Decoder Interface

Decoding Problems

We have 3 types of decoding problems. ClassicalDecodingProblem is for the case that the error model is independent flip error. IndependentDepolarizingDecodingProblem is the decoding problem for the case that the error model is independent depolarizing error. GeneralDecodingProblem is the decoding problem for the case that error model on different qubits are correlated. We use a tensor network to represent the error probability distribution. Here is an example of how to construct a decoding problem.

using TensorQEC
tanner = CSSTannerGraph(SurfaceCode(3,3))
problem = IndependentDepolarizingDecodingProblem(tanner,iid_error(0.05,0.05,0.05,9))

IndependentDepolarizingDecodingProblem(CSSTannerGraph(SimpleTannerGraph(9, 4, [[1], [1], [3], [1, 4], [1, 2], [2, 3], [4], [2], [2]], [[1, 2, 4, 5], [5, 6, 8, 9], [3, 6], [4, 7]], Mod2[1₂ 1₂ … 0₂ 0₂; 0₂ 0₂ … 1₂ 1₂; 0₂ 0₂ … 0₂ 0₂; 0₂ 0₂ … 0₂ 0₂]), SimpleTannerGraph(9, 4, [[3], [1, 3], [1], [2], [1, 2], [1], [2], [2, 4], [4]], [[2, 3, 5, 6], [4, 5, 7, 8], [1, 2], [8, 9]], Mod2[0₂ 1₂ … 0₂ 0₂; 0₂ 0₂ … 1₂ 0₂; 1₂ 1₂ … 0₂ 0₂; 0₂ 0₂ … 1₂ 1₂])), IndependentDepolarizingError{Float64}([0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05], [0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05], [0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05]))

Decoding Process

Decoders

There are 2 types of decoders. AbstractClassicalDecoder and AbstractGeneralDecoder solve ClassicalDecodingProblem and GeneralDecodingProblem, respectively. For IndependentDepolarizingDecodingProblem, we can transfer it to GeneralDecodingProblem and use AbstractGeneralDecoder to solve it. Also, for an IndependentDepolarizingDecodingProblem of a CSS code, we can transfer it to two ClassicalDecodingProblem and use AbstractClassicalDecoder to solve them. Here is a list of supported decoders.

Here we use the integer programming decoder to solve the decoding problem.

decoder = IPDecoder()

IPDecoder(SCIP.Optimizer, false)

Compilation

Usually, we use decoders to run monte carlo simulations to estimate the code capacity. We use the same decoder to solve the decoding problem of the same QEC code and error model for different error and syndrome configurations. Ones the error model and the QEC code are fixed, we can compile the decoder to avoid the overhead of decoding. For example, in Lookup Table decoder, we can make the truth table once and use it for all the decoding problems. And in tensor network decoders, we can make the tensor network once and connect it to different syndrome configurations when decoding. This is also the reason why there is no syndrome information in the decoding problem or in the decoder.

compiled_decoder = compile(decoder, problem);

Decoding

Now we randomly generate an error configuration.

using Random
Random.seed!(123)
error_qubits = random_error_qubits(problem.pvec)

IIIIIIYII

The corresponding syndrome is

syndrome = syndrome_extraction(error_qubits, tanner)

CSSSyndrome(Mod2[0₂, 0₂, 0₂, 1₂], Mod2[0₂, 1₂, 0₂, 0₂])

We can use the compiled decoder to decode the syndrome with decode. The decoding result is a DecodingResult object.

res = decode(compiled_decoder, syndrome)

Success
IIIIIIYII

We can check the result by comparing the syndrome of the decoding result.

syndrome == syndrome_extraction(res.error_qubits, tanner)

true

Also, to check wether there is a logical error, we can first generate the logical operators with logical_operator.

logicalx_operators,logicalz_operators = logical_operator(tanner)

(Mod2[0₂ 0₂ … 1₂ 1₂], Mod2[1₂ 0₂ … 0₂ 1₂])

Then we can check the syndrome of the logical operators with check_logical_error.

check_logical_error(error_qubits, res.error_qubits, logicalx_operators, logicalz_operators)

false

Simply decode function can also be used to decode the syndrome. The compilation step is contained in the function.

decode(decoder,problem,syndrome)

Success
IIIIIIYII

This page was generated using Literate.jl.