Gate-Error-Resilient Quantum Steane Codes

Abstract

An encoderless quantum code is capable of connecting quantum information by replacing the encoder circuit with a fault-tolerant single-qubit gate arrangement. As a further benefit, in contrast to state preparation techniques, our encoderless scheme requires no prior knowledge of the input information, therefore totally unknown states can be encoded fault-tolerantly. Our encoderless quantum code delivers a frame error rate that is three orders of magnitude lower than that of the corresponding scheme relying on a non-fault-tolerant encoder, when the gate error probability is as high as 10 −3 .

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

“…For example, if a certain CNOT gate in the [4, 2, 2] code's encoding circuit has an erroneous output and this error in turn proliferates to an even number of qubit errors in the output state, then this error cannot be detected and the circuit is not fault-tolerant, as will be briefly exemplified below. Further discussions on error proliferation and fault-tolerant circuit design can be found for example in [25], [36].…”

“…. after the normal functioning of the gate (see [25], [36] and Appendix VII-A). Each error has a probability of 2 /15, since there are 15 combinations of {X, Y, Z, I} excluding II representing the identity operation that has no effect.…”

“…This method is comparable to those numerical methods, where the gate errors are modelled independently by a Pauli error channel[25],[36]. Each gate error is treated as an independent error event, whereby the proliferation of qubit errors is mitigated by decoding.…”