
     assert fusion.verify_fusion_result(TopoCharge.from_ising(IsingTopoCharge.Sigma), AnyonModel.Ising)
+
+@pytest.mark.fusion
+def test_minimum_possible_anyons(state):
+
+    fusion = Fusion(state)
+
+    assert (fusion.minimum_possible_anyons(10, AnyonModel.Ising) == [21,22])
+    assert (fusion.minimum_possible_anyons(5, AnyonModel.Ising) == [11,12])
+
+
+    assert(fusion.minimum_possible_anyons(10, AnyonModel.Fibonacci) == [17,18]);
+    assert(fusion.minimum_possible_anyons(0, AnyonModel.Fibonacci) == [0,1,2,3]);
diff --git a/src/fusion/fusion.rs b/src/fusion/fusion.rs
index 5574eb2..9f94dc9 100644
--- a/src/fusion/fusion.rs
+++ b/src/fusion/fusion.rs
@@ -311,4 +311,12 @@ impl Fusion {
             _ => false,
         }
     }
+    fn minimum_possible_anyons(&self, qubits: u32, anyon_model: &AnyonModel) -> PyResult<Vec<u32>>{
+        match anyon_model{
+            AnyonModel::Ising => Ok(self.ising_possible_sigmas(qubits)),
+            AnyonModel::Fibonacci => Ok(self.fibonacci_possible_taus(qubits)),
+            _ => Err(PyValueError::new_err("This model is not supported yet"))
+        }
+
+    }
 }