Experimental Characterization of Fault-Tolerant Circuits in Small-Scale Quantum Processors

Abstract

Experiments conducted on open-access cloud-based IBM Quantum devices are presented for characterizing their fault tolerance using [4, 2, 2]-encoded gate sequences. Up to 100 logical gates are activated in the Ibmq_Bogota and Ibmq_Santiago devices and we found that a [4, 2, 2] code's logical gate set may be deemed fault-tolerant for gate sequences larger than 10 gates. However, certain circuits did not satisfy the fault tolerance criterion. In some cases the encoded-gate sequences show a high error rate that is lower bounded at ≈ 0.1, whereby the error inherent in these circuits cannot be mitigated by classical post-selection. A comparison of the experimental results to a simple error model reveal that the dominant gate errors cannot be readily represented by the popular Pauli error model. Finally, it is most accurate to assess the fault tolerance criterion when the circuits tested are restricted to those that give rise to an output state with a low dimension.INDEX TERMS quantum error correction codes, quantum gates, ibm quantum, quantum circuits, fault tolerant circuit, encoded gates

Optical demonstration of quantum fault-tolerant threshold

“…It is shown that errors in this protocol cannot be corrected. Following this protocol, fault-tolerant error detection of encoding has been demonstrated in trapped ions 34 , superconducting qubits 35 , and the IBM quantum devices 36 – 38 . However, the key aspect of the quantum circuit implementing with fault-tolerant operations, that is, the existence of the threshold of error rate below which the circuit is realized in a fault-tolerant manner, has not been explicitly demonstrated.…”