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Performing measurements for high-weight operators has been a practicalproblem in quantum computation, especially for quantum codes in the stabilizerformalism. The conventional procedure of measuring a high-weight operatorrequires multiple pairwise unitary operations, which can be slow and prone toerrors. We provide an alternative method to passively detect the value of ahigh-weight operator using only two-local interactions and single-qubitcontinuous measurements. This approach involves joint interactions between thesystem and continuously-monitored ancillary qubits. The measurement outcomesfrom the monitor qubits reveal information about the value of the operator.This information can be retrieved by using a numerical estimator or byevaluating the time average of the signals. The interaction Hamiltonian can beeffectively built using only two-local operators, based on techniques fromperturbation theory. We apply this indirect detection scheme to the four-qubitBacon-Shor code, where the two stabilizers are indirectly monitored using fourancillary qubits. Due to the fact that the four-qubit Bacon-Shor code is anerror-detecting code and that the Quantum Zeno Effect can suppress errors, wealso study the error suppression under the indirect measurement process. Inthis example, we show that various types of non-Markovian errors can besuppressed.

Continuous quantum error detection and suppression with pairwise local interactions