A quantum system configured to extract and decode a syndrome using a Bacon-Shor quantum error correction code, the quantum system comprising: an array of qubits configured to store an item of quantum information, the array of qubits including a plurality of data qubits and a plurality of measurement qubits configured to extract a first syndrome representing agreement among the plurality of data qubits with respect to a first basis; an integrated circuit, implemented using reciprocal quantum logic, the integrated circuit comprising: validation logic configured to determine if the first syndrome is valid, wherein a valid syndrome has an even number of bits representing mismatches between adjacent qubits, and, if the first syndrome is valid, compare the first syndrome to a most recent valid syndrome, wherein the most recent valid syndrome is a last syndrome that was successfully validated at the validation logic prior to the first syndrome; decoding logic configured to evaluate the first syndrome to determine locations of errors within the plurality of data qubits if the validation logic determines the first syndrome to be valid; and an error register configured to store the determined locations of errors; wherein the validation logic is configured to refrain from passing the first syndrome to the decoding logic and the error register if the first syndrome is identical to the most recent valid syndrome. an array of qubits configured to store an item of quantum information, the array of qubits including a plurality of data qubits and a plurality of measurement qubits configured to extract a first syndrome representing agreement among the plurality of data qubits with respect to a first basis; an integrated circuit, implemented using reciprocal quantum logic, the integrated circuit comprising: validation logic configured to determine if the first syndrome is valid, wherein a valid syndrome has an even number of bits representing mismatches between adjacent qubits, and, if the first syndrome is valid, compare the first syndrome to a most recent valid syndrome, wherein the most recent valid syndrome is a last syndrome that was successfully validated at the validation logic prior to the first syndrome; decoding logic configured to evaluate the first syndrome to determine locations of errors within the plurality of data qubits if the validation logic determines the first syndrome to be valid; and an error register configured to store the determined locations of errors; wherein the validation logic is configured to refrain from passing the first syndrome to the decoding logic and the error register if the first syndrome is identical to the most recent valid syndrome. validation logic configured to determine if the first syndrome is valid, wherein a valid syndrome has an even number of bits representing mismatches between adjacent qubits, and, if the first syndrome is valid, compare the first syndrome to a most recent valid syndrome, wherein the most recent valid syndrome is a last syndrome that was successfully validated at the validation logic prior to the first syndrome; decoding logic configured to evaluate the first syndrome to determine locations of errors within the plurality of data qubits if the validation logic determines the first syndrome to be valid; and an error register configured to store the determined locations of errors; wherein the validation logic is configured to refrain from passing the first syndrome to the decoding logic and the error register if the first syndrome is identical to the most recent valid syndrome. <EOS>