Abstract: A signal comprises a plurality of codewords associated with a set of codewords, each codeword comprising a plurality of symbols associated with a symbol constellation. Processing includes: mapping quantum states associated with symbols of a particular codeword of the signal to a plurality of input qubits, and applying quantum operations to the input qubits according to a quantum circuit for decoding the signal. The quantum operations comprise: controlled unitary multi-qubit operations performed on two or more qubits in a first set of qubits controlled based on two or more qubits in a second set of qubits, an initial quantum measurement performed on an initially measured qubit in the first set of qubits, at least one controlled unitary single-qubit operation performed on a post-measurement state associated with the initially measured qubit, and quantum operations that invert at least a portion of the operations in the plurality of controlled unitary multi-qubit operations.