Merge pull request #60 from f64u/error-correction

Error correction

_CoqProject

@@ -1,4 +1,5 @@
 -R _build/default/SQIR SQIR
 -R _build/default/examples/examples Examples
 -R _build/default/examples/shor Shor
+-R _build/default/examples/error-correction ErrorCorrection
 -R _build/default/VOQC VOQC

examples/error-correction/Common.v

@@ -0,0 +1,88 @@
+Require Export SQIR.UnitaryOps.
+
+Module Common.
+
+Local Open Scope ucom.
+
+(** A toffoli gate but controlled on the first qubit 
+    being zero. *)
+Definition ZCCX {dim} (a b c : nat) : base_ucom dim :=
+  X a;
+  CCX a b c;
+  X a.
+
+Lemma zero_3_f_to_vec : 
+  ∣0,0,0⟩ = f_to_vec 3 (fun _ => false).
+Proof.
+  lma'. simpl. auto with wf_db.
+Qed.
+
+Lemma one_3_f_to_vec : 
+  ∣1,0,0⟩ = f_to_vec 3 (fun n => n =? 0).
+Proof.
+  lma'. simpl. auto with wf_db.
+Qed.
+
+Lemma two_3_f_to_vec : 
+  ∣0,1,0⟩ = f_to_vec 3 (fun n => n =? 1).
+Proof.
+  lma'. simpl. auto with wf_db.
+Qed.
+
+Lemma three_3_f_to_vec : 
+  ∣1,1,0⟩ = f_to_vec 3 (fun n => orb (n =? 0) (n =? 1)).
+Proof.
+  lma'. simpl. auto with wf_db.
+Qed.
+
+Lemma four_3_f_to_vec : 
+  ∣0,0,1⟩ = f_to_vec 3 (fun n => n =? 2).
+Proof.
+  lma'. simpl. auto with wf_db.
+Qed.
+
+Lemma five_3_f_to_vec : 
+  ∣1,0,1⟩ = f_to_vec 3 (fun n => orb (n =? 0) (n =? 2)).
+Proof.
+  lma'. simpl. auto with wf_db.
+Qed.
+
+Lemma six_3_f_to_vec : 
+  ∣0,1,1⟩ = f_to_vec 3 (fun n => orb (n =? 1) (n =? 2)).
+Proof.
+  lma'. simpl. auto with wf_db.
+Qed.
+
+Lemma seven_3_f_to_vec : 
+  ∣1,1,1⟩ = f_to_vec 3 (fun _ => true).
+Proof.
+  lma'. simpl. auto with wf_db.
+Qed.
+
+#[export] Hint Rewrite
+  zero_3_f_to_vec
+  one_3_f_to_vec
+  two_3_f_to_vec
+  three_3_f_to_vec
+  four_3_f_to_vec
+  five_3_f_to_vec
+  six_3_f_to_vec
+  seven_3_f_to_vec
+  : f_to_vec_3_db.
+
+
+Ltac f_to_vec_simpl_light :=
+  first
+  [ rewrite f_to_vec_H
+  | rewrite f_to_vec_X
+  | rewrite f_to_vec_CCX
+  | rewrite f_to_vec_CNOT
+  ];
+  try lia;
+  simpl update;
+  do 2 (
+    repeat rewrite Mmult_plus_distr_l;
+    repeat rewrite Mscale_mult_dist_r
+  ).
+
+End Common.