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arXiv:1504.06780 · Automatica

Fault tolerant quantum filtering and fault detection for quantum systems

Qing Zhong Gao, Daoyi Dong, Ian R. Petersen

Published May 31, 2016• 46 citations
arXivHTMLPDF
DOI
10.1016/j.automatica.2016.04.045

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A quantum-classical probability space model is developed for a class of open quantum systems where the system dynamics involve both classical and quantum random variables. This model provides a unified framework for analyzing open quantum systems subject to stochastic faults. A fault tolerant quantum filter and a fault detection equation are simultaneously derived for this class of open quantum systems using a reference probability approach. A two-level open quantum system subject to Poisson-type faults is presented to illustrate the proposed method. These results have the potential for the systematic development of new fault tolerant control theory for quantum systems.
A fully fault-tolerant implementation of the quantum error-detecting Iceberg [[2m,2m−2,2]][[2m, 2m-2, 2]][[2m,2m−2,2]] code applied to a Toffoli circuit achieved beyond-break-even error detection on a leading trapped-ion quantum computer, where the effect of encoding a circuit with a quantum error-detection code enables increased fidelity compared to an unencoded circuit. This code was also applied to Bell state preparation circuits, where a lean non-fault-tolerant implementation of the Iceberg code enables a fidelity gain as well. This highlights the important point that, at least for small-scale circuits with a substantial portion of error-free runs, it can be effective simply to use error detection to filter out the runs with errors. Furthermore, experiments performed in this work highlight the necessity for judicious compilation of circuits not only for a given hardware but also within a quantum error detection code.
Quantum error-detecting codes offer a near-term path for improving the performance of quantum simulations on noisy hardware. Using IBM's superconducting quantum computer ibm_boston, we show that partially fault-tolerant encoded quantum simulations of the Ising model in 1+1D and 2+1D outperform their unencoded counterparts in estimating local observables. To represent 42 logical qubits on the heavy-hex quantum processor, 21 blocks of the [[4, 2, 2]] Iceberg code and up to 136 physical qubits are used. By pairing fault-tolerant syndrome extraction with non-fault-tolerant logical operations, this scheme preserves many of the benefits of error detection while avoiding the overhead typically required for a fully fault-tolerant logical gate set. The encoding's square logical connectivity, together with the freedom to place logical qubits within each block, enables simulations of a 2D spatial lattice with lower circuit depth than the unencoded implementation requires. We introduce Observable-Ranked Postselection, a selective-filtering technique based on syndrome correlations that recovers reliable results without the prohibitive shot loss of full syndrome postselection. Under the cumulative effect of device errors, this encoding improves local-observable accuracy over the unencoded baseline by 2-6% at intermediate times in 1+1D simulations, growing with circuit depth to over 200% in 2+1D at the latest times studied.