I'm just waiting for the final verdict, the multi-way graph representations of the classical & quantum Tic-Tac-Toe games.

gate = "";
rChoice := With[
  {tempGate = 
    RandomChoice[{"XRotation", "YRotation", "ZRotation", "CNOT"}]},
  gate = tempGate;
  If[gate == "CNOT",
   Module[{ctrl, trg},
    ctrl = RandomChoice[Range[4]];
    trg = RandomChoice@Complement[Range[4], {ctrl}];
    QuantumOperator["CNOT", {ctrl, trg}]],
   QuantumOperator[
    {gate, RandomReal[{0, 2 \[Pi]}]},
    {RandomChoice[Range[4]]}
    ]]]
qc42 = QuantumCircuitOperator[Table[rChoice, {i, 42}]]
qc42["Diagram",
 FontSize -> 6,
 ImageSize -> 1270
 ]
MatrixPlot[
 qc42[g0]["MatrixRepresentation"],
 Mesh -> All,
 PlotTheme -> "Detailed",
 ColorFunction -> "TemperatureMap",
 Epilog -> Inset[gate, {Left, Top}, {-1.5, 1}]
 ]
Show[
 QuantumMeasurementOperator[][qc42[g0]]["ProbabilityPlot"],
 ImageSize -> 203
 ]

I'm sorry..but all these random choices of gates, angles, and orders to create a circuit and then apply it to the initial state gets me begging for larger dimensions and developing a game app.

randomGate3 := With[
  {gate = RandomChoice[{"XRotation", "YRotation", "CNOT"}]},
  If[gate == "CNOT",
   Module[
    {ctrl, trg},
    ctrl = RandomChoice[Range[4]];
    trg = RandomChoice@Complement[Range[4], {ctrl}];
    If[ctrl < trg,
     QuantumOperator["CNOT", {ctrl, trg}],
     QuantumOperator["CNOT", {trg, ctrl}]
     ]],
   QuantumOperator[{gate, 
     RandomReal[{0, 2 \[Pi]}]}, {RandomChoice[Range[4]]}]
   ]]
qc3 = QuantumCircuitOperator[Table[randomGate3, {i, 20}]];
qc3["Diagram", FontSize -> 8]
altgen = qc3[g0]
altgenm = QuantumMeasurementOperator[][altgen];
altgenm["Probabilities"]
CircuitMultiwayGraph[qc3]
Rotate[VertexReplace[CircuitMultiwayGraph[qc3, "George Cooks Fries"], 
  PerformanceGoal -> "Size", ImageSize -> 400], -\[Pi]/2]

Instead of UpValue Hell, @Akhilesh Dubey hey is it necessary to open up the quantum Tic-Tac-Toe & Wolfram Language functions used in the project big or small?

randomGate3 := 
 With[{gate = RandomChoice[{"XRotation", "YRotation", "CNOT"}]}, 
  If[gate == "CNOT", 
   Module[{ctrl, trg}, ctrl = RandomChoice[Range[4]]; 
    trg = RandomChoice@Complement[Range[4], {ctrl}]; 
    If[ctrl < trg, QuantumOperator["CNOT", {ctrl, trg}], 
     QuantumOperator["CNOT", {trg, ctrl}]]], 
   QuantumOperator[{gate, 
     RandomReal[{0, 2 \[Pi]}]}, {RandomChoice[Range[4]]}]]]
qc3 = QuantumCircuitOperator[Table[randomGate3, {i, 20}]];
qc3["Diagram", FontSize -> 8]
altgen = qc3[g0]
altgenm = QuantumMeasurementOperator[][altgen];
altgenm["Probabilities"]
ticTacToe3 = 
 CircuitMultiwayGraph[qc3, Table[N@QuantumState["Plus"], 4]]
Rotate[VertexReplace[
  CircuitMultiwayGraph[qc3, "Betsy Eats Apple Dumpling"], 
  PerformanceGoal -> "Size", ImageSize -> 400], -\[Pi]/2]

@Akhilesh Dubey These Quantum Gates keep me coming back for more and more, isn't that wild?

Thanks to people like you Akhilesh, I couldn't believe it when you and your article were aggregated. This is like the combinatory calculus, and I know this gets romanticized because like the typed hypergraphs it's happening.

qccm = QuantumMeasurementOperator[][qcs];
Properties[qccm]
qccm["ProbabilityPlot"]
ResourceFunction[
ResourceObject[<|
   "Name" -> "TTTGraph", "UUID" -> 
    "9d201d30-f5b4-480f-afcd-3a8d99a6dce8", "ResourceType" -> 
    "Function", "ResourceLocations" -> {
CloudObject[
      "https://www.wolframcloud.com/obj/wolframphysics/Resources/9d2/\
9d201d30-f5b4-480f-afcd-3a8d99a6dce8"]}, "Version" -> None, 
    "DocumentationLink" -> 
    URL["https://www.wolframcloud.com/obj/wolframphysics/\
MultiwayGames/TTTGraph"], "ExampleNotebookData" -> Automatic, 
    "FunctionLocation" -> 
    CloudObject[
     "https://www.wolframcloud.com/obj/wolframphysics/Resources/9d2/\
9d201d30-f5b4-480f-afcd-3a8d99a6dce8/download/DefinitionData"], 
    "ShortName" -> "TTTGraph", "SymbolName" -> 
    "FunctionRepository`$9d201d30f5b4480fafcd3a8d99a6dce8`TTTGraph"|>]\
][2, {{{{0, 0}, {1, 0}}, 0}}, AspectRatio -> 1, VertexSize -> 1]

For each qubit your post is the search engine that measures the aggregate probabilities and visualizes the game through a multi-way graph.

@Akhilesh Dubey if it's your quantum superposition, your @Akhilesh Dubey entanglement with the aid of qutrits and quantum gates, then...check out this Automated Theorem Proving & Axiomatic Mathematics by @Jonathan Gorard.

Even though the non-deterministic measurement process is in a slump since time immemorial, you could chance upon the legalized moves and winning criteria of the set of quantum gates to apply to the qubits, and make some headway on the secret tips and tricks of our local surroundings that only a local would know.