Public release

Q3/Documentation/English/SearchIndex/5/indexMetadata.wl

@@ -1,9 +1,8 @@
 <|"IndexedPaths" -> None, "Driver" -> "Lucene", 
- "CreationDate" -> DateObject[{2023, 7, 26, 15, 29, 
-    28.097825`8.201247684806715}, "Instant", "Gregorian", 9.], 
- "Version" -> 5, "Synonyms" -> None, "Method" -> "BM25", 
- "Language" -> "English", "ContentFieldOptions" -> 
-  <|"Title" -> <|"Stored" -> True, "Weight" -> 2|>, 
+ "CreationDate" -> DateObject[{2023, 7, 29, 23, 31, 
+    51.8458`8.467288555440298}, "Instant", "Gregorian", 9.], "Version" -> 5, 
+ "Synonyms" -> None, "Method" -> "BM25", "Language" -> "English", 
+ "ContentFieldOptions" -> <|"Title" -> <|"Stored" -> True, "Weight" -> 2|>, 
    "ExactTitle" -> <|"Stored" -> True, "Tokenized" -> False, 
      "LengthWeighted" -> False|>, "NormalizedTitle" -> 
     <|"Tokenized" -> False, "LengthWeighted" -> False|>, 

Q3/Kernel/Abel.wl

@@ -4,8 +4,8 @@ BeginPackage["Q3`"]
 
 `Abel`$Version = StringJoin[
   $Input, " v",
-  StringSplit["$Revision: 3.46 $"][[2]], " (",
-  StringSplit["$Date: 2023-07-23 11:17:49+09 $"][[2]], ") ",
+  StringSplit["$Revision: 3.53 $"][[2]], " (",
+  StringSplit["$Date: 2023-07-28 22:30:12+09 $"][[2]], ") ",
   "Mahn-Soo Choi"
  ];
 
@@ -1341,25 +1341,33 @@ MultiplyDot[a_?ArrayQ, b_?ArrayQ] := Inner[Multiply, a, b]
 
 (**** <Garner> ****)
 
-Garner::usage = "Garner[expr] collects together terms involving the same species objects (operators, Kets, Bras, etc.) and simplifies the coefficients by using Simplify.\nGarner[expr, function] uses function instead of Simplify."
-
 FullGarner::usage = "FullGarner[expr] collects together terms involving the same species objects (operators, Kets, Bras, etc.) and simplifies the coefficients by using FullSimplify."
 
-SetAttributes[Garner, Listable]
-
 SetAttributes[FullGarner, Listable]
 
+FullGarner[expr_] := Garner[expr, FullSimplify]
+
+
+Garner::usage = "Garner[expr] collects together terms involving the same species objects (operators, Kets, Bras, etc.) and simplifies the coefficients by using Simplify.\nGarner[expr, function] uses function instead of Simplify."
+
+SetAttributes[Garner, Listable]
+
 Garner[expr_, tool_:Simplify] := Module[
-  { bb = $GarnerPatterns["Heads"],
-    tt = $GarnerPatterns["Tests"],
-    qq },
-  bb = Union @ Cases[expr, bb, Infinity];
-  qq = expr /. {_Multiply -> 0};
-  qq = Union @ Cases[qq, tt, Infinity];
-  Collect[KetRegulate @ expr, Join[qq, bb], tool]
+  { pp = Alternatives @@ Values[$GarnerPatterns],
+    gg = expr /. {op:$GarnerPatterns["Heads"]->Hold[op]} },
+  gg = theGarner[Expand @ gg];
+  gg = Union @ Cases[ReleaseHold @ gg, pp];
+  Collect[KetRegulate @ expr, gg, tool]
  ]
 
-FullGarner[expr_] := Garner[expr, FullSimplify]
+
+theGarner::usage = "Breaks into elementary parts."
+
+theGarner[expr_Plus] := Flatten @ Map[theGarner, List @@ expr]
+
+theGarner[expr_Times] := List @@ expr
+
+theGarner[any_] := {any}
 
 
 AddGarnerPatterns::usage = "AddGarnerPatterns[pattern$1,pattern$2,\[Ellipsis]] adds patterns to be handled by Garner."
@@ -1424,7 +1432,7 @@ $ElaborationPatterns = Association[
 
 DistributableQ::usage = "DistributableQ[x, y, \[Ellipsis]] returns True if any of the arguments x, y, \[Ellipsis] has head of Plus."
 
-DistributableQ[args__] := Not @ MissingQ @ FirstCase[ {args}, _Plus ]
+DistributableQ[args__] := Not @ MissingQ @ FirstCase[{args}, _Plus]
 
 
 MultiplyGenus::usage = "MultiplyGenus[op] returns the Genus of op, which may be a Species or related function.\nMultiplyGenus is a category class of Species and functions for Multiply that ranks above MultiplyKind. It affects how Multiply rearranges the non-commutative elements.\nMultiplyGenus is intended for internal use."
@@ -1475,7 +1483,7 @@ NonCommutativeMultiply[a___] := Multiply[a]
 
 Multiply[] = 1 (* See also Times[]. *)
 
-Multiply[c_] := c
+Multiply[c_] = c
 
 (* Associativity *)
 

Q3/Kernel/Gottesman.wl

@@ -5,8 +5,8 @@ BeginPackage["Q3`"]
 
 `Gottesman`$Version = StringJoin[
   $Input, " v",
-  StringSplit["$Revision: 2.57 $"][[2]], " (",
-  StringSplit["$Date: 2023-07-19 23:48:01+09 $"][[2]], ") ",
+  StringSplit["$Revision: 2.70 $"][[2]], " (",
+  StringSplit["$Date: 2023-07-28 07:28:00+09 $"][[2]], ") ",
   "Mahn-Soo Choi"
  ];
 
@@ -21,7 +21,7 @@ BeginPackage["Q3`"]
 
 { CliffordDecompose };
 
-{ Stabilizer, StabilizerStateQ };
+{ Stabilizer, StabilizerStateQ, StabilizerStateCount };
 
 { BinarySymplecticGroup,
   BinarySymplecticGroupElements };
@@ -481,29 +481,34 @@ GottesmanInner[v_?VectorQ, w_?VectorQ] := (
   Message[GottesmanInner::incon, v, w];
   0 ) /; Not @ ArrayQ @ {v, w}
 
+
 GottesmanBasis::usage = "GottesmanBasis[{v1, v2, \[Ellipsis]}] returns a symplectic basis of the vector space spanned by {v1, v2, \[Ellipsis]}.\nGottesmanBasis[v] returns a symplectic basis {v, \[Ellipsis]} spanning the Gottesman vector space containing v.\nGottesmanBasis[n] returns the standard basis of the n-qubit (2n-dimensional) Gottesman vector space, which happens to be a symplectic basis with respect to GottesmanInner."
 
-GottesmanBasis[bs:{__?VectorQ}] := Module[
+(* See: Koenig and Smolin (2021) *)
+
+GottesmanBasis[{}] = {} (* fallback *)
+
+GottesmanBasis[bs_?MatrixQ] := Module[
   { v = First @ bs,
     w, new },
+  If[ContainsOnly[v, {0}], Return @ GottesmanBasis @ Rest @ bs];
+
   w = Select[bs, GottesmanInner[v, #]==1&];
-  If[ Length[w] == 0,
-    Return[bs],
-    w = First[w]
-   ];
+  If[Length[w] == 0, Return[bs], w = First[w]];
+
   new = Map[
     Mod[# + w * GottesmanInner[v, #] + v * GottesmanInner[w, #], 2]&,
     DeleteCases[Rest @ bs, w]
    ];
-  Join[{v, w}, new]
- ] /; ArrayQ @ bs
+  Join[{v, w}, GottesmanBasis @ DeleteCases[new, Table[0, Length @ v]]]
+ ]
 
-GottesmanBasis[v_?VectorQ] := One[Length @ v] /;
+GottesmanBasis[v_?VectorQ] := IdentityMatrix[Length @ v] /;
   v == UnitVector[Length @ v, 1]
 
 GottesmanBasis[v_?VectorQ] := With[
   { id = IdentityMatrix[Length @ v] },
-  GottesmanBasis @ Join[{v}, Rest @ id]
+  GottesmanBasis @ Join[{v}, id]
  ]
 
 GottesmanBasis[n_Integer] := One[2*n] /; n > 0
@@ -631,6 +636,16 @@ StabilizerStateQ[expr_] := StabilizerStateQ[Matrix @ expr]
 
 StabilizerStateQ[expr_, ss:{__?QubitQ}] := StabilizerStateQ[Matrix @ expr]
 
+
+StabilizerStateCount::usage = "StabilizerStateCount[n] returns the number of stabilizer states on an n-qubit system.\nStabilizerStateCount[{s1,s2,\[Ellipsis],sn}] is equivalent to StabilizerStateCount[n] for qubits s1, s2, \[Ellipsis], sn."
+(* See: Aaronson and Gottesman (2004). *)
+
+StabilizerStateCount[n_Integer] :=
+  Power[2, n] * Product[Power[2, k] + 1, {k, n}]
+
+StabilizerStateCount[ss:{___?QubitQ}] :=
+  StabilizerStateCount[Length @ ss]
+
 (**** </Stabilizer> ****)
 
 
@@ -810,7 +825,7 @@ GottesmanMatrixQ[mat_?MatrixQ] := Module[
 
 GottesmanMatrix::usage = "GottesmanMatrix[mat] returns the binary symplectic matrix corresponding to the Clifford operator represented with matrix representation mat.\nGottesmanMatrix[op, {s$1,s$2,$$}] returns the binary symplectic matrix corresponding to Clifford operator op."
 
-GottesmanMatrix::dimen = "`` has wrong dimensions and is not a valid matrix representation of a Clifford operator."
+GottesmanMatrix::dim = "`` has wrong dimensions and is not a valid matrix representation of a Clifford operator."
 
 GottesmanMatrix[op_, S_?QubitQ] := GottesmanMatrix[op, {FlavorNone @ S}]
 
@@ -839,7 +854,7 @@ GottesmanMatrix[mat_?MatrixQ] := Module[
   { n = Log[2, First @ Dimensions @ mat],
     xz },
   If[ Not @ IntegerQ[n],
-    Message[GottesmanMatrix::dimen, MatrixForm @ mat];
+    Message[GottesmanMatrix::dim, MatrixForm @ mat];
     Return[{{}}]
    ];
   xz = ThePauli @@@ Riffle[
@@ -852,7 +867,7 @@ GottesmanMatrix[mat_?MatrixQ] := Module[
 
 FromGottesmanMatrix::usage = "FromGottesmanMatrix[mat, {s$1,s$2,$$}] returns the Clifford operator corresponding to binary symplectic matrix mat."
 
-FromGottesmanMatrix::badmat = "`` is not a valid binary symplectic matrix."
+FromGottesmanMatrix::spmat = "`` is not a valid binary symplectic matrix."
 
 FromGottesmanMatrix[mat_?MatrixQ, ss:{_?QubitQ, __?QubitQ}] := Module[
   { n = Length @ ss,
@@ -863,12 +878,13 @@ FromGottesmanMatrix[mat_?MatrixQ, ss:{_?QubitQ, __?QubitQ}] := Module[
   ff = Transpose[Partition[#, 2]& /@ Take[mat, 2]];
   kk = FirstPosition[GottesmanInner @@@ ff, 1];
 
-  If[ MissingQ[kk], 
-    Message[FromGottesmanMatrix::badmat, MatrixForm @ mat];
-    Return[1]
+  If[ MissingQ[kk],
+    Message[FromGottesmanMatrix::spmat, MatrixForm @ mat];
+    Return[1],
+    kk = First[kk]
    ];
 
-  If[ (kk = First[kk]) != 1,
+  If[ kk != 1,
     cyc = CircleTimes[
       PermutationMatrix[Cycles @ {{1, kk}}, n],
       One[2]
@@ -1002,27 +1018,27 @@ GottesmanStandard[mat_?MatrixQ, off_?MatrixQ] := (
 GottesmanStandard[mat_?MatrixQ, off_?MatrixQ] := Module[
   { vv = off,
     xx, zz, rx, rz,
-    prm, new, m, n },
+    cx, cz, new, m, n },
   {xx, zz} = GottesmanSplit[mat];
   {m, n} = Dimensions[xx];
 
   (* Gaussian elimitation of the X-part *)
-  
+
   new = RowReduce[ArrayFlatten @ {{xx, zz, vv}}, Modulus->2];
   xx = new[[;;, ;;n]];
   zz = new[[;;, n+1;;2n]];
   vv = new[[;;, 2n+1;;]];
 
   rx = MatrixRank[xx, Modulus->2];
-  prm = columnPivoting[new, 0, Range @ rx];
+  cx = columnPivoting[xx, 0, Range @ rx];
 
-  xx = Transpose @ Permute[Transpose @ xx, prm];
-  zz = Transpose @ Permute[Transpose @ zz, prm];
+  xx = Transpose @ Permute[Transpose @ xx, cx];
+  zz = Transpose @ Permute[Transpose @ zz, cx];
 
-  If[rx == m, Return @ {xx, zz, vv, prm}];
+  If[rx == m, Return @ {xx, zz, vv, cx}];
 
   (* Gaussian elimitation of the Z-part *)
-  
+
   new = RotateLeft[#, n+rx]& /@ ArrayFlatten @ {{xx, zz, vv}};
   new = Join[ new[[;;rx]], RowReduce[new[[rx+1;;]], Modulus->2] ];
   new = RotateRight[#, n+rx]& /@ new;
@@ -1031,12 +1047,12 @@ GottesmanStandard[mat_?MatrixQ, off_?MatrixQ] := Module[
   vv = new[[;;, 2n+1;;]];
 
   rz = MatrixRank[zz[[rx+1;;, rx+1;;]], Modulus->2];
-  prm = columnPivoting[new, rx, Range @ rz];
+  cz = columnPivoting[zz, rx, Range @ rz];
 
-  xx = Transpose @ Permute[Transpose @ xx, prm];
-  zz = Transpose @ Permute[Transpose @ zz, prm];
+  xx = Transpose @ Permute[Transpose @ xx, cz];
+  zz = Transpose @ Permute[Transpose @ zz, cz];
 
-  Return @ {xx, zz, vv, prm}
+  Return @ {xx, zz, vv, PermutationProduct[cx, cz]}
  ]
 
 

Q3/Kernel/Gray.wl

@@ -5,8 +5,8 @@ BeginPackage["Q3`"]
 
 `Gray`$Version = StringJoin[
   $Input, " v",
-  StringSplit["$Revision: 1.88 $"][[2]], " (",
-  StringSplit["$Date: 2023-07-23 12:10:11+09 $"][[2]], ") ",
+  StringSplit["$Revision: 1.89 $"][[2]], " (",
+  StringSplit["$Date: 2023-07-28 00:03:42+09 $"][[2]], ") ",
   "Mahn-Soo Choi"
  ];
 
@@ -79,7 +79,7 @@ Elaborate @ GrayTransform[ss:{__?QubitQ}] :=
   Elaborate @ ExpressionFor[TheGrayTransform[Length @ ss], ss]
 
 GrayTransform /:
-Elaborate @ GrayTransform[n_Integer] := TheGrayTransform[n]
+Elaborate @ GrayTransform[n_Integer] :=
   Elaborate @ ExpressionFor[TheGrayTransform[n]]
 
 

Q3/Kernel/Pauli.wl

@@ -4,8 +4,8 @@ BeginPackage["Q3`"]
 
 `Pauli`$Version = StringJoin[
   $Input, " v",
-  StringSplit["$Revision: 6.4 $"][[2]], " (",
-  StringSplit["$Date: 2023-07-22 19:37:14+09 $"][[2]], ") ",
+  StringSplit["$Revision: 6.5 $"][[2]], " (",
+  StringSplit["$Date: 2023-07-30 10:41:31+09 $"][[2]], ") ",
   "Mahn-Soo Choi"
  ];
 
@@ -2703,6 +2703,14 @@ Rotation[a:{_, {_, _, _}}, b:{_, {_, _, _}}..] :=
 
 Rotation::axis = "The axis in `` is not proper."
 
+Format[ op:Rotation[phi_, v:{_, _, _}, S:(_?SpinQ|_?QubitQ), rest___] ] :=
+  Interpretation[
+    DisplayForm @ RowBox @ { Exp,
+      RowBox @ {"(", -I * (phi/2) * Dot[S @ All, Normalize @ v], ")"}
+     },
+    op ]
+
+
 Options[Rotation] = { "Label" -> Automatic }
 
 Rotation[phi_, S:(_?SpinQ|_?QubitQ), opts___?OptionQ] := (