Error-Detection-Based Quantum Fault-Tolerance Threshold

Jesse Fern

S. D. Barrett, Thomas M. Stace

Many proposals for fault tolerant quantum computation (FTQC) suffer detectable loss processes. Here we show that topological FTQC schemes, which are known to have high error thresholds, are also extremely robust against losses. We demonstrate that these schemes tolerate loss rates up to 24.9%, determined by bond percolation on a cubic lattice. Our numerical results show that these schemes retain good performance when loss and computational errors are simultaneously present.

Ivan B. Djordjević

Zhan-Yun Wang

Abstract We investigate the impact of the correlation between error gates on the fault-tolerant threshold in quantum circuits under three typical noise models. In the fault-tolerant encoding schemes for two fundamental quantum logical operations, we extend the conventional error injection method by simultaneously applying error gates to both control and target qubits after two-qubit gate operations, with a quantitative characterization of the correlation strength between these error gates. The results show that the fault-tolerant error threshold can be noticeably enhanced by the presence of correlations between error gates, resulting in more robust quantum circuit implementations. We further apply fault-tolerant encoding to the single-qubit teleportation circuit and investigate the effect of correlated noise on its error threshold. The results show that the threshold varies non-monotonically with the correlation strength and that the system’s fault-tolerance differs significantly across noise models.

Aparna Kanungo

Quantum error correcting codes have been introduced to encode the data bits\nin extra redundant bits in order to accommodate errors and correct them. However,\ndue to the delicate nature of the quantum states or faulty gate operations, there is\na possibility of catastrophic spread of errors which might render the error correction\ntechniques ineffective. Hence, in this thesis we concentrate on how various operations\ncan be carried out fault-tolerantly so that the errors are not propagated in the same\nblock. We prove universal fault-tolerance for nonbinary CSS codes. This thesis is\nfocussed only on nonbinary quantum codes and all the results pertain to nonbinary\ncodes.\nEfficient error detection and correction techniques using fault-tolerant techniques\ncan help as long as we ensure that the gate error probability is below a certain\nthreshold. The calculation of this threshold is therefore important to see if quantum\ncomputations are realizable or not, even with fault-tolerant operations. We derive an\nexpression to compute the gate error threshold for nonbinary quantum codes and test\nthis result for different classes of codes, to get codes with best threshold results.

Ivan B. Djordjević