YES! That did it....THANK YOU!

Hi Mads,

Not sure if you saw my last comment, but I'm basically finding that even relatively simple calculations are unworkable and hoping there might be some significant speed ups to be had - either on my end or on Wolframs end.

I'm attaching my notebook that shows what I'm doing. It's only a 1-dimensional 4-qubit circuit with nearest neighbor interactions with periodic boundary conditions, and is designed to simulate a transverse field Ising model. If you run the notebook, I think you'll find that the noiseless circuit can be computed just fine, but including the noise channels still bogs things down very quickly (basically after a single Trotter step).

Thank you for any help, Dave

Wonderful, everything is working beautifully now.

Cool, I have it working now after the bug fix.

This isn't really a bug, as I have found a work around, but thought I'd bring it up as a potential upgrade.

I've noticed that composing channels seems to get bogged down fairly quickly compared to composing quantum operators. For context, I've constructed a 2-qubit depolarizing channels to apply along with each two-qubit gate in my circuit.

   TQDepol[\[Epsilon]_] := 
  Sqrt[\[Epsilon]/
   15.0] {QuantumOperator["IX"], QuantumOperator["IY"], 
    QuantumOperator["IZ"], QuantumOperator["XI"], 
    QuantumOperator["XX"], QuantumOperator["XY"], 
    QuantumOperator["XZ"], QuantumOperator["YI"], 
    QuantumOperator["YX"], QuantumOperator["YY"], 
    QuantumOperator["YZ"], QuantumOperator["ZI"], 
    QuantumOperator["ZX"], 
    Sqrt[\[Epsilon]/15.0] QuantumOperator["ZY"], 
    QuantumOperator["ZZ"], 
    Sqrt[1 - \[Epsilon]]/Sqrt[\[Epsilon]/15.0] QuantumOperator["II"]};

TQDepolChannel[\[Epsilon]_, i_, j_] := 
 QuantumChannel[TQDepol[\[Epsilon]], {i, j}]

I can compose a couple of these maps, like this works just fine:

TQDepolChannel[\[Epsilon], 1, 2]@TQDepolChannel[\[Epsilon], 3, 4]

But the calculation quickly bogs down if I try to compose 3 or more of these channels. My work around is to apply the channels to a state. For example, this composition takes a very long time to evaluate,

TQDepolChannel[\[Epsilon], 1, 2]@ TQDepolChannel[\[Epsilon], 1, 2]@TQDepolChannel[\[Epsilon], 3, 4]

But this evaluates pretty quickly

TQDepolChannel[\[Epsilon], 1, 2]@ TQDepolChannel[\[Epsilon], 1, 2]@TQDepolChannel[\[Epsilon], 3, 4]@QuantumState["0000"]

While the second option is fast, it would sometimes be better to calculate the map for an arbitrary initial state. Maybe the slowdown comes from dealing with super-operators that act on density matrices and perhaps moving to the Liouville representation where the density matrix is vectorized will help - just speculating.

Anyway, thank you for the help.

That all works great, except I run into trouble when trying to apply the channels to qubits and 1 & 3 or qubits 2 & 4(for example). Seems like some default "ordering" behavior with channels that I don't see with the QuantumOperators.

So, changing your code to

ops = {QuantumOperator["XX", {2, 3}], 
    QuantumOperator["YY", {2, 3}]} Sqrt[.5];
channel = QuantumChannel[ops]

applies the channel to qubits 2&3 just fine.

But similar code fails to apply the channel to qubits 2&4 and throws an error saying the Order size should be less than or equal to the number or qudits. Here is the code I tried for applying the channel to qubits 2&4.

ops = {QuantumOperator["XX", {2, 4}], 
    QuantumOperator["YY", {2, 4}]} Sqrt[.5];
channel = QuantumChannel[ops]

Note this same kind of code works fine for QuantumOperators, just not the Channels.