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While simulating any Stabilizer code on STIM do we need an explicit encoding circuit before performing circuit-level noise simulation and error-correction ?

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2 Answers 2

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Yes, Stim needs you to explain your code as a circuit, so you end up needing things like encoders. However, nothing stops you from making the encoding circuit just a series of MPP instructions measuring each stabilizer and observable.

Stim can also automatically generate a bad encoding circuit from the stabilizers. It won't be fault tolerant, but it will produce the correct state:

import stim
stabilizers_and_obs = [
    # stabilizers of perfect code
    stim.PauliString("XZZX_"),
    stim.PauliString("_XZZX"),
    stim.PauliString("X_XZZ"),
    stim.PauliString("ZX_XZ"),
    # observable to prepare
    stim.PauliString("ZZZZZ"),
]
tableau = stim.Tableau.from_stabilizers(stabilizers_and_obs)

print(tableau.to_circuit("elimination").diagram())
# q0: -X-@-X-H-@-@---X-------------------------------------------S-S-------
#      | | |   | |   |
# q1: -|-|-|---|-|---|-X-@-X-H-S-@-@---X---------------------------S-S-----
#      | | |   | |   | | | |     | |   |
# q2: -@-X-@---|-|-H-@-|-|-|---S-X-|---|-X-@-X-H-@-@-----------------S-S---
#              | |     | | |       |   | | | |   | |
# q3: ---------X-|-----@-X-@-------|-H-@-|-|-|-H-X-|-X-@-X-H-S-@-----------
#                |                 |     | | |     | | | |     |
# q4: -----------X-------------H---X-----@-X-@-H---X-@-X-@-----X-H-----S-S-

There's a more compact state-prep circuit method coming in v1.13 called "graph_state":

# Needs v1.13.dev or later
print(tableau.to_circuit("graph_state").diagram())
#         /-----------\ /-\
# q0: -RX-@-@-@---------Z---
#         | | |
# q1: -RX-|-|-|-@-@---------
#         | | | | |
# q2: -RX-@-|-|-@-|-@-@-X-H-
#           | |   | | |
# q3: -RX---@-|---|-@-|-----
#             |   |   |
# q4: -RX-----@---@---@-Z---
#         \-----------/ \-/

There will also be "mpp_state" and "mpp_state_unsigned" which just measure the stabilizers using MPP, which is what I always do. If it's not fault tolerant anyways, no point in worrying about the details.

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  • $\begingroup$ just to confirm if I got it right: You are suggesting to start the data qubits in all |0> state and project this state into simultaneous +1-eigenspace of all the stabilizers using MPP instruction. The final resultant state will be our code space. $\endgroup$ Jan 30 at 0:56
  • $\begingroup$ @OmprakashChandra that's right. Assuming you don't need the initialization itself to be fault tolerant, that is sufficient. $\endgroup$ Jan 30 at 2:13
  • $\begingroup$ how can we force the state into +1 eigenspace of the stabilizers? Is there a specific instruction in STIM accomplishing this? How do you do it? $\endgroup$ Jan 31 at 3:30
  • $\begingroup$ You can use feedback operations and the destabilizers of the code to force them. But what I always do is just include the initial measurement in the detector/observable declarations which makes it work regardless of the initial measurement result. $\endgroup$ Jan 31 at 5:31
  • $\begingroup$ Thank you very much for your help. I have rewritten the circuit in my own way and it's working now. $\endgroup$ Feb 6 at 11:37
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To supplement @Craig Gidney's answer, the TQEC project is under development for the purpose of assisting researchers who build error-correcting circuits. This project takes Stim as a dependency in circuit construction on the backend.

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    $\begingroup$ thanks for this. I will have a look at the project. $\endgroup$ Jan 30 at 0:57

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