From 393e59a39f5cc103373fc97da27e467a56e0ad50 Mon Sep 17 00:00:00 2001
From: Fe-r-oz <feroz.ahmad.email@gmail.com>
Date: Sun, 3 Nov 2024 11:46:01 +0500
Subject: [PATCH] noncliff: better error message for inapplicable project! of
 GeneralizedStabilizer

---
 src/nonclifford.jl | 22 ++++++++++++++++++----
 1 file changed, 18 insertions(+), 4 deletions(-)

diff --git a/src/nonclifford.jl b/src/nonclifford.jl
index 70f99e42f..2439e13a8 100644
--- a/src/nonclifford.jl
+++ b/src/nonclifford.jl
@@ -172,15 +172,29 @@ function _allthreesumtozero(a,b,c)
     true
 end
 
-function project!(sm::GeneralizedStabilizer, p::PauliOperator)
+project!(::GeneralizedStabilizer, ::PauliOperator) =
+    error("The method `𝐩𝐫𝐨𝐣𝐞𝐜𝐭!` is not applicable for `𝐆𝐞𝐧𝐞𝐫𝐚𝐥𝐢𝐳𝐞𝐝𝐒𝐭𝐚𝐛𝐢𝐥𝐢𝐳𝐞𝐫` with hermitian `𝐏𝐚𝐮𝐥𝐢𝐎𝐩𝐞𝐫𝐚𝐭𝐨𝐫`, 𝐌.\n\n" *
+    "The `𝐆𝐞𝐧𝐞𝐫𝐚𝐥𝐢𝐳𝐞𝐝𝐒𝐭𝐚𝐛𝐢𝐥𝐢𝐳𝐞𝐫` 𝝉 is updated by measuring 𝐌 = 𝒶𝒹ₘ𝓈ₙ, resulting in the new state 𝝉′ defined as:\n\n" *
+    "    𝝉′ = ¼(𝐈 + 𝐌)𝝉(𝐈 + 𝐌) = (𝝌′, 𝐁(𝐒′, 𝐃′)),\n\n" *
+    "where (𝐒′, 𝐃′) is derived from (𝐒, 𝐃) through the traditional stabilizer update.\n\n" *
+    "Note that ¼(𝐈 − 𝐌)𝝉(𝐈 − 𝐌) can be obtained by changing the sign of 𝒶.\n\n" *
+    "This projection requires a probabilistic approach, as measurement outcomes depend on the expectation value of the `𝐏𝐚𝐮𝐥𝐢𝐎𝐩𝐞𝐫𝐚𝐭𝐨𝐫`.\n\n" *
+    "Specifically, this expectation value is derived from the trace 𝐓𝐫[𝝉′] = 𝐓𝐫[𝝌′] in the expression:\n\n" *
+    "    𝝉′ = 𝚺 𝝌'ᵢⱼ 𝐏ᵢ 𝛒 𝐏ⱼ†,\n\n" *
+    "where 𝝌′ is the updated density matrix. \n\n" *
+    "The trace 𝐓𝐫[𝝉′] = 𝐓𝐫[𝝌′] represents the probability of measuring either 𝟬 or a non-zero outcome and serves as the normalization required for 𝝉′.\n\n" *
+    "To correctly perform the 'nondeterministic' projection, please use `𝐩𝐫𝐨𝐣𝐞𝐜𝐭𝐫𝐚𝐧𝐝!(::𝐆𝐞𝐧𝐞𝐫𝐚𝐥𝐢𝐳𝐞𝐝𝐒𝐭𝐚𝐛𝐢𝐥𝐢𝐳𝐞𝐫, ::𝐏𝐚𝐮𝐥𝐢𝐎𝐩𝐞𝐫𝐚𝐭𝐨𝐫)`.\n\n" *
+    "`𝐩𝐫𝐨𝐣𝐞𝐜𝐭!` in this library operates as a 'deterministic' method to verify whether a measurement operator commutes with stabilizers.\n\n" *
+    "Based on this commutation, it executes additional steps to determine the resultant state after projection.\n\n" *
+    "Therefore, there are semantic nuances in defining `𝐩𝐫𝐨𝐣𝐞𝐜𝐭!` consistently for `𝐆𝐞𝐧𝐞𝐫𝐚𝐥𝐢𝐳𝐞𝐝𝐒𝐭𝐚𝐛𝐢𝐥𝐢𝐳𝐞𝐫`, particularly regarding the interpretations of `𝐚𝐧𝐭𝐢𝐜𝐨𝐦` and `𝐫𝐞𝐬` in this context.")
+
+function projectrand!(sm::GeneralizedStabilizer, p::PauliOperator)
     eval = expect(p, sm)
     prob₁ = (real(eval)+1)/2
     error("This functionality is not implemented yet")
 end
 
-function _proj₋(sm::GeneralizedStabilizer, p::PauliOperator)
-end
-function _proj₊(sm::GeneralizedStabilizer, p::PauliOperator)
+function _proj(sm::GeneralizedStabilizer, p::PauliOperator)
 end
 
 nqubits(sm::GeneralizedStabilizer) = nqubits(sm.stab)