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Chinese Control Conference (CCC)

A unified framework for fault tolerant quantum filtering and fault detection

Qing Zhong Gao, Daoyi Dong, Ian R. Petersen

Published Jul 1, 2015• 2 citations
Publisher

Abstract

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.

DOI
10.1109/chicc.2015.7260965

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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.
This paper solves the problem of discrete-time fault-tolerant quantum filtering for a class of laser-atom open quantum systems subject to the stochastic faults. We show that by using the discrete-time quantum measurements, optimal estimates of both the atomic observables and the classical fault process can be simultaneously determined in terms of recursive quantum stochastic difference equations. A dispersive interaction quantum system example is used to demonstrate the proposed filtering approach.
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In quantum engineering, faults may occur in a quantum control system, which will cause the quantum control system unstable or deteriorate other relevant performance of the system. This note presents an estimator-based fault-tolerant control design approach for a class of linear quantum stochastic systems subject to fault signals. In this approach, the fault signals and some commutative components of the quantum system observables are estimated, and a fault-tolerant controller is designed to compensate the effect of the fault signals. Numerical procedures are developed for controller design and an example is presented to demonstrate the proposed design approach.
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We present a unified algebraic theory of Clifford spacetime quantum fault tolerance, which underpins universal fault-tolerant quantum computation. We construct a spacetime chain complex from a tensor network representation of a circuit that encodes fault propagation, detector syndromes, and logical actions through the associated gauge and stabilizer structure. We show that this theory (1) unifies various formulations of quantum fault tolerance including spacetime codes, Gottesman's gadget framework, fault complexes, and ZX calculus; (2) connects spacetime distances to the gadget-level correctness properties in Gottesman's formalism; (3) naturally accommodates a range of fault models, in particular phenomenological and circuit-level models, bringing these often separately formulated descriptions into a common algebraic framework through different tensor decompositions and fault assignments; and (4) recovers many known fault tolerance constructions and results as special cases, including repeated syndrome extraction, correlated detectors for transversal and fold-transversal gates, Steane- and Knill-type syndrome extraction gadgets, and single-shot error correction.