Fault tolerant preparation of quantum polar codes

A method of preparation of quantum polar code states in a quantum computing system materializing qubits, quantum gates and quantum circuits, comprising:

• preparing an initial quantum system ={1, . . . ,N}, of N=2n single-qubit states associated to an initial quantum base,
• preparing a quantum polar code |q2n of codelength N=2n referenced by predetermined first and second sets of frozen indices ={1, . . . ,i}, ={i+1, . . . , N} with respect to first and second quantum bases respectively, the quantum polar code |q2n being prepared by recursively using two qubit Pauli measurement P⊗P circuits, and
• at each recursive level k, where k=1 to n, preparing a set of 2n/2k quantum polar code states {|q_(2{circumflex over ( )}k)>_(_j(k)),j(k)=1 to (2{circumflex over ( )}n)/2{circumflex over ( )}k} of codelengths 2k, referenced by corresponding sets j(k) of indices comprising first and second sets of frozen indices j(k)={1j, . . . , ij(k)} and
• 𝒳
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• wherein
• each quantum polar code state is prepared by applying two qubit Pauli measurement P⊗P circuits on two equivalent polar code states
• |
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• belonging to an output of an antecedent recursive level k−1 and referenced by two corresponding sets of indices
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• each of which comprising first and second sets of frozen indices j(k−1) and j(k−1) corresponding to first and second quantum bases respectively, the antecedent of the recursive level k=1 being the initial quantum system of single-qubit states.