diff --git a/.github/workflows/binaries.yml b/.github/workflows/binaries.yml
index 0c1c73ea..cd729325 100644
--- a/.github/workflows/binaries.yml
+++ b/.github/workflows/binaries.yml
@@ -32,7 +32,7 @@ jobs:
           
   cpu_macos_x86_build:
     name: MacOS_x86
-    runs-on: macos-latest
+    runs-on: macos-15-intel
     steps:
       - uses: actions/checkout@v2
         with:
diff --git a/.github/workflows/macos.yml b/.github/workflows/macos.yml
index 711fab14..88e8a204 100644
--- a/.github/workflows/macos.yml
+++ b/.github/workflows/macos.yml
@@ -9,7 +9,7 @@ on:
 jobs:
   cpu_macos_x86_build:
     name: MacOS_x86
-    runs-on: macos-latest
+    runs-on: macos-15-intel
     steps:
       - uses: actions/checkout@v2
         with:
diff --git a/.gitmodules b/.gitmodules
index aa85eb41..b181281d 100644
--- a/.gitmodules
+++ b/.gitmodules
@@ -1,4 +1,4 @@
 [submodule "QuEST"]
 	path = QuEST
 	url = https://github.com/QuEST-Kit/QuEST
-	branch = develop
+	branch = temp-questlink-submodule
diff --git a/Link/QuESTlink.m b/Link/QuESTlink.m
index b7e10c74..3f52c8dd 100644
--- a/Link/QuESTlink.m
+++ b/Link/QuESTlink.m
@@ -35,12 +35,14 @@
     Unset[$MessagePrePrint];
 
     (* display launch message *)
-    Message[QuESTlink::notice, 
-        "Bug alert! Prior to this version (v0.19), SimplifyPaulis[] contained a bug whereby multiplying X and Z operators (targeting the same qubit) produced a Y operator with an incorrect sign. " <>
-        "This bug occurred only when multiplying Pauli strings together, and did not affect other algebraic forms (like summing or exponentiation), though did affect the downstream function CalcPauliExpressionMatrix[]. " <>
-        "Please check any previous calculations which passed products of Pauli-strings to SimplifyPaulis[] and CalcPauliExpressionMatrix[]. " <>
-        "We sincerely apologise for any arising issues! Silence this warning using Quiet[]."];
-
+    (* MSG BELOW REMOVED BUT PRESERVED FOR FUTURE EXAMPLE *)
+        (*
+        Message[QuESTlink::notice, 
+            "Bug alert! Prior to this version (v0.19), SimplifyPaulis[] contained a bug whereby multiplying X and Z operators (targeting the same qubit) produced a Y operator with an incorrect sign. " <>
+            "This bug occurred only when multiplying Pauli strings together, and did not affect other algebraic forms (like summing or exponentiation), though did affect the downstream function CalcPauliExpressionMatrix[]. " <>
+            "Please check any previous calculations which passed products of Pauli-strings to SimplifyPaulis[] and CalcPauliExpressionMatrix[]. " <>
+            "We sincerely apologise for any arising issues! Silence this warning using Quiet[]."];
+        *)
     (* restore subsequent message truncation (as per user settings) *)
     $MessagePrePrint = initPrePrintVal;
 
@@ -363,35 +365,43 @@ The sum of the expected values of the (potentially unnormalised) state-vectors o
     RecompileCircuit::error = "`1`"
 
     CalcPauliTransferMatrix::usage = "CalcPauliTransferMatrix[circuit] returns a single PTM operator equivalent to the given circuit.
-CalcPauliTranferMatrix /@ circuit returns an equivalent sequence of individual (and likely smaller) PTM operators.
-CalcPauliTransferMatrix accepts optional argument AssertValidChannels."
+CalcPauliTransferMatrix /@ circuit returns an equivalent sequence of individual (and likely smaller) PTM operators.
+CalcPauliTransferMatrix accepts the below options:
+\[Bullet] AssertValidChannels->False to disable the automatic simplification of the matrix through the assertion of valid channel parameters. See ?AssertValidChannels.
+\[Bullet] \"Picture\" which can be either \"Schrodinger\" (default) or \"Heisenberg\", which returns the PTM of the adjoint channel, as operates upon observables in the Heisenberg picture."
     CalcPauliTransferMatrix::error = "`1`"
 
     CalcPauliTransferMap::usage = "CalcPauliTransferMap[ptm] produces a PTMap equivalent to the given PTM operator. See ?PTM.
 CalcPauliTransferMap[circuit] produces a PTMap from the given gate or circuit, by merely first invoking CalcPauliTransferMatrix[].
 The returned map encodes how each basis Pauli-string (encoded by its integer index) is mapped to a weighted sum of other strings (encoded as {index, coefficient} pairs) by the PTM. The indexing convention is the same as used by GetPauliString[] where the subscripted qubits of the PTM are treated as though given in order of increasing significance.
 For improved performance, gate parameters should be kept symbolic (and optionally substituted thereafter) so that algebraic simplification can identify zero elements without interference by finite-precision numerical errors.
-CalcPauliTransferMap also accepts option AssertValidChannels->False to disable the automatic simplification of the map's coefficients through the assertion of valid channel parameters. See ?AssertValidChannels."
+CalcPauliTransferMap also accepts options:
+\[Bullet] AssertValidChannels->False to disable the automatic simplification of the map's coefficients through the assertion of valid channel parameters. See ?AssertValidChannels.
+\[Bullet] \"Picture\" which can be either \"Schrodinger\" (default) or \"Heisenberg\", which returns the map of the adjoint channel, as operates upon observables in the Heisenberg picture."
     CalcPauliTransferMap::error = "`1`"
 
     DrawPauliTransferMap::usage = "DrawPauliTransferMap[map] visualises the given PTMap as a graph where nodes are basis Pauli strings, and edges indicate the transformative action of the map.
 DrawPauliTransferMap also accepts PTM, circuit and gate instances, for which the corresponding PTMap is automatically calculated.
-DrawPauliTransferMap accepts options \"PauliStringForm\", \"ShowCoefficients\" and \"EdgeDegreeStyles\", in addition to all options accepted by Graph[].
+DrawPauliTransferMap accepts options \"PauliStringForm\", \"ShowCoefficients\" and \"EdgeDegreeStyles\", in addition to all options accepted by CalcPauliTransferMap and Graph[].
 \[Bullet] \"ShowCoefficients\" -> False hides the map's Pauli string coefficients which are otherwise shown as edge labels.
 \[Bullet] \"PauliStringForm\" sets the vertex label format to one of \"Subscript\" (default), \"Index\", \"Kronecker\", \"String\" or \"Hidden\". These (except the latter) are the formats are supported by GetPauliStringReformatted[].
 \[Bullet] \"EdgeDegreeStyles\" specifies a list of styles (default informed by ColorData[\"Pastel\"]) to set upon edges from nodes with increasing outdegree. For example, \"EdgeDegreeStyles\"->{Red,Green,Blue} sets edges from Pauli states which are mapped to a single other state to the colour Red, but two-outdegree node out-edges become Green, and three-outdegree become Blue. The list is assumed repeated for higher outdegree nodes than specified.
-\[Bullet] Graph[] options override these settings, so specifying EdgeStyle -> Black will set all edges to Black regardless of their node's outdegree."
+\[Bullet] Graph[] options override these settings, so specifying EdgeStyle -> Black will set all edges to Black regardless of their node's outdegree.
+\[Bullet] \"Picture\" -> \"Heisenberg\" can be passed when the given circuit excludes existing PTMs or PTMap, and will compute new maps in the Heisenberg picture.
+\[Bullet] AssertValidChannels -> False will disable analytic simplifications made by assuming the input circuit/channel/map represents a CPTP operation."
     DrawPauliTransferMap::error = "`1`"
 
     ApplyPauliTransferMap::usage = "ApplyPauliTransferMap[pauliString, ptMap] returns the Pauli string produced by the given PTMap acting upon the given initial Pauli string.
 ApplyPauliTransferMap[pauliString, circuit] automatically transforms the given circuit (composed of gates, channels, and PTMs, possibly intermixed) into PTMaps before applying them to the given Pauli string.
 For improved performance, gate parameters should be kept symbolic (and optionally substituted thereafter) so that algebraic simplification can identify zero elements without interference by finite-precision numerical errors.
+ApplyPauliTransferMap accepts all optional arguments accepted by CalcPauliTransferMap, including:
+\[Bullet] \"Picture\" -> \"Heisenberg\" to apply the adjoint channel of the given circuit, useful when Heisenberg-evolving an osbervable operator.
+\[Bullet] AssertValidChannels -> False to disable automatic simplification of the Pauli transfer maps (and as a result, the coefficients of the output Pauli string) through assuming CPTPness.
 This method uses automatic caching to avoid needless re-computation of an operator's PTMap, agnostic to the targeted and controlled qubits, at the cost of additional memory usage. Caching behaviour can be controlled using option \"CacheMaps\":
 \[Bullet] \"CacheMaps\" -> \"UntilCallEnd\" (default) caches all computed PTMaps but clears the cache when ApplyPauliTransferMap[] returns.
 \[Bullet] \"CacheMaps\" -> \"Forever\" maintains the cache even between multiple calls to ApplyPauliTransferMap[].
-\[Bullet] \"CacheMaps\" -> \"Never\" disables caching (and clears the existing cache before computation), re-computing each operqtors' PTMap when encountered in the circuit.
-ApplyPauliTransferMap also accepts all options of CalcPauliTransferMap, like AssertValidChannels. See ?AssertValidChannels."
-    ApplyPauliTransferMap::error = "`1`"
+\[Bullet] \"CacheMaps\" -> \"Never\" disables caching (and clears the existing cache before computation), re-computing each operqtors' PTMap when encountered in the circuit."
+ApplyPauliTransferMap::error = "`1`"
 
     CalcPauliTransferEval::usage = "CalcPauliTransferEval[pauliString, ptMaps] returns the full evolution history of the given Pauli string under the given list of PTMap operators. This is often unnecessary to call directly - most users can call ApplyPauliTransferMap[] or DrawPauliTransferEval[] instead - unless you wish to store or process the evaluation history.
 CalcPauliTransferEval[pauliString, circuit] evolves the Pauli string under the PTMaps automatically calculated from the given circuit. 
@@ -416,6 +426,7 @@ The sum of the expected values of the (potentially unnormalised) state-vectors o
 \[Bullet] \"OutputForm\" -> \"Simple\" (default) or \"Detailed\", as explained above.
 \[Bullet] \"CombineStrings\" -> False which disables combining incident Pauli strings, so that the result is an acyclic tree, and each node has a single parent.
 \[Bullet] \"CacheMaps\" which controls the automatic caching of generated PTMaps (see ?ApplyPauliTransferMap).
+\[Bullet] \"Picture\" -> \"Heisenberg\" to evaluate the adjoint channel of the given circuit, useful when Heisenberg-evolving an osbervable operator.
 \[Bullet] AssertValidChannels -> False which disables the simplification of symbolic Pauli string coefficients (see ?AssertValidChannels)."
     CalcPauliTransferEval::error = "`1`"
 
@@ -428,6 +439,7 @@ The sum of the expected values of the (potentially unnormalised) state-vectors o
 \[Bullet] \"ShowCoefficients\" -> True or False explicitly shows or hides the PTMap coefficient associated with each edge. The default is Automatic which auto-hides edge labels if there are too many.
 \[Bullet] \"EdgeDegreeStyles\" specifies the style of edges from nodes of increasing outdegree. See ?DrawPauliTransferMap.
 \[Bullet] \"CacheMaps\" controls the automatic caching of generated PTMaps. See ?ApplyPauliTransferMap.
+\[Bullet] \"Picture\" -> \"Heisenberg\" draws the evaluation of the adjoint channel of the given circuit, evolving the intial Pauli string in the Heisenberg picture as if it were an observable operator.
 \[Bullet] AssertValidChannels -> False disables the simplification of symbolic Pauli string coefficients, only noticeable when \"ShowCoefficients\"->True. See ?AssertValidChannels.
 \[Bullet] Graph[] options override these settings. For example, specifying EdgeStyle -> Black will set all edges to Black regardless of their node's outdegree."
     DrawPauliTransferEval::error = "`1`"
@@ -460,7 +472,12 @@ The sum of the expected values of the (potentially unnormalised) state-vectors o
     GetPauliStringOverlap::usage = "GetPauliStringOverlap[a, b] returns the Pauli products common to both given weighted sums of Pauli strings, with coefficients equal to the conjugate of the 'a' coefficients multiplied by those of 'b'."
     GetPauliStringOverlap::error = "`1`"
 
-    
+    DrawPauliStringAsTree::usage = "DrawPauliStringAsTree[paulis] draws the given sum of Pauli strings as a tree, where Pauli products with the same prefix operators share ancestors. This visualises a compressed form of the ensemble without coefficients.
+DrawPauliStringAsTree also accepts option \"SmallestIsRoot\"->True to reverse the ordering of the strings such that increasing tree depth corresponds to increasing qubit index."
+    DrawPauliStringAsTree::error = "`1`"
+
+
+
     (*
      * optional arguments to public functions
      *)
@@ -573,6 +590,9 @@ The sum of the expected values of the (potentially unnormalised) state-vectors o
     Damp::usage = "Damp[prob] is 1 qubit amplitude damping with the given decay probability."
     Protect[Damp]
     
+    PauliError::usage = "PauliError[pX,pY,pZ] is a 1 qubit inhomogeneous depolarising channel, where pX, pY, pZ are the probabilities of X, Y and Z errors respectively."
+    Protect[PauliError]
+
     SWAP::usage = "SWAP is a 2 qubit gate which swaps the state of two qubits."
     Protect[SWAP]
     
@@ -775,7 +795,7 @@ The probability of the forced measurement outcome (as if it were hypothetically
                
         (* opcodes which correlate with the global IDs in circuits.hpp *)
         getOpCode[gate_] :=
-            gate /. {H->0,X->1,Y->2,Z->3,Rx->4,Ry->5,Rz->6,R->7,S->8,T->9,U->10,Deph->11,Depol->12,Damp->13,SWAP->14,M->15,P->16,Kraus->17,G->18,Id->19,Ph->20,KrausNonTP->21,Matr->22,UNonNorm->23,Fac->24,_->-1}
+            gate /. {H->0,X->1,Y->2,Z->3,Rx->4,Ry->5,Rz->6,R->7,S->8,T->9,U->10,Deph->11,Depol->12,Damp->13,SWAP->14,M->15,P->16,Kraus->17,G->18,Id->19,Ph->20,KrausNonTP->21,Matr->22,UNonNorm->23,Fac->24,PauliError->25,_->-1}
         
         
         
@@ -948,7 +968,7 @@ The probability of the forced measurement outcome (as if it were hypothetically
         circContainsDecoherence[circuit_List] :=
             MemberQ[
                 circuit, 
-                Subscript[ Damp | Deph | Depol | Kraus | KrausNonTP, __ ][__]]
+                Subscript[ Damp | Deph | Depol | Kraus | KrausNonTP | PauliError, __ ][__]]
             
         
         
@@ -1023,6 +1043,7 @@ The probability of the forced measurement outcome (as if it were hypothetically
          *)
         
         encodeDerivParams[Subscript[Rx|Ry|Rz|Ph|Damp|Deph|Depol, __][f_], x_] := {D[f,x]}
+        encodeDerivParams[Subscript[PauliError, __][f__], x_] := D[{f},x]
         encodeDerivParams[R[f_,_], x_] := {D[f,x]}
         encodeDerivParams[G[f_], x_] := {D[f,x]}
         encodeDerivParams[Fac[f_], x_] := With[{df=D[f,x]}, {Re@N@df, Im@N@df}]
@@ -1217,6 +1238,11 @@ The probability of the forced measurement outcome (as if it were hypothetically
             DestroyQuregInternal @ ReleaseHold @ qureg
         DestroyQureg[___] := invalidArgError[DestroyQureg]
 
+
+        (* Mathematica v14 silently changed Ket... *)
+        getPrettyKet[x_] :=
+            If[$VersionNumber < 14, Ket[x], Ket[{x}]]
+
         (* get a local matrix representation of the qureg. GetQuregMatrixInternal provided by WSTP *)
         GetQuregState[qureg_Integer, "ZBasisMatrix"] :=
             With[{data = GetQuregMatrixInternal[qureg]},
@@ -1246,11 +1272,11 @@ The probability of the forced measurement outcome (as if it were hypothetically
                     (* project state-vector into kets *)
                     Length @ Dimensions @ matr === 1,
                         matr . Table[
-                            Ket @ IntegerString[i, 2, nQb], {i, 0, 2^nQb - 1}],
+                            getPrettyKet @ IntegerString[i, 2, nQb], {i, 0, 2^nQb - 1}],
                     (* project density-matrix into ket-bra's *)
                     Length @ Dimensions @ matr === 2,
                         Flatten[matr] . Flatten @ Table[
-                            Ket @ IntegerString[i, 2, nQb] ** 
+                            getPrettyKet @ IntegerString[i, 2, nQb] ** 
                             Bra @ IntegerString[j, 2, nQb],
                             {i, 0, 2^nQb - 1}, {j, 0, 2^nQb - 1}]
                 (* tidy up some amplitudes for visual clarity *)
@@ -1266,6 +1292,7 @@ The probability of the forced measurement outcome (as if it were hypothetically
 
         GetQuregState[___] := invalidArgError[GetQuregState]
 
+
         (* overwrite the state of a qureg. InitStateFromAmps provided by WSTP *)
         SetQuregMatrix[qureg_Integer, elems_List] :=
             With[{flatelems = N @ 
@@ -1703,9 +1730,55 @@ The probability of the forced measurement outcome (as if it were hypothetically
             getCompactStringFormOfPauliString[string, nQb]
         
         GetPauliStringReformatted[___] := invalidArgError[GetPauliStringReformatted]
-            
 
+
+
+        (*
+         * Drawing Pauli strings
+         *)
+                
+        getEdgesFromPauliProduct[prod_String] := 
+            Rule @@@ Partition[StringTake[prod, Table[{1,n},{n,StringLength@prod}]], 2, 1]
+    
+        getEdgesFromPauliString[paulis_, smallestIsRoot_] := 
+            Module[
+                {strings, rules},
+                strings = GetPauliStringReformatted[paulis, "String"];
+
+                (* ensure output is a list of strings and coefficients *)
+                If[StringQ[strings], strings = {{strings,1}}];
+
+                (* discard coefficients (hehe) *)
+                strings = First /@ strings;
+
+                (* reverse strings is smallest index is root *)
+                If[smallestIsRoot, strings = StringReverse /@ strings];
+
+                (* give strings a common blank ancestor, i.e. the tree's root *)
+                strings = (" " <> #&) /@ strings;
+
+                (* decompose each string into a tree, then merge *)
+                rules = getEdgesFromPauliProduct /@ strings;
+                rules = DeleteDuplicates @ Flatten @ rules;
+                rules
+            ]
+
+        Options[DrawPauliStringAsTree] = {
+            "SmallestIsRoot" -> False
+        };
         
+        DrawPauliStringAsTree[paulis_?isValidSymbolicPauliString, opts:OptionsPattern[{DrawPauliStringAsTree,Graph}]] :=
+            Graph[
+                getEdgesFromPauliString[paulis, OptionValue["SmallestIsRoot"]], 
+                Sequence @@ FilterRules[{opts}, Options[Graph]],
+                VertexLabels->{s_ :> StringTake[s,-1]},
+                VertexStyle -> White,
+                GraphLayout -> "LayeredDigraphEmbedding"
+            ]
+        DrawPauliStringAsTree[___] := invalidArgError[DrawPauliStringAsTree]
+
+
+
         (*
          * Analytic and numerical channel decompositions for statevector simulation
          *)
@@ -1725,6 +1798,11 @@ The probability of the forced measurement outcome (as if it were hypothetically
             Circuit[ Fac@Sqrt[x/3] Subscript[X, q] ],
             Circuit[ Fac@Sqrt[x/3] Subscript[Y, q] ],
             Circuit[ Fac@Sqrt[x/3] Subscript[Z, q] ]}
+        convertOpToPureCircs[Subscript[PauliError, q_][px_,py_,pz_]] := {
+            Circuit[ Fac@Sqrt[1-(px+py+pz)] ],
+            Circuit[ Fac@Sqrt[px] Subscript[X, q] ],
+            Circuit[ Fac@Sqrt[py] Subscript[Y, q] ],
+            Circuit[ Fac@Sqrt[pz] Subscript[Z, q] ]}
         convertOpToPureCircs[Subscript[Depol, q1_,q2_][x_]] := 
             Join[{{Fac@Sqrt[1-x]}}, Rest @ Flatten[
                 Table[{Fac@Sqrt[x/15], Subscript[a, q1], Subscript[b, q2]}, {a,{Id,X,Y,Z}}, {b,{Id,X,Y,Z}}] /. Subscript[Id, _] -> Nothing, 1]]
@@ -1753,7 +1831,9 @@ The probability of the forced measurement outcome (as if it were hypothetically
                 Subscript[Deph, _][x_ /; x < 0 || x > 1/2] |
                 Subscript[Deph, _, _][x_ /; x < 0 || x > 3/4] |
                 Subscript[Depol, _][x_ /; x < 0 || x > 3/4] |
-                Subscript[Depol, _, _][x_ /; x < 0 || x > 15/16]],
+                Subscript[Depol, _, _][x_ /; x < 0 || x > 15/16]
+                (Subscript[PauliError, _][x_, y_, z_] /; ( x<0 || y<0 || z<0 || x+y+z>1 || Max[x,y,z] > 1-(x+y+z) ))
+                ],
                 Message[GetRandomCircuitFromChannel::error, "A unitary-mixture channel had an invalid probability which was negative or exceeded that causing maximal mixing."];
                 Return[$Failed]];
 
@@ -2437,11 +2517,16 @@ The probability of the forced measurement outcome (as if it were hypothetically
         drawGate[Ph, {ctrls___}, {targs__}, col_] := {
             drawControls[{ctrls,targs},{},col],
             Text["\[Theta]", {col+.75,Min[{ctrls,targs}]+.75}]}
-        drawGate[label:(Kraus|KrausNonTP|Damp|Deph|Depol), {}, targs_List, col_] := {
+        drawGate[label:(Kraus|KrausNonTP|Damp|Deph|Depol|PauliError), {}, targs_List, col_] := {
             EdgeForm[Dashed],
             drawGate[label /. {
-                    Kraus -> \[Kappa], KrausNonTP -> \[Kappa]NTP, Damp -> \[Gamma], 
-                    Deph -> \[Phi], Depol -> \[CapitalDelta]},
+                    Kraus -> \[Kappa], 
+                    KrausNonTP -> \[Kappa]NTP, 
+                    Damp -> \[Gamma], 
+                    Deph -> \[Phi], 
+                    Depol -> \[CapitalDelta],
+                    PauliError -> \[Sigma]
+                },
                 {}, targs, col]}
 
         (* single qubit gate graphics *)
@@ -2459,9 +2544,6 @@ The probability of the forced measurement outcome (as if it were hypothetically
                 Circle[{col+.5,targ+.5-.4}, .4, {.7,\[Pi]-.7}],
                 Line[{{col+.5,targ+.5-.25}, {col+.5+.2,targ+.5+.3}}]
                 }, {targ, {targs}}]
-
-        drawGate[Depol, {}, {targ_}, col_] := {
-            EdgeForm[Dashed], drawGate[\[CapitalDelta], {}, {targ}, col]}
         drawGate[X, {}, {targ_}, col_] := {
             Circle[{col+.5,targ+.5},.25],
             Line[{{col+.5,targ+.5-.25},{col+.5,targ+.5+.25}}]}
@@ -3046,6 +3128,11 @@ The probability of the forced measurement outcome (as if it were hypothetically
                     Sqrt[p/3] PauliMatrix[1],
                     Sqrt[p/3] PauliMatrix[2],
                     Sqrt[p/3] PauliMatrix[3]}],
+                Subscript[PauliError, q_][px_,py_,pz_] :> Subscript[Kraus, q][{
+                    Sqrt[1-(px+py+pz)] PauliMatrix[0],
+                    Sqrt[px] PauliMatrix[1],
+                    Sqrt[py] PauliMatrix[2],
+                    Sqrt[pz] PauliMatrix[3]}],
                 Subscript[Depol, q1_,q2_][p_] :> Subscript[Kraus, q1,q2][ Join[
                     {Sqrt[1-p] IdentityMatrix[4]},
                     Flatten[ Table[
@@ -3133,8 +3220,8 @@ The probability of the forced measurement outcome (as if it were hypothetically
         
         (* Damp, Deph are entirely real (when valid), else we assume principal Sqrts,
          * and although Depol contains Y, its superoperator/application cancels conj(Y)=-Y *)
-        getGateConj[valid_] @ (g:Subscript[Damp|Deph|Depol, __]) @ x_ :=
-            If[valid, g[x], g @ Conjugate @ x]
+        getGateConj[valid_] @ (g:Subscript[Damp|Deph|Depol|PauliError, __]) @ x__ :=
+            If[valid, g[x], g @@ Conjugate @ {x}]
 
         (* unmatched operators *)
         getGateConj[valid_][g_] := Message[GetCircuitConjugated::error,
@@ -3159,12 +3246,19 @@ The probability of the forced measurement outcome (as if it were hypothetically
 
         (* rules to simplify operators when AssertValidChannels -> True *)
         (* note we do not simplify/assert real-parameterised gates like rotations, out of laziness *)
+        (* beware we are simplifying under the constraints that the channels never surpass maximum mixing,
+         * which is in-fact distinct and stronger than constraining they are merely CPTP. *)
         assertReal[x_] := Element[x, Reals]
         getValidChannelAssumps @ Subscript[Damp, _][x_]    := assertReal[x] && (0 <= x <= 1)
         getValidChannelAssumps @ Subscript[Deph, _][x_]    := assertReal[x] && (0 <= x <= 1/2)
         getValidChannelAssumps @ Subscript[Deph, _,_][x_]  := assertReal[x] && (0 <= x <= 3/4)
         getValidChannelAssumps @ Subscript[Depol, _][x_]   := assertReal[x] && (0 <= x <= 3/4)
         getValidChannelAssumps @ Subscript[Depol, _,_][x_] := assertReal[x] && (0 <= x <= 15/16)
+        getValidChannelAssumps @ Subscript[PauliError, _][x_,y_,z_] := (
+            assertReal[x] && (0 <= x <= 1) && x <= (1 - (x+y+z)) && 
+            assertReal[y] && (0 <= y <= 1) && y <= (1 - (x+y+z)) && 
+            assertReal[z] && (0 <= z <= 1) && z <= (1 - (x+y+z))
+        )
         
         (* un-targeted operators merge with their conjugate *)
         getSuperOpCirc[numQb_,valid_] @ G[x_] :=
@@ -3177,8 +3271,8 @@ The probability of the forced measurement outcome (as if it were hypothetically
             {supermatr = Total[(KroneckerProduct[Conjugate[#], #]&) /@ matrs]},
             {Subscript[Matr, q, Sequence @@ ({q} + numQb)] @ supermatr}]
 
-        (* Damp, Depol, Deph must first be generalised to Kraus, then recursed upon... *)
-        getSuperOpCirc[numQb_,valid_] @ g:Subscript[Damp|Deph|Depol, q__][x_] := With[
+        (* Damp, Depol, Deph, PauliError must first be generalised to Kraus, then recursed upon... *)
+        getSuperOpCirc[numQb_,valid_] @ g:Subscript[Damp|Deph|Depol|PauliError, q__][__] := With[
             {supers = getSuperOpCirc[numQb, valid] /@ GetCircuitGeneralised @ g},
             {assumps = getValidChannelAssumps @ g},
             (* and the result is optionally simplified, if CPTP condition is possible (else caller Aborts) *)
@@ -3330,7 +3424,7 @@ The probability of the forced measurement outcome (as if it were hypothetically
                                     " which is not supported by the given device specification. Note this may be due to preceding gates," <> 
                                     " if the spec contains constraints which depend on dynamic variables. See ?GetUnsupportedGates."];
                                 $Failed],
-                            (* if match, but targeted qubits don't exist, throw top-level error *)
+                            (* if match, but targeted qubits do not exist, throw top-level error *)
                             Not @ AllTrue[gateQubits, LessThan[spec[NumAccessibleQubits]]],
                             Throw[
                                 Message[InsertCircuitNoise::error, "The gate " <> ToString@StandardForm@gate <> 
@@ -3380,11 +3474,11 @@ The probability of the forced measurement outcome (as if it were hypothetically
             Do[
                 With[
                     {qubitProps = Replace[qubit, spec[Qubits]]},
-                    (* continue only if qubit matches a rule in spec[Qubits] (don't noise unspecified qubits) *)
+                    (* continue only if qubit matches a rule in spec[Qubits] (do not noise unspecified qubits) *)
                     If[
                         qubitProps =!= qubit,
                         With[
-                            (* work out start-time and duration of qubit's passive noise (pre-determined) *)
+                            (* work out start-time and duration of passive noise of qubits (pre-determined) *)
                             {passiveTime = subcircTime + qubitActiveDurs[[ 1 + qubit ]]},
                             {passiveDur = subcircDur - qubitActiveDurs[[ 1 + qubit ]]},
                             (* work out passive noise (time, dur and var dependent *)
@@ -3417,7 +3511,7 @@ The probability of the forced measurement outcome (as if it were hypothetically
                 spec[InitVariables][]];
             
             Do[
-                (* get each subcirc's noise (updates circuit variables) *)
+                (* get noise of each subcirc (updates circuit variables) *)
                 {curDur, curActive, curPassive} = getDurAndNoiseFromSubcirc[sub, curTime, spec];
                     
                 (* losing info here (mering separate gate infos into subcirc-wide) *)
@@ -4004,7 +4098,7 @@ variable renaming in nested scoping structs (Module[ Function[]]) *)
                 Subscript[C, c__Integer|{c__Integer}][g_] :> Subscript[C, tidyInds@c][g],
                 (* sort targets of target-order-agnostic gates *)
                 Subscript[(g:(H|X|Y|Z|Id|SWAP|Ph|M||T|S)), t__Integer|{t__Integer}] :> Subscript[g, tidyInds@t],
-                Subscript[(g:(Rx|Ry|Rz|Damp|Deph|Depol)), t__Integer|{t__Integer}][x__] :> Subscript[g, tidyInds@t][x],
+                Subscript[(g:(Rx|Ry|Rz|Damp|Deph|Depol|PauliError)), t__Integer|{t__Integer}][x__] :> Subscript[g, tidyInds@t][x],
                 (* unpack all qubit lists *)
                 Subscript[s_, {t__}] :> Subscript[s, t],
                 Subscript[s_, {t__}][x_] :> Subscript[s, t][x],
@@ -4105,6 +4199,7 @@ variable renaming in nested scoping structs (Module[ Function[]]) *)
                         Subscript[C, __][Nothing] -> Nothing,
                         (* remove zero-parameter gates *)
                         Subscript[(Ph|Rx|Ry|Rz|Damp|Deph|Depol), __][0|0.] -> Nothing,
+                        Subscript[PauliError, __][0|0., 0|0., 0|0.] -> Nothing,
                         R[0|0.,_] -> Nothing,
                         G[0|0.] -> Nothing,
                         Fac[1|1.] -> Nothing,
@@ -4334,7 +4429,7 @@ variable renaming in nested scoping structs (Module[ Function[]]) *)
             Subscript[C, retargetQubits[c, map]] @ retargetGate[map] @ g
 
         (* avoid modifying arg of parameterised gates *)
-        retargetGate[map_][ Subscript[s:Damp|Deph|Depol|Kraus|KrausNonTP|Matr|P|Ph|Rx|Ry|Rz|U|UNonNorm, t__][args__] ] :=
+        retargetGate[map_][ Subscript[s:Damp|Deph|Depol|PauliError|Kraus|KrausNonTP|Matr|P|Ph|Rx|Ry|Rz|U|UNonNorm, t__][args__] ] :=
             Subscript[s, retargetQubits[t, map]] @ args
 
         (* modify only the qubits of the Pauli product in R gates *)
@@ -4427,7 +4522,7 @@ variable renaming in nested scoping structs (Module[ Function[]]) *)
         getGateParameterised[r_, _, exclParamsPatt_, g_ ] /; isParamInExcludeList[exclParamsPatt, g] :=
             {g, None}
 
-        (* re-paramaterise non-controlled gates *)
+        (* re-paramaterise non-controlled one-parameter gates *)
         getGateParameterised[r_, _,_, (g:Subscript[Damp|Deph|Depol|Ph|Rx|Ry|Rz, __])[x_]] := 
             {g[r], x}
         getGateParameterised[r_, _,_, (g:Fac|G)[x_]] := 
@@ -4435,6 +4530,10 @@ variable renaming in nested scoping structs (Module[ Function[]]) *)
         getGateParameterised[r_, _,_, R[x_, p_]] := 
             {R[r,p], x}
 
+        (* re-parameterise non-controlled multi-parameter gates (to a list) *)
+        getGateParameterised[s_[i_], _,_, (g:Subscript[PauliError, __])[px_,py_,pz_]] := 
+            {g[s[i], s[i+1], s[i+2]], {px,py,pz}}
+
         (* re-param control gates, removing excludes *)
         getGateParameterised[r_, _, exclParamsPatt_, (c:Subscript[C,__])[g_] ] /; Not @ isParamInExcludeList[exclParamsPatt, g] := 
             With[
@@ -4445,11 +4544,11 @@ variable renaming in nested scoping structs (Module[ Function[]]) *)
         getGateParameterised[r_, _,_, g_] :=
             {g, None}
 
-        GetCircuitParameterised[gate_?isGateFormat, s_Symbol, opts:OptionsPattern[]] :=
-            GetCircuitParameterised[{gate}, s, opts]
+        GetCircuitParameterised[gate_?isGateFormat, paramsym_Symbol, opts:OptionsPattern[]] :=
+            GetCircuitParameterised[{gate}, paramsym, opts]
 
-        GetCircuitParameterised[circuit_?isCircuitFormat, s_Symbol, OptionsPattern[]] := Module[
-            {exclGatesPatt,exclParamsPatt, paramInd,outGate,paramVal, outCircuit,outParams, newSymb,newParams,symbSubs},
+        GetCircuitParameterised[circuit_?isCircuitFormat, paramsym_Symbol, OptionsPattern[]] := Module[
+            {exclGatesPatt,exclParamsPatt, paramInd,outGate,paramValOrVals, outCircuit,outParams, newSymb,newParams,symbSubs},
 
             (* validate all options are recognised *)
             Check[ OptionValue @ "ExcludeChannels", Return @ $Failed];
@@ -4468,19 +4567,22 @@ variable renaming in nested scoping structs (Module[ Function[]]) *)
             If[ Head @ exclParamsPatt === List, 
                 exclParamsPatt = Alternatives @@ exclParamsPatt];
             If[ OptionValue @ "ExcludeChannels", 
-                exclGatesPatt = exclGatesPatt | Subscript[Damp|Deph|Depol,__][_]];
+                exclGatesPatt = exclGatesPatt | Subscript[Damp|Deph|Depol|PauliError,__][__]];
 
             paramInd = 1;
             outCircuit = {};
             outParams = {};
             Do[
                 (* conditionally insert symbolic param from each gate... *)
-                {outGate, paramVal} = getGateParameterised[
-                    s[paramInd], exclGatesPatt, exclParamsPatt, inGate];
+                {outGate, paramValOrVals} = getGateParameterised[
+                    paramsym[paramInd], exclGatesPatt, exclParamsPatt, inGate];
                 AppendTo[outCircuit, outGate];
 
-                (* and if performed, increment the symbolic param counter *)
-                If[paramVal =!= None, AppendTo[outParams, s[paramInd++] -> paramVal]],
+                (* and if performed, increment the symbolic param counter for each value *)
+                If[paramValOrVals =!= None, 
+                    Do[
+                        AppendTo[outParams, paramsym[paramInd++] -> val],
+                        {val, If[ListQ@paramValOrVals, paramValOrVals, {paramValOrVals}]}]],
                 {inGate, circuit}];
 
             paramInd = 1;
@@ -4505,8 +4607,8 @@ variable renaming in nested scoping structs (Module[ Function[]]) *)
                 outCircuit = outCircuit /. Flatten @ symbSubs;
 
                 (* re-param circuit and subs back to user symbol*)
-                outCircuit = outCircuit /. TEMPSYMBOL[i_] :> s[i];
-                outParams = newParams /. TEMPSYMBOL[i_] :> s[i];
+                outCircuit = outCircuit /. TEMPSYMBOL[i_] :> paramsym[i];
+                outParams = newParams /. TEMPSYMBOL[i_] :> paramsym[i];
             ];
 
             {outCircuit, outParams}
@@ -5029,7 +5131,7 @@ variable renaming in nested scoping structs (Module[ Function[]]) *)
             u01 = m[[;;dim/2, dim/2+1;;]];
 
             (* perform cosine-sine (CS) decomposition via numerical GSVD *)
-            {{l0,l1},{d00,d10},r0} = SingularValueDecomposition @ N @ {u00, u10};	
+            {{l0,l1},{d00,d10},r0} = SingularValueDecomposition @ N @ {u00, u10};
             
             (* TODO: we should implement the general CS decomposition, in order to handle when 
              * the diagonals include zeros; see https://arxiv.org/abs/2302.14324
@@ -5237,6 +5339,20 @@ variable renaming in nested scoping structs (Module[ Function[]]) *)
          * and Pauli-basis.
          *)
 
+        assertValidPictureFlag[flag_, canBeHeisen:True, caller_] := If[
+            Or[
+                Not @ StringQ[flag],
+                Not @ StringMatchQ[flag, "Schrodinger"|"Heisenberg"]
+            ],
+            Message[caller::error, "Optional argument \"Picture\" must be either \"Heisenberg\" or \"Schrodinger\"."]]
+        assertValidPictureFlag[flag_, canBeHeisen:False, caller_] := Switch[flag,
+            "Schrodinger",
+                True, (* i.e. nothing happens; valid **)
+            "Heisenberg",
+                Message[caller::error, "Cannot specify optional argument \"Picture\" as \"Heisenberg\" when passing an existing PTM or PTMap, since their picture has already been determined when created."],
+            _,
+                Message[caller::error, "Unrecognised value for optional argument \"Picture\" which should anyway not be specified (defaulting to \"Schrodinger\") when passing existing PTMs or PTMaps."]]
+
         getChoiVecFromMatrix[m_] := 
             Transpose @ {Flatten @ Transpose @ m}
             
@@ -5255,7 +5371,8 @@ variable renaming in nested scoping structs (Module[ Function[]]) *)
             ]
             
         Options[CalcPauliTransferMatrix] = {
-            AssertValidChannels -> True
+            AssertValidChannels -> True,
+            "Picture" -> "Schrodinger"  (* or "Heisenberg" *)
         };
     
         CalcPauliTransferMatrix[circ_?isCircuitFormat, opts:OptionsPattern[]] :=
@@ -5264,7 +5381,8 @@ variable renaming in nested scoping structs (Module[ Function[]]) *)
                     {simpFlag, qubits, targCirc, compCirc, superMatr, ptMatr},
 
                      (* trigger option validation (and show error message immediately )*)
-                    simpFlag = OptionValue[AssertValidChannels];
+                    simpFlag = OptionValue[AssertValidChannels] // ConfirmQuiet;
+                    assertValidPictureFlag[OptionValue @ "Picture", True, CalcPauliTransferMatrix] // ConfirmQuiet;
 
                     (* replace global phase gates with equivalent unitary on arbitrary qubit *)
                     qubits = GetCircuitQubits[circ] // ConfirmQuiet;
@@ -5278,12 +5396,15 @@ variable renaming in nested scoping structs (Module[ Function[]]) *)
                     compCirc = First @ GetCircuitCompacted[targCirc] // ConfirmQuiet;
 
                     (* compute superator of entire circuit (passing on AssertValidChannels) *)
-                    superMatr = SparseArray @ CalcCircuitMatrix[compCirc, AsSuperoperator -> True, opts] // ConfirmQuiet;
+                    superMatr = SparseArray @ CalcCircuitMatrix[compCirc, AsSuperoperator -> True, FilterRules[{opts}, Options @ CalcCircuitMatrix]] // ConfirmQuiet;
                     If[superMatr === {}, Message[CalcPauliTransferMatrix::error, "Could not compute circuit superoperator."]] // ConfirmQuiet;
 
                     (* compute PTM from superoperator (and optionally simplify it) **)
                     ptMatr = getSuperOpPTM[superMatr, If[simpFlag, FullSimplify, Identity]];
 
+                    (* transpose PTM in Heisenberg picture (preserving simplifications of AssertValidChannels) *)
+                    If[ OptionValue["Picture"] === "Heisenberg", ptMatr = Transpose[ptMatr]];
+
                     (* return PTM[] symbol *)
                     Subscript[PTM, Sequence @@ qubits] @ ptMatr
                 ],
@@ -5314,12 +5435,15 @@ variable renaming in nested scoping structs (Module[ Function[]]) *)
 
 
         Options[CalcPauliTransferMap] = {
-            AssertValidChannels -> True
+            AssertValidChannels -> True,
+            "Picture" -> "Schrodinger" (* or "Heisenberg" when not applied to existing PTMs *)
         };
 
         CalcPauliTransferMap[ Subscript[PTM, q__Integer][m_], OptionsPattern[] ] := (
             Check[ OptionValue[AssertValidChannels], Return @ $Failed];
-            Subscript[PTMap, q] @@ getMapOfPauliIndicesFromPTM[m] )
+            Check[ assertValidPictureFlag[OptionValue["Picture"], False, CalcPauliTransferMap], Return @ $Failed];
+            Subscript[PTMap, q] @@ getMapOfPauliIndicesFromPTM[m]
+        )
 
         CalcPauliTransferMap[ Subscript[PTM, q__Integer][m_], OptionsPattern[] ] /; 
             Not[ And@@(NonNegative/@{q}) ] || Not @ DuplicateFreeQ[{q}] := (
@@ -5334,13 +5458,18 @@ variable renaming in nested scoping structs (Module[ Function[]]) *)
         CalcPauliTransferMap[circ_?isCircuitFormat, opts:OptionsPattern[]] := Module[
             {ptm},
             Check[ OptionValue[AssertValidChannels], Return @ $Failed];
+            Check[ assertValidPictureFlag[OptionValue["Picture"], True, CalcPauliTransferMap], Return @ $Failed];
+            If[ 
+                MemberQ[circ, Subscript[PTM, __][___] ], 
+                Message[CalcPauliTransferMap::error, "Circuit must not contain existing PTM instances; only a single PTM in isolation can be passed."]; 
+                Return @ $Failed];
 
             ptm = Check[
                 CalcPauliTransferMatrix[circ, FilterRules[{opts}, Options @ CalcPauliTransferMatrix]], 
                 Message[CalcPauliTransferMap::error, "Unable to determine PTM as per the above error."];
                 Return @ $Failed];
-            
-            CalcPauliTransferMap[ptm, FilterRules[{opts}, Options @ CalcPauliTransferMap]]
+
+            CalcPauliTransferMap[ptm] (* discard opts which have already been utilised *)
         ]
 
 
@@ -5381,15 +5510,17 @@ variable renaming in nested scoping structs (Module[ Function[]]) *)
         Options[DrawPauliTransferMap] = {
             "PauliStringForm" -> "Subscript", (* or "Index", "Kronecker", "String", "Hidden" *)
             "ShowCoefficients" -> True,
-            "EdgeDegreeStyles" -> Automatic (* or a list of styles *),
+            "EdgeDegreeStyles" -> Automatic, (* or a list of styles *)
+            "Picture" -> "Schrodinger", (* or "Heisenberg", though which is not accepted when passing PTMs *)
             AssertValidChannels -> True
         };
 
         DrawPauliTransferMap[ Subscript[PTMap, q__Integer?NonNegative][rules__], opts:OptionsPattern[{DrawPauliTransferMap,Graph}] ] := Module[
             {edges, edgeLabels, vertInds, vertFormFunc, vertLabels, vertDegrees, maxDegree, degreeStyles, edgeStyles},
 
-            (* fail immediately if given unrecognised option *)
+            (* fail immediately if given unrecognised or invalid option *)
             Check[OptionValue["PauliStringForm"], Return @ $Failed];
+            Check[ assertValidPictureFlag[OptionValue @ "Picture", False, DrawPauliTransferMap], Return @ $Failed];
 
             (* warn about not plotting null entries *)
             If[ MemberQ[{rules}, _->{}], Message[DrawPauliTransferMap::error, 
@@ -5438,8 +5569,13 @@ variable renaming in nested scoping structs (Module[ Function[]]) *)
 
         DrawPauliTransferMap[ ptmOrCirc:(Subscript[PTM,_][_] | _?isCircuitFormat), opts:OptionsPattern[{CalcPauliTransferMap,DrawPauliTransferMap,Graph}] ] :=
             Module[
-                {map, calcOpts, drawOpts, errFlag=False},
+                {map, isPTM, calcOpts, drawOpts, errFlag=False},
 
+                (* fail immediately if given unrecognised or invalid option *)
+                Check[OptionValue["PauliStringForm"], Return @ $Failed];
+                isPTM = MatchQ[ptmOrCirc, Subscript[PTM,_][_]];
+                Check[ assertValidPictureFlag[OptionValue @ "Picture", Not @ isPTM, DrawPauliTransferMap], Return @ $Failed];
+                
                 (* attempt to auto-generate PTM of circuit, passing along CalcPauliTransferMap[] options *)
                 calcOpts = FilterRules[{opts}, Options[CalcPauliTransferMap]];
                 map = Enclose[ 
@@ -5451,8 +5587,9 @@ variable renaming in nested scoping structs (Module[ Function[]]) *)
                 (* return immediately if PTM generation failed *)
                 If[errFlag, Return @ $Failed];
 
-                (* otherwise recurse, passing along Graph styling options *)
+                (* otherwise recurse, passing along Graph styling options, removing Picture argument *)
                 drawOpts = FilterRules[{opts}, Options[DrawPauliTransferMap] ~Join~ Options[Graph]];
+                drawOpts = drawOpts /. ("Picture" -> _) -> Nothing;
                 DrawPauliTransferMap[map, Sequence @@ drawOpts]
             ]
 
@@ -5467,7 +5604,9 @@ variable renaming in nested scoping structs (Module[ Function[]]) *)
 
 
         Options[ApplyPauliTransferMap] = {
-            "CacheMaps" -> "UntilCallEnd" (* or "Forever" or "Never" *)
+            "CacheMaps" -> "UntilCallEnd", (* or "Forever" or "Never" *)
+            "Picture" -> "Schrodinger", (* or "Heisenberg" when not passing any PTMs directly *)
+            AssertValidChannels -> True
         };
 
         (* ApplyPauliTransferMap additionally accepts all options to CalcPauliTransferMap which is called internally *)
@@ -5494,13 +5633,14 @@ variable renaming in nested scoping structs (Module[ Function[]]) *)
         (* immediately call clear to create initial definition *)
         resetCachedPTMaps[];
 
-        calcAndCachePTMaps[mixed_List, cacheOpt_String, opts___ ] :=
+        calcAndCachePTMaps[mixed_List, cacheOpt_String, opts___ ] := Module[
+            {calcRules = FilterRules[{opts}, Options @ CalcPauliTransferMap]},
             Table[
                 Switch[item,
 
                     (* keep PTMaps, and convert all PTMs to PTMaps*)
                     ptmapPatt, item,
-                    ptmatrPatt, CalcPauliTransferMap[item],
+                    ptmatrPatt, CalcPauliTransferMap[item, calcRules],
 
                     (* but for gates and sub-circuits... *)
                     _, If[
@@ -5515,10 +5655,11 @@ variable renaming in nested scoping structs (Module[ Function[]]) *)
                             First @ GetCircuitRetargeted[ptmap, rules]
                         ],
                         (* else compute the map afresh *)
-                        CalcPauliTransferMap[item]]
+                        CalcPauliTransferMap[item, calcRules]]
                 ],
                 {item, mixed}
             ]
+        ]
 
         validatePauliTransferMapOptions[caller_Symbol, applyPTMapOptPatt] := (
 
@@ -5587,8 +5728,9 @@ variable renaming in nested scoping structs (Module[ Function[]]) *)
             Module[
                 {out, scalars},
 
-                (* we don't actually use the options (they inform PTMap gen), but we still validate them *)
+                (* check options are valid *)
                 Check[ validatePauliTransferMapOptions[ApplyPauliTransferMap, opts], Return @ $Failed];
+                Check[ assertValidPictureFlag[OptionValue["Picture"], False, ApplyPauliTransferMap], Return @ $Failed];
 
                 (* apply the PTM to each input pauli product ... *)
                 out = Plus @@ Flatten[ Table[
@@ -5627,17 +5769,20 @@ variable renaming in nested scoping structs (Module[ Function[]]) *)
 
         ApplyPauliTransferMap[ pauliStr_?isValidSymbolicPauliString, maps:{ptmapPatt..}, opts:OptionsPattern[] ] :=
             (
-                (* we don't use nor pass on the options (they inform PTMap gen), but we still validate them  *)
+                (* validate options  *)
                 Check[ validatePauliTransferMapOptions[ApplyPauliTransferMap, opts], Return @ $Failed];
+                Check[ assertValidPictureFlag[OptionValue["Picture"], False, ApplyPauliTransferMap], Return @ $Failed];
 
                 (* apply each map in turn to the growing pauli string, and simplify the end result *)
                 SimplifyPaulis @ Fold[ApplyPauliTransferMap, pauliStr, maps]
             )
 
         ApplyPauliTransferMap[ pauliStr_?isValidSymbolicPauliString, mixed:mixedGatesAndMapsPatt, opts:OptionsPattern[] ] := 
-            Module[{maps},
+            Module[{maps, hasPTMs},
                 (* validate the options *)
                 Check[ validatePauliTransferMapOptions[ApplyPauliTransferMap, opts], Return @ $Failed];
+                hasPTMs = MemberQ[mixed, ptmapPatt|ptmatrPatt];
+                Check[ assertValidPictureFlag[OptionValue["Picture"], Not @ hasPTMs, ApplyPauliTransferMap], Return @ $Failed];
 
                 (* validate and pre-compute all PTMaps, managing all caching *)
                 maps = Check[ getAndValidateAllGatesAsPTMaps[mixed, ApplyPauliTransferMap, opts], Return @ $Failed ];
@@ -5768,10 +5913,11 @@ variable renaming in nested scoping structs (Module[ Function[]]) *)
 
         Options[CalcPauliTransferEval] = {
             "CombineStrings" -> True,
-            "OutputForm" -> "Simple" (* or "Detailed" *)
+            "OutputForm" -> "Simple", (* or "Detailed" *)
+            "Picture" -> "Schrodinger" (* "Heisenberg", which are not accepted when passing only PTMs *)
         };
 
-        (*CalcPauliTransferEval additionally accepts all options to ApplyPauliTransferMap (and its subroutines) which are internally called *)
+        (* CalcPauliTransferEval additionally accepts all options to ApplyPauliTransferMap (and its subroutines) which are internally called *)
         calcPTEvalOptPatt = OptionsPattern @ {CalcPauliTransferEval, Sequence @@ First @ applyPTMapOptPatt};
 
         validateCalcPauliTransferEvalOptions[caller_Symbol, opts:calcPTEvalOptPatt] := 
@@ -5798,6 +5944,7 @@ variable renaming in nested scoping structs (Module[ Function[]]) *)
 
                 (* validate options (including those for inner functions like CalcPauliTransferMap) *)
                 Check[validateCalcPauliTransferEvalOptions[CalcPauliTransferEval, opts], Return @ $Failed];
+                Check[ assertValidPictureFlag[OptionValue["Picture"], False, CalcPauliTransferEval], Return @ $Failed];
 
                 (* compute simple evaluation graph *)
                 inStates = getPauliStringInitStatesForPTMapSim[pauliStr, maps];
@@ -5811,16 +5958,21 @@ variable renaming in nested scoping structs (Module[ Function[]]) *)
             ]
 
         CalcPauliTransferEval[ pauliStr_?isValidSymbolicPauliString, mixed:mixedGatesAndMapsPatt, opts:calcPTEvalOptPatt ] := 
-            Module[{maps,mapGenOpts},
+            Module[{maps, hasPTMs, mapGenOpts},
 
                 (* validate CalcPauliTransferEval options, and those needed by subsequent PTMap generation *)
                 Check[validateCalcPauliTransferEvalOptions[CalcPauliTransferEval, opts], Return @ $Failed];
+                hasPTMs = MemberQ[mixed, ptmapPatt|ptmatrPatt];
+                Check[ assertValidPictureFlag[OptionValue["Picture"], Not @ hasPTMs, CalcPauliTransferEval], Return @ $Failed];
 
                 (* validate and pre-compute all PTMaps, managing all caching *)
-                mapGenOpts = FilterRules[{opts}, Except @ Options @ CalcPauliTransferEval];
+                mapGenOpts = FilterRules[{opts}, {Except @ Options @ CalcPauliTransferEval, Options @ CalcPauliTransferMap}];
                 maps = Check[ getAndValidateAllGatesAsPTMaps[mixed, CalcPauliTransferEval, mapGenOpts], Return @ $Failed ];
 
-                CalcPauliTransferEval[pauliStr, maps, opts]
+                If[ OptionValue["Picture"] === "Heisenberg", maps = Reverse[maps] ];
+
+                (* once all maps are calculated, the "Picture" value is erased *)
+                CalcPauliTransferEval[pauliStr, maps, Sequence @@ ({opts} /. ("Picture"->_) -> Nothing)]
             ]
 
         CalcPauliTransferEval[ pauliStr_?isValidSymbolicPauliString, gate_?isGateFormat, opts:calcPTEvalOptPatt ] :=
@@ -5910,6 +6062,7 @@ variable renaming in nested scoping structs (Module[ Function[]]) *)
 
                 (* validate options *)
                 Check[validateDrawPauliTransferEvalOptions[opts], Return @ $Failed];
+                Check[assertValidPictureFlag[OptionValue["Picture"], False, DrawPauliTransferEval], Return @ $Failed];
 
                 (* warn if eval history contains null states (e.g. by fully-mixing channels) *)
                 If[
@@ -5984,6 +6137,7 @@ variable renaming in nested scoping structs (Module[ Function[]]) *)
 
                 (* validate options *)
                 Check[validateDrawPauliTransferEvalOptions[opts], Return @ $Failed];
+                Check[assertValidPictureFlag[OptionValue["Picture"], False, DrawPauliTransferEval], Return @ $Failed];
 
                 (* compute a simplified 'Detailed' Association containing only the necessary keys *)
                 keys = {"Ids", "NumQubits", "Children", "Outdegree"};
@@ -6006,7 +6160,12 @@ variable renaming in nested scoping structs (Module[ Function[]]) *)
 
         DrawPauliTransferEval[ pauliStr_?isValidSymbolicPauliString, circ:(mixedGatesAndMapsPatt|_?isGateFormat), opts:drawPTEvalOptPatt ] := (
             Check[validateDrawPauliTransferEvalOptions[opts], Return @ $Failed];
-            DrawPauliTransferEval[CalcPauliTransferEval[pauliStr, circ, extractCalcPTEvalOptions @ opts], opts] )
+            Check[assertValidPictureFlag[OptionValue["Picture"], FreeQ[circ,PTM|PTMap], DrawPauliTransferEval], Return @ $Failed];
+            DrawPauliTransferEval[
+                CalcPauliTransferEval[pauliStr, circ, extractCalcPTEvalOptions @ opts], 
+                Sequence @@ ({opts} /. ("Picture" -> _) -> Nothing)
+            ]
+        )
 
         DrawPauliTransferEval[___] := invalidArgError[DrawPauliTransferEval];
 
diff --git a/Link/circuits.cpp b/Link/circuits.cpp
index f7e36c7c..c4aa9e29 100644
--- a/Link/circuits.cpp
+++ b/Link/circuits.cpp
@@ -196,6 +196,7 @@ std::string Gate::getName() {
         case OPCODE_Deph :
         case OPCODE_Depol :
         case OPCODE_Damp :
+        case OPCODE_PauliError : 
         case OPCODE_Kraus :
         case OPCODE_KrausNonTP :
             if (numTargs == 0)
@@ -488,6 +489,15 @@ void Gate::validate() {
             if (numTargs != 1)
                 throw local_wrongNumGateTargsExcep(getSyntax(), getSymb(), numTargs, 1); // throws
             return;
+
+        case OPCODE_PauliError :
+            if (numParams != 3)
+                throw local_wrongNumGateParamsExcep(getSyntax(), getSymb(), numParams, 3); // throws
+            if (numCtrls != 0)
+                throw local_gateUnsupportedExcep(getSyntax(), getName()); // throws
+            if (numTargs != 1)
+                throw local_wrongNumGateTargsExcep(getSyntax(), getSymb(), numTargs, 1); // throws
+            return;
             
         case OPCODE_SWAP :
             if (numParams != 0)
@@ -736,6 +746,12 @@ void Gate::applyTo(Qureg qureg, qreal* outputs) {
                 if (numTargs == 2)
                     mixTwoQubitDepolarising(qureg, targs[0], targs[1], params[0]); // throws
                 break;
+
+            case OPCODE_PauliError : 
+                if (params[0] == 0 && params[1] == 0 && params[2] == 0)
+                    break; // permit zero-prob decoherence to act on state-vectors
+                mixPauli(qureg, targs[0], params[0], params[1], params[2]); // throws
+                break;
                 
             case OPCODE_Damp :
                 if (params[0] == 0)
@@ -889,6 +905,7 @@ void Gate::applyDaggerTo(Qureg qureg) {
         case OPCODE_Z :
         case OPCODE_Deph :
         case OPCODE_Depol :
+        case OPCODE_PauliError : 
             applyTo(qureg); // throws
             break;
 
@@ -1014,6 +1031,7 @@ bool Gate::isUnitary() {
         case OPCODE_Deph :
         case OPCODE_Depol :
         case OPCODE_Damp :
+        case OPCODE_PauliError :
         case OPCODE_Kraus :
         case OPCODE_KrausNonTP :
         case OPCODE_Fac :
@@ -1039,6 +1057,7 @@ bool Gate::isPure() {
         
         case OPCODE_Deph :
         case OPCODE_Depol :
+        case OPCODE_PauliError :
         case OPCODE_Damp :
         case OPCODE_Kraus :
         case OPCODE_KrausNonTP :
@@ -1081,6 +1100,12 @@ bool Gate::isInvertible() {
             if (numTargs == 2)
                 return local_isNonZero(15 - 16*params[0]);
         
+        case OPCODE_PauliError :
+            return local_isNonZero(
+                (1 - 2*params[1] - 2*params[2]) *
+                (1 - 2*params[0] - 2*params[2]) *
+                (1 - 2*params[0] - 2*params[1]));
+
         case OPCODE_Damp :
             if (numTargs == 1)
                 return local_isNonZero(1 - params[0]);
@@ -1116,6 +1141,7 @@ bool Gate::isTracePreserving() {
         case OPCODE_Damp :
         case OPCODE_Deph : 
         case OPCODE_Depol :
+        case OPCODE_PauliError :
         case OPCODE_Kraus :
             return true;
             
@@ -1200,12 +1226,30 @@ void Gate::applyInverseTo(Qureg qureg) {
                 densmatr_mixTwoQubitDepolarising(qureg, targs[0], targs[1], (16*invParam)/15.);
             }
             return;
+
+        case OPCODE_PauliError : { ;
+            qreal oldX = params[0];
+            qreal oldY = params[1];
+            qreal oldZ = params[2];
+
+            qreal termX = 1 / (1 - 2*oldY - 2*oldZ); // Gate::isInvertible assures these won't divide-by-zero
+            qreal termY = 1 / (1 - 2*oldX - 2*oldZ);
+            qreal termZ = 1 / (1 - 2*oldX - 2*oldY);
+            
+            qreal newI = (1 + termX + termY + termZ) / 4;
+            qreal newX = (1 + termX - termY - termZ) / 4;
+            qreal newY = (1 + termX - termY + termZ * 2 * (oldX + oldY)) / 4;
+            qreal newZ = oldZ + 2 * (oldX + oldY - 1) * (oldX + oldZ) * (oldY + oldZ);
+                  newZ /= - termX * termY * termZ;
+
+            densmatr_mixArbitraryPauli(qureg, targs[0], newI, newX, newY, newZ);
+        }
+            return;
         
-        case OPCODE_Damp :
-            if (numTargs == 1) {
-                qreal invParam = params[0] / (params[0] - 1);
-                densmatr_mixDamping(qureg, targs[0], invParam);
-            }
+        case OPCODE_Damp : { ;
+            qreal invParam = params[0] / (params[0] - 1);
+            densmatr_mixDamping(qureg, targs[0], invParam);
+        }
             return;
                 
         case OPCODE_Kraus :
@@ -1248,6 +1292,9 @@ int Gate::getNumDecomps() {
                 return 4;
             if (numTargs == 2)
                 return 16;
+
+        case OPCODE_PauliError :
+            return 4;
         
         case OPCODE_Kraus :
         case OPCODE_KrausNonTP :
@@ -1397,6 +1444,36 @@ qreal Gate::applyDecompTo(Qureg qureg, int decompInd) {
             }
                 break;
             
+            case OPCODE_PauliError : { ;
+                qreal pX = params[0];
+                qreal pY = params[1];
+                qreal pZ = params[2];
+                qreal pI = 1 - (pX + pY + pZ);
+
+                if (pX < 0 || pY < 0 || pZ < 0)
+                    throw local_invalidProbExcep(getName(), pX, pY, pZ); // throws
+                
+                qreal pMax = 0;
+                if (pX > pMax) pMax = pX;
+                if (pY > pMax) pMax = pY;
+                if (pZ > pMax) pMax = pZ;
+                if (pMax > pI)
+                    throw local_invalidProbExcep(getName(), pX, pY, pZ); // throws
+
+                // apply I, X, Y or Z
+                qreal probs[] = {pI, pX, pY, pZ};
+                int r = (isRand)? local_getRandomIndex(probs, 4) : decompInd;
+                if (r == 1)
+                    pauliX(qureg, targs[0]); // throws
+                if (r == 2)
+                    pauliY(qureg, targs[0]); // throws
+                if (r == 3)
+                    pauliZ(qureg, targs[0]); // throws
+                    
+                return probs[r];
+            }
+                break;
+
             case OPCODE_Kraus :
             case OPCODE_KrausNonTP : { ;
                 int numOps = (int) params[0];
diff --git a/Link/circuits.hpp b/Link/circuits.hpp
index 63877615..8a6758fc 100644
--- a/Link/circuits.hpp
+++ b/Link/circuits.hpp
@@ -38,8 +38,9 @@
 #define OPCODE_Matr 22
 #define OPCODE_UNonNorm 23
 #define OPCODE_Fac 24
+#define OPCODE_PauliError 25
 
-#define NUM_OPCODES 25
+#define NUM_OPCODES 26
 
 static const std::string opcodeStrings[] = {
     "H",			// OPCODE_H 0
@@ -67,6 +68,7 @@ static const std::string opcodeStrings[] = {
     "Matr",			// OPCODE_Matr 22
     "UNonNorm",		// OPCODE_UNonNorm 23
     "Fac",          // OPCODE_Fac 24
+    "PauliError",   // OPCODE_PauliError 25
 };
 
 static const std::string opcodeNames[] = {
@@ -95,6 +97,7 @@ static const std::string opcodeNames[] = {
     "general matrix",                   // OPCODE_Matr 22
     "unnormalised general unitary",     // OPCODE_UNonNorm 23
     "factor",                           // OPCODE_Fac 24
+    "inhomogeneous Pauli error",        // OPCODE_PauliError 25
 };
 
 
diff --git a/Link/derivatives.cpp b/Link/derivatives.cpp
index 4d3b9587..da911087 100644
--- a/Link/derivatives.cpp
+++ b/Link/derivatives.cpp
@@ -339,6 +339,10 @@ void Gate::applyDerivTo(Qureg qureg, qreal* derivParams, int numDerivParams) {
                 if (numTargs == 2)
                     extension_mixTwoQubitDepolarisingDeriv(qureg, targs[0], targs[1], derivParams[0]);  // throws
                 break;
+
+            case OPCODE_PauliError : 
+                throw QuESTException("", "Derivatives of operator " + getSymb() + " have not yet been implemented."); // throws, caught by below
+                break;
                 
             case OPCODE_Damp :
                 if (numDerivParams != 1)
diff --git a/Link/errors.cpp b/Link/errors.cpp
index a44bc967..37d020b4 100644
--- a/Link/errors.cpp
+++ b/Link/errors.cpp
@@ -155,6 +155,19 @@ QuESTException local_invalidProbExcep(std::string gateName, qreal prob, std::str
         " for which " + gateName + " is maximally mixing."); // throws
 }
 
+QuESTException local_invalidProbExcep(std::string gateName, qreal probX, qreal probY, qreal probZ) {
+
+    if (probX < 0 || probY < 0 || probZ < 0)
+        return QuESTException("", "An error probability is negative and ergo invalid.");
+    if (probX > 1 || probY > 1 || probZ > 1)
+        return QuESTException("", "An error probability exceeded one and is ergo invalid.");
+    
+    if (probX + probY + probZ > 1)
+        return QuESTException("", "The error probabilities together exceeded one and are ergo invalid.");
+
+    return QuESTException("", "The error probabilities together exceeded those which induce maximal mixing.");
+}
+
 void local_throwExcepIfUserAborted() {
     
     /* Dear ancient Wolfram Gods; why does this no longer work? 
diff --git a/Link/errors.hpp b/Link/errors.hpp
index 05c8f494..c137375e 100644
--- a/Link/errors.hpp
+++ b/Link/errors.hpp
@@ -46,6 +46,7 @@ QuESTException local_wrongNumDerivParamsExcep(std::string gate, int wrongNumPara
 QuESTException local_unrecognisedGateExcep(std::string gateSyntax, int opcode, const char* caller);
 
 QuESTException local_invalidProbExcep(std::string gateName, qreal prob, std::string maxProb);
+QuESTException local_invalidProbExcep(std::string gateName, qreal probX, qreal probY, qreal probZ);
 
 void sendDebugEcho(std::string msg);
 
diff --git a/QuEST b/QuEST
index ce6bdedf..a30025b6 160000
--- a/QuEST
+++ b/QuEST
@@ -1 +1 @@
-Subproject commit ce6bdedfa07a22df8ee29424d9f0f62160833b2f
+Subproject commit a30025b6cf28b8dde2128b4b6d81414f84ee705a
diff --git a/Tests/v020_DrawPauliStringAsTree.nb b/Tests/v020_DrawPauliStringAsTree.nb
new file mode 100644
index 00000000..ed29c973
--- /dev/null
+++ b/Tests/v020_DrawPauliStringAsTree.nb
@@ -0,0 +1,8035 @@
+(* Content-type: application/vnd.wolfram.mathematica *)
+
+(*** Wolfram Notebook File ***)
+(* http://www.wolfram.com/nb *)
+
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+
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+(* Internal cache information:
+NotebookFileLineBreakTest
+NotebookFileLineBreakTest
+NotebookDataPosition[       158,          7]
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+NotebookOutlinePosition[    413828,       7960]
+CellTagsIndexPosition[    413785,       7957]
+WindowFrame->Normal*)
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+       " XYIXIXZYXYYZYYY", " XYIXIXZYXYYZYYYI", " XYIXIXZYXYYZYYYIX", 
+       " XYIXIXZYXYYZYYYIXZ", " XYIXIXZYXYYZYYYIXZZ", " XYIXIXZYXYYZYYYIXZZI",
+        " XYIXIXZYXYYZYYYIXZZII", " XYIXIXZYXYYZYYYIXZZIIY", 
+       " XYIXIXZYXYYZYYYIXZZIIYX", " XYIXIXZYXYYZYYYIXZZIIYXZ", 
+       " XYIXIXZYXYYZYYYIXZZIIYXZX", " XYIXIXZYXYYZYYYIXZZIIYXZXI", 
+       " XYIXIXZYXYYZYYYIXZZIIYXZXIX", " XYIXIXZYXYYZYYYIXZZIIYXZXIXZ", 
+       " XYIXIXZYXYYZYYYIXZZIIYXZXIXZX", " XYIXIXZYXYYZYYYIXZZIIYXZXIXZXZ", 
+       " Y", " YY", " YYX", " YYXI", " YYXIY", " YYXIYX", " YYXIYXZ", 
+       " YYXIYXZY", " YYXIYXZYZ", " YYXIYXZYZY", " YYXIYXZYZYX", 
+       " YYXIYXZYZYXX", " YYXIYXZYZYXXI", " YYXIYXZYZYXXIZ", 
+       " YYXIYXZYZYXXIZY", " YYXIYXZYZYXXIZYX", " YYXIYXZYZYXXIZYXY", 
+       " YYXIYXZYZYXXIZYXYX", " YYXIYXZYZYXXIZYXYXZ", " YYXIYXZYZYXXIZYXYXZX",
+        " YYXIYXZYZYXXIZYXYXZXX", " YYXIYXZYZYXXIZYXYXZXXY", 
+       " YYXIYXZYZYXXIZYXYXZXXYX", " YYXIYXZYZYXXIZYXYXZXXYXY", 
+       " YYXIYXZYZYXXIZYXYXZXXYXYX", " YYXIYXZYZYXXIZYXYXZXXYXYXX", 
+       " YYXIYXZYZYXXIZYXYXZXXYXYXXY", " YYXIYXZYZYXXIZYXYXZXXYXYXXYI", 
+       " YYXIYXZYZYXXIZYXYXZXXYXYXXYIZ", " YYXIYXZYZYXXIZYXYXZXXYXYXXYIZX", 
+       " XX", " XXX", " XXXI", " XXXIX", " XXXIXZ", " XXXIXZX", " XXXIXZXX", 
+       " XXXIXZXXY", " XXXIXZXXYX", " XXXIXZXXYXX", " XXXIXZXXYXXY", 
+       " XXXIXZXXYXXYI", " XXXIXZXXYXXYIX", " XXXIXZXXYXXYIXY", 
+       " XXXIXZXXYXXYIXYY", " XXXIXZXXYXXYIXYYZ", " XXXIXZXXYXXYIXYYZI", 
+       " XXXIXZXXYXXYIXYYZIY", " XXXIXZXXYXXYIXYYZIYI", 
+       " XXXIXZXXYXXYIXYYZIYII", " XXXIXZXXYXXYIXYYZIYIIY", 
+       " XXXIXZXXYXXYIXYYZIYIIYI", " XXXIXZXXYXXYIXYYZIYIIYIX", 
+       " XXXIXZXXYXXYIXYYZIYIIYIXY", " XXXIXZXXYXXYIXYYZIYIIYIXYX", 
+       " XXXIXZXXYXXYIXYYZIYIIYIXYXX", " XXXIXZXXYXXYIXYYZIYIIYIXYXXZ", 
+       " XXXIXZXXYXXYIXYYZIYIIYIXYXXZZ", " XXXIXZXXYXXYIXYYZIYIIYIXYXXZZX", 
+       " XXY", " XXYI", " XXYIZ", " XXYIZX", " XXYIZXY", " XXYIZXYY", 
+       " XXYIZXYYZ", " XXYIZXYYZX", " XXYIZXYYZXZ", " XXYIZXYYZXZX", 
+       " XXYIZXYYZXZXX", " XXYIZXYYZXZXXX", " XXYIZXYYZXZXXXZ", 
+       " XXYIZXYYZXZXXXZZ", " XXYIZXYYZXZXXXZZI", " XXYIZXYYZXZXXXZZII", 
+       " XXYIZXYYZXZXXXZZIII", " XXYIZXYYZXZXXXZZIIIX", 
+       " XXYIZXYYZXZXXXZZIIIXI", " XXYIZXYYZXZXXXZZIIIXIZ", 
+       " XXYIZXYYZXZXXXZZIIIXIZI", " XXYIZXYYZXZXXXZZIIIXIZIZ", 
+       " XXYIZXYYZXZXXXZZIIIXIZIZY", " XXYIZXYYZXZXXXZZIIIXIZIZYI", 
+       " XXYIZXYYZXZXXXZZIIIXIZIZYIY", " XXYIZXYYZXZXXXZZIIIXIZIZYIYZ", 
+       " XXYIZXYYZXZXXXZZIIIXIZIZYIYZZ", " XXYIZXYYZXZXXXZZIIIXIZIZYIYZZZ", 
+       " YI", " YIX", " YIXY", " YIXYZ", " YIXYZY", " YIXYZYY", " YIXYZYYZ", 
+       " YIXYZYYZX", " YIXYZYYZXZ", " YIXYZYYZXZZ", " YIXYZYYZXZZY", 
+       " YIXYZYYZXZZYX", " YIXYZYYZXZZYXZ", " YIXYZYYZXZZYXZY", 
+       " YIXYZYYZXZZYXZYY", " YIXYZYYZXZZYXZYYX", " YIXYZYYZXZZYXZYYXX", 
+       " YIXYZYYZXZZYXZYYXXX", " YIXYZYYZXZZYXZYYXXXI", 
+       " YIXYZYYZXZZYXZYYXXXII", " YIXYZYYZXZZYXZYYXXXIIY", 
+       " YIXYZYYZXZZYXZYYXXXIIYI", " YIXYZYYZXZZYXZYYXXXIIYIY", 
+       " YIXYZYYZXZZYXZYYXXXIIYIYX", " YIXYZYYZXZZYXZYYXXXIIYIYXZ", 
+       " YIXYZYYZXZZYXZYYXXXIIYIYXZX", " YIXYZYYZXZZYXZYYXXXIIYIYXZXY", 
+       " YIXYZYYZXZZYXZYYXXXIIYIYXZXYY", " YIXYZYYZXZZYXZYYXXXIIYIYXZXYYY", 
+       " IIYZ", " IIYZX", " IIYZXZ", " IIYZXZX", " IIYZXZXZ", " IIYZXZXZY", 
+       " IIYZXZXZYI", " IIYZXZXZYIX", " IIYZXZXZYIXX", " IIYZXZXZYIXXX", 
+       " IIYZXZXZYIXXXX", " IIYZXZXZYIXXXXY", " IIYZXZXZYIXXXXYY", 
+       " IIYZXZXZYIXXXXYYY", " IIYZXZXZYIXXXXYYYY", " IIYZXZXZYIXXXXYYYYI", 
+       " IIYZXZXZYIXXXXYYYYIZ", " IIYZXZXZYIXXXXYYYYIZZ", 
+       " IIYZXZXZYIXXXXYYYYIZZX", " IIYZXZXZYIXXXXYYYYIZZXI", 
+       " IIYZXZXZYIXXXXYYYYIZZXIZ", " IIYZXZXZYIXXXXYYYYIZZXIZZ", 
+       " IIYZXZXZYIXXXXYYYYIZZXIZZI", " IIYZXZXZYIXXXXYYYYIZZXIZZII", 
+       " IIYZXZXZYIXXXXYYYYIZZXIZZIIX", " IIYZXZXZYIXXXXYYYYIZZXIZZIIXZ", 
+       " IIYZXZXZYIXXXXYYYYIZZXIZZIIXZY", " XI", " XIZ", " XIZI", " XIZII", 
+       " XIZIIY", " XIZIIYY", " XIZIIYYY", " XIZIIYYYZ", " XIZIIYYYZX", 
+       " XIZIIYYYZXX", " XIZIIYYYZXXX", " XIZIIYYYZXXXY", " XIZIIYYYZXXXYX", 
+       " XIZIIYYYZXXXYXX", " XIZIIYYYZXXXYXXX", " XIZIIYYYZXXXYXXXI", 
+       " XIZIIYYYZXXXYXXXIX", " XIZIIYYYZXXXYXXXIXX", " XIZIIYYYZXXXYXXXIXXZ",
+        " XIZIIYYYZXXXYXXXIXXZI", " XIZIIYYYZXXXYXXXIXXZIY", 
+       " XIZIIYYYZXXXYXXXIXXZIYY", " XIZIIYYYZXXXYXXXIXXZIYYZ", 
+       " XIZIIYYYZXXXYXXXIXXZIYYZY", " XIZIIYYYZXXXYXXXIXXZIYYZYY", 
+       " XIZIIYYYZXXXYXXXIXXZIYYZYYX", " XIZIIYYYZXXXYXXXIXXZIYYZYYXY", 
+       " XIZIIYYYZXXXYXXXIXXZIYYZYYXYY", " XIZIIYYYZXXXYXXXIXXZIYYZYYXYYZ", 
+       " IX", " IXZ", " IXZX", " IXZXY", " IXZXYX", " IXZXYXZ", " IXZXYXZY", 
+       " IXZXYXZYX", " IXZXYXZYXY", " IXZXYXZYXYZ", " IXZXYXZYXYZZ", 
+       " IXZXYXZYXYZZX", " IXZXYXZYXYZZXZ", " IXZXYXZYXYZZXZZ", 
+       " IXZXYXZYXYZZXZZX", " IXZXYXZYXYZZXZZXY", " IXZXYXZYXYZZXZZXYY", 
+       " IXZXYXZYXYZZXZZXYYI", " IXZXYXZYXYZZXZZXYYII", 
+       " IXZXYXZYXYZZXZZXYYIIX", " IXZXYXZYXYZZXZZXYYIIXZ", 
+       " IXZXYXZYXYZZXZZXYYIIXZX", " IXZXYXZYXYZZXZZXYYIIXZXX", 
+       " IXZXYXZYXYZZXZZXYYIIXZXXZ", " IXZXYXZYXYZZXZZXYYIIXZXXZY", 
+       " IXZXYXZYXYZZXZZXYYIIXZXXZYI", " IXZXYXZYXYZZXZZXYYIIXZXXZYIY", 
+       " IXZXYXZYXYZZXZZXYYIIXZXXZYIYY", " IXZXYXZYXYZZXZZXYYIIXZXXZYIYYZ", 
+       " XIZY", " XIZYY", " XIZYYI", " XIZYYIZ", " XIZYYIZX", " XIZYYIZXZ", 
+       " XIZYYIZXZI", " XIZYYIZXZIZ", " XIZYYIZXZIZI", " XIZYYIZXZIZII", 
+       " XIZYYIZXZIZIII", " XIZYYIZXZIZIIIZ", " XIZYYIZXZIZIIIZY", 
+       " XIZYYIZXZIZIIIZYZ", " XIZYYIZXZIZIIIZYZI", " XIZYYIZXZIZIIIZYZIX", 
+       " XIZYYIZXZIZIIIZYZIXX", " XIZYYIZXZIZIIIZYZIXXY", 
+       " XIZYYIZXZIZIIIZYZIXXYX", " XIZYYIZXZIZIIIZYZIXXYXI", 
+       " XIZYYIZXZIZIIIZYZIXXYXIY", " XIZYYIZXZIZIIIZYZIXXYXIYI", 
+       " XIZYYIZXZIZIIIZYZIXXYXIYIX", " XIZYYIZXZIZIIIZYZIXXYXIYIXY", 
+       " XIZYYIZXZIZIIIZYZIXXYXIYIXYZ", " XIZYYIZXZIZIIIZYZIXXYXIYIXYZX", 
+       " XIZYYIZXZIZIIIZYZIXXYXIYIXYZXI", " YIZ", " YIZI", " YIZIY", 
+       " YIZIYZ", " YIZIYZY", " YIZIYZYX", " YIZIYZYXY", " YIZIYZYXYI", 
+       " YIZIYZYXYIY", " YIZIYZYXYIYZ", " YIZIYZYXYIYZY", " YIZIYZYXYIYZYI", 
+       " YIZIYZYXYIYZYIX", " YIZIYZYXYIYZYIXY", " YIZIYZYXYIYZYIXYX", 
+       " YIZIYZYXYIYZYIXYXZ", " YIZIYZYXYIYZYIXYXZI", " YIZIYZYXYIYZYIXYXZIY",
+        " YIZIYZYXYIYZYIXYXZIYI", " YIZIYZYXYIYZYIXYXZIYIY", 
+       " YIZIYZYXYIYZYIXYXZIYIYX", " YIZIYZYXYIYZYIXYXZIYIYXX", 
+       " YIZIYZYXYIYZYIXYXZIYIYXXY", " YIZIYZYXYIYZYIXYXZIYIYXXYY", 
+       " YIZIYZYXYIYZYIXYXZIYIYXXYYX", " YIZIYZYXYIYZYIXYXZIYIYXXYYXI", 
+       " YIZIYZYXYIYZYIXYXZIYIYXXYYXII", " YIZIYZYXYIYZYIXYXZIYIYXXYYXIIX", 
+       " XIZX", " XIZXZ", " XIZXZX", " XIZXZXZ", " XIZXZXZX", " XIZXZXZXZ", 
+       " XIZXZXZXZY", " XIZXZXZXZYI", " XIZXZXZXZYIY", " XIZXZXZXZYIYI", 
+       " XIZXZXZXZYIYIZ", " XIZXZXZXZYIYIZZ", " XIZXZXZXZYIYIZZX", 
+       " XIZXZXZXZYIYIZZXX", " XIZXZXZXZYIYIZZXXX", " XIZXZXZXZYIYIZZXXXX", 
+       " XIZXZXZXZYIYIZZXXXXX", " XIZXZXZXZYIYIZZXXXXXI", 
+       " XIZXZXZXZYIYIZZXXXXXIZ", " XIZXZXZXZYIYIZZXXXXXIZZ", 
+       " XIZXZXZXZYIYIZZXXXXXIZZI", " XIZXZXZXZYIYIZZXXXXXIZZIZ", 
+       " XIZXZXZXZYIYIZZXXXXXIZZIZY", " XIZXZXZXZYIYIZZXXXXXIZZIZYY", 
+       " XIZXZXZXZYIYIZZXXXXXIZZIZYYX", " XIZXZXZXZYIYIZZXXXXXIZZIZYYXI", 
+       " XIZXZXZXZYIYIZZXXXXXIZZIZYYXIZ", " XYZ", " XYZZ", " XYZZY", 
+       " XYZZYY", " XYZZYYY", " XYZZYYYZ", " XYZZYYYZZ", " XYZZYYYZZZ", 
+       " XYZZYYYZZZX", " XYZZYYYZZZXI", " XYZZYYYZZZXIX", " XYZZYYYZZZXIXX", 
+       " XYZZYYYZZZXIXXZ", " XYZZYYYZZZXIXXZZ", " XYZZYYYZZZXIXXZZI", 
+       " XYZZYYYZZZXIXXZZIZ", " XYZZYYYZZZXIXXZZIZY", " XYZZYYYZZZXIXXZZIZYY",
+        " XYZZYYYZZZXIXXZZIZYYY", " XYZZYYYZZZXIXXZZIZYYYX", 
+       " XYZZYYYZZZXIXXZZIZYYYXY", " XYZZYYYZZZXIXXZZIZYYYXYY", 
+       " XYZZYYYZZZXIXXZZIZYYYXYYZ", " XYZZYYYZZZXIXXZZIZYYYXYYZI", 
+       " XYZZYYYZZZXIXXZZIZYYYXYYZIY", " XYZZYYYZZZXIXXZZIZYYYXYYZIYY", 
+       " XYZZYYYZZZXIXXZZIZYYYXYYZIYYY", " XYZZYYYZZZXIXXZZIZYYYXYYZIYYYZ", 
+       " IY", " IYZ", " IYZZ", " IYZZX", " IYZZXZ", " IYZZXZX", " IYZZXZXX", 
+       " IYZZXZXXY", " IYZZXZXXYI", " IYZZXZXXYIX", " IYZZXZXXYIXX", 
+       " IYZZXZXXYIXXX", " IYZZXZXXYIXXXZ", " IYZZXZXXYIXXXZZ", 
+       " IYZZXZXXYIXXXZZI", " IYZZXZXXYIXXXZZIY", " IYZZXZXXYIXXXZZIYX", 
+       " IYZZXZXXYIXXXZZIYXI", " IYZZXZXXYIXXXZZIYXIY", 
+       " IYZZXZXXYIXXXZZIYXIYZ", " IYZZXZXXYIXXXZZIYXIYZZ", 
+       " IYZZXZXXYIXXXZZIYXIYZZX", " IYZZXZXXYIXXXZZIYXIYZZXY", 
+       " IYZZXZXXYIXXXZZIYXIYZZXYX", " IYZZXZXXYIXXXZZIYXIYZZXYXZ", 
+       " IYZZXZXXYIXXXZZIYXIYZZXYXZX", " IYZZXZXXYIXXXZZIYXIYZZXYXZXZ", 
+       " IYZZXZXXYIXXXZZIYXIYZZXYXZXZY", " IYZZXZXXYIXXXZZIYXIYZZXYXZXZYX", 
+       " XZ", " XZI", " XZIY", " XZIYI", " XZIYIX", " XZIYIXY", " XZIYIXYY", 
+       " XZIYIXYYI", " XZIYIXYYIY", " XZIYIXYYIYI", " XZIYIXYYIYIZ", 
+       " XZIYIXYYIYIZI", " XZIYIXYYIYIZIX", " XZIYIXYYIYIZIXX", 
+       " XZIYIXYYIYIZIXXX", " XZIYIXYYIYIZIXXXI", " XZIYIXYYIYIZIXXXIY", 
+       " XZIYIXYYIYIZIXXXIYZ", " XZIYIXYYIYIZIXXXIYZY", 
+       " XZIYIXYYIYIZIXXXIYZYX", " XZIYIXYYIYIZIXXXIYZYXZ", 
+       " XZIYIXYYIYIZIXXXIYZYXZY", " XZIYIXYYIYIZIXXXIYZYXZYX", 
+       " XZIYIXYYIYIZIXXXIYZYXZYXX", " XZIYIXYYIYIZIXXXIYZYXZYXXZ", 
+       " XZIYIXYYIYIZIXXXIYZYXZYXXZZ", " XZIYIXYYIYIZIXXXIYZYXZYXXZZI", 
+       " XZIYIXYYIYIZIXXXIYZYXZYXXZZIX", " XZIYIXYYIYIZIXXXIYZYXZYXXZZIXX", 
+       " YZ", " YZI", " YZIY", " YZIYY", " YZIYYX", " YZIYYXZ", " YZIYYXZI", 
+       " YZIYYXZIX", " YZIYYXZIXX", " YZIYYXZIXXZ", " YZIYYXZIXXZI", 
+       " YZIYYXZIXXZII", " YZIYYXZIXXZIII", " YZIYYXZIXXZIIII", 
+       " YZIYYXZIXXZIIIIY", " YZIYYXZIXXZIIIIYI", " YZIYYXZIXXZIIIIYIX", 
+       " YZIYYXZIXXZIIIIYIXY", " YZIYYXZIXXZIIIIYIXYI", 
+       " YZIYYXZIXXZIIIIYIXYIX", " YZIYYXZIXXZIIIIYIXYIXX", 
+       " YZIYYXZIXXZIIIIYIXYIXXI", " YZIYYXZIXXZIIIIYIXYIXXII", 
+       " YZIYYXZIXXZIIIIYIXYIXXIII", " YZIYYXZIXXZIIIIYIXYIXXIIII", 
+       " YZIYYXZIXXZIIIIYIXYIXXIIIIX", " YZIYYXZIXXZIIIIYIXYIXXIIIIXI", 
+       " YZIYYXZIXXZIIIIYIXYIXXIIIIXIX", " YZIYYXZIXXZIIIIYIXYIXXIIIIXIXY", 
+       " YZY", " YZYY", " YZYYY", " YZYYYZ", " YZYYYZZ", " YZYYYZZX", 
+       " YZYYYZZXX", " YZYYYZZXXI", " YZYYYZZXXIX", " YZYYYZZXXIXY", 
+       " YZYYYZZXXIXYX", " YZYYYZZXXIXYXZ", " YZYYYZZXXIXYXZX", 
+       " YZYYYZZXXIXYXZXZ", " YZYYYZZXXIXYXZXZZ", " YZYYYZZXXIXYXZXZZY", 
+       " YZYYYZZXXIXYXZXZZYI", " YZYYYZZXXIXYXZXZZYIZ", 
+       " YZYYYZZXXIXYXZXZZYIZY", " YZYYYZZXXIXYXZXZZYIZYZ", 
+       " YZYYYZZXXIXYXZXZZYIZYZY", " YZYYYZZXXIXYXZXZZYIZYZYZ", 
+       " YZYYYZZXXIXYXZXZZYIZYZYZI", " YZYYYZZXXIXYXZXZZYIZYZYZII", 
+       " YZYYYZZXXIXYXZXZZYIZYZYZIIZ", " YZYYYZZXXIXYXZXZZYIZYZYZIIZI", 
+       " YZYYYZZXXIXYXZXZZYIZYZYZIIZII", " YZYYYZZXXIXYXZXZZYIZYZYZIIZIII", 
+       " YZYI", " YZYIZ", " YZYIZY", " YZYIZYZ", " YZYIZYZX", " YZYIZYZXX", 
+       " YZYIZYZXXI", " YZYIZYZXXIX", " YZYIZYZXXIXZ", " YZYIZYZXXIXZI", 
+       " YZYIZYZXXIXZIY", " YZYIZYZXXIXZIYI", " YZYIZYZXXIXZIYII", 
+       " YZYIZYZXXIXZIYIII", " YZYIZYZXXIXZIYIIIX", " YZYIZYZXXIXZIYIIIXI", 
+       " YZYIZYZXXIXZIYIIIXII", " YZYIZYZXXIXZIYIIIXIIZ", 
+       " YZYIZYZXXIXZIYIIIXIIZI", " YZYIZYZXXIXZIYIIIXIIZIZ", 
+       " YZYIZYZXXIXZIYIIIXIIZIZZ", " YZYIZYZXXIXZIYIIIXIIZIZZI", 
+       " YZYIZYZXXIXZIYIIIXIIZIZZII", " YZYIZYZXXIXZIYIIIXIIZIZZIII", 
+       " YZYIZYZXXIXZIYIIIXIIZIZZIIII", " YZYIZYZXXIXZIYIIIXIIZIZZIIIIX", 
+       " YZYIZYZXXIXZIYIIIXIIZIZZIIIIXX", " YZYIZZ", " YZYIZZZ", " YZYIZZZY", 
+       " YZYIZZZYZ", " YZYIZZZYZX", " YZYIZZZYZXY", " YZYIZZZYZXYI", 
+       " YZYIZZZYZXYIY", " YZYIZZZYZXYIYI", " YZYIZZZYZXYIYII", 
+       " YZYIZZZYZXYIYIIX", " YZYIZZZYZXYIYIIXZ", " YZYIZZZYZXYIYIIXZY", 
+       " YZYIZZZYZXYIYIIXZYZ", " YZYIZZZYZXYIYIIXZYZY", 
+       " YZYIZZZYZXYIYIIXZYZYY", " YZYIZZZYZXYIYIIXZYZYYZ", 
+       " YZYIZZZYZXYIYIIXZYZYYZZ", " YZYIZZZYZXYIYIIXZYZYYZZZ", 
+       " YZYIZZZYZXYIYIIXZYZYYZZZI", " YZYIZZZYZXYIYIIXZYZYYZZZIX", 
+       " YZYIZZZYZXYIYIIXZYZYYZZZIXX", " YZYIZZZYZXYIYIIXZYZYYZZZIXXZ", 
+       " YZYIZZZYZXYIYIIXZYZYYZZZIXXZZ", " YZYIZZZYZXYIYIIXZYZYYZZZIXXZZZ", 
+       " IZ", " IZY", " IZYZ", " IZYZX", " IZYZXI", " IZYZXII", " IZYZXIII", 
+       " IZYZXIIII", " IZYZXIIIIX", " IZYZXIIIIXI", " IZYZXIIIIXIX", 
+       " IZYZXIIIIXIXX", " IZYZXIIIIXIXXX", " IZYZXIIIIXIXXXY", 
+       " IZYZXIIIIXIXXXYZ", " IZYZXIIIIXIXXXYZX", " IZYZXIIIIXIXXXYZXY", 
+       " IZYZXIIIIXIXXXYZXYI", " IZYZXIIIIXIXXXYZXYIZ", 
+       " IZYZXIIIIXIXXXYZXYIZI", " IZYZXIIIIXIXXXYZXYIZIY", 
+       " IZYZXIIIIXIXXXYZXYIZIYZ", " IZYZXIIIIXIXXXYZXYIZIYZX", 
+       " IZYZXIIIIXIXXXYZXYIZIYZXX", " IZYZXIIIIXIXXXYZXYIZIYZXXI", 
+       " IZYZXIIIIXIXXXYZXYIZIYZXXIY", " IZYZXIIIIXIXXXYZXYIZIYZXXIYX", 
+       " IZYZXIIIIXIXXXYZXYIZIYZXXIYXX", " IZYZXIIIIXIXXXYZXYIZIYZXXIYXXZ", 
+       " IZI", " IZIZ", " IZIZY", " IZIZYX", " IZIZYXI", " IZIZYXIZ", 
+       " IZIZYXIZX", " IZIZYXIZXY", " IZIZYXIZXYI", " IZIZYXIZXYIZ", 
+       " IZIZYXIZXYIZI", " IZIZYXIZXYIZIY", " IZIZYXIZXYIZIYI", 
+       " IZIZYXIZXYIZIYIY", " IZIZYXIZXYIZIYIYX", " IZIZYXIZXYIZIYIYXY", 
+       " IZIZYXIZXYIZIYIYXYX", " IZIZYXIZXYIZIYIYXYXI", 
+       " IZIZYXIZXYIZIYIYXYXIY", " IZIZYXIZXYIZIYIYXYXIYY", 
+       " IZIZYXIZXYIZIYIYXYXIYYI", " IZIZYXIZXYIZIYIYXYXIYYIX", 
+       " IZIZYXIZXYIZIYIYXYXIYYIXZ", " IZIZYXIZXYIZIYIYXYXIYYIXZY", 
+       " IZIZYXIZXYIZIYIYXYXIYYIXZYI", " IZIZYXIZXYIZIYIYXYXIYYIXZYII", 
+       " IZIZYXIZXYIZIYIYXYXIYYIXZYIIY", " IZIZYXIZXYIZIYIYXYXIYYIXZYIIYI", 
+       " YZZ", " YZZY", " YZZYY", " YZZYYX", " YZZYYXX", " YZZYYXXI", 
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diff --git a/Tests/v020_DrawPauliStringAsTree.pdf b/Tests/v020_DrawPauliStringAsTree.pdf
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