4
$\begingroup$

I just started using stim to simulate the performance of quantum error correcting codes. I hope this is the right place to ask questions about the subject. The example code with the repetition code and depolarizing channel worked fine. Now I want to try one of my codes and the same channel. How would I import my code into stim? I can write the stabilizers as an $m \times n$ array ($m$ stabilizers, $n$ qubits) with entries from $(0,1,2,3)$; this seems like the most straight forward way. $(0=I,1=X,2=Z,3=Y)$.

For example, for the $[[5,1,3]]$ code $S:=[[1,2,2,1,0],[0,1,2,2,1],[1,0,1,2,2],[2,1,0,1,2]];$

Is this the preferred way? Do I also need to specify the logicals or destabilizers (I have these for some codes but maybe stim calculates them from the stabilizer...)

Improve this question
$\endgroup$

1 Answer 1

Reset to default
2
$\begingroup$

Stim is very much a circuit focused simulator. It speaks quantum operations, not stabilizer configurations, so you have to convert your table of stabilizers into a stabilizer circuit. This is a bit inconvenient, but ultimately makes Stim much more flexible as a tool (e.g. it has no issues with gauge codes or non-foliated codes).

The "proper" thing for you to do would be to find the encoding circuit for your code and put that into Stim. A fallback strategy could be to use the MPP instruction (Measure Pauli Product) to measure the stabilizers of the code. For example, here is a circuit that projects into your given code, applies single qubit depolarizing noise, re-measures the stabilizers, and produces detection events based on whether or not each stabilizer was flipped:

MPP X0*Z1*Z2*X3 X1*Z2*Z3*X4 X0*X2*Z3*Z4 Z0*X1*X3*Z4
DEPOLARIZE1(0.001) 0 1 2 3 4
MPP X0*Z1*Z2*X3 X1*Z2*Z3*X4 X0*X2*Z3*Z4 Z0*X1*X3*Z4
DETECTOR rec[-1] rec[-5]
DETECTOR rec[-2] rec[-6]
DETECTOR rec[-3] rec[-7]
DETECTOR rec[-4] rec[-8]

In python, you append MPP instructions like this:

circuit.append_operation("MPP", [
    stim.target_x(0),
    stim.target_combiner(),
    stim.target_z(1),
    stim.target_combiner(),
    stim.target_z(2),
    stim.target_combiner(),
    stim.target_x(3),
])

(The target combiners (*) are needed because you can give multiple products to MPP.)

Measuring the stabilizers will randomly project the system into their +1 or -1 eigenstates. If for some reason you need the +1 eigenstate you can do a conditional Pauli correction, e.g. CNOT rec[-1] 3 would apply an X gate to qubit 3 if the most recent measurement was True (presumably indicating the associated stabilizer measurement said the system was in the -1 eigenstate). The stim.TableauSimulator.measure_kickback method is a bit technical but can be used for finding a Pauli correction that won't ruin the other stabilizers of the state.

Anyways, ideally you would know an encoding circuit already. Otherwise, Stim provides a few basic tools like MPP andmeasure_kickback to help discover some of the pieces of such a circuit, but doesn't currently have an end-to-end "give me a well formed list of stabilizers and I give you a circuit" helper method.

Improve this answer
$\endgroup$
6
  • $\begingroup$ I think I can get the encoding circuit for most codes; so I'll move in that direction if there's no better way. There are algorithms to put the stabilizers into canonical form and then derive the encoding circuit from that; there's a fair amount of details that I was hoping to avoid with complications if you have redundant stabilizers...maybe someone know of a separate package that performs this step. Assuming I can get the encoding circuit, is the decoder used in the repetition code example generic enough to handle an arbitrary code? $\endgroup$
    – unknown
    Oct 9, 2021 at 20:15
  • $\begingroup$ @unknown No, most codes can't be decoded by a matching decoder which is what the repetition code example uses. Stim is not a decoding library; even the rep code example is using pymatching to do the decoding not Stim itself. Stim's decoding story focuses on providing building block tools (stim.Circuit.detector_error_model and stim.Circuit.compile_detector_sampler in this case) that are useful for getting configuration data and detection event data into a decoder. $\endgroup$
    – Craig Gidney
    Oct 9, 2021 at 20:19
  • $\begingroup$ oh that's too bad...I was encouraged by how quickly you were able to simulate the honeycomb code but I guess many parts of that sim are not part of stim $\endgroup$
    – unknown
    Oct 9, 2021 at 20:22
  • 1
    $\begingroup$ @unknown The honeycomb also has the surprising property that it can be decoded by matching, so I could use PyMatching for it. If it had required eg. a color code decoder I definitely would have struggled more, since I'm not familiar with those. Stim would still have been able to give me measurement results, and detection events, and a detector error model (corresponding to a hypergraph instead of a graph), but I wouldn't have had a ready tool for decoding. $\endgroup$
    – Craig Gidney
    Oct 9, 2021 at 20:25
  • $\begingroup$ @unknown Having a decoder that could efficiently decode any stabilizer code sure would be magical. But seems a bit... utterly insanely difficult. $\endgroup$
    – Craig Gidney
    Oct 9, 2021 at 20:39

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.