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A major goal of developing high-precision control of many-body quantumsystems is to realise their potential as quantum computers. Probably the mostsignificant obstacle in this direction is the problem of "decoherence": theextreme fragility of quantum systems to environmental noise and other controllimitations. The theory of fault-tolerant quantum error correction has shownthat quantum computation is possible even in the presence of decoherenceprovided that the noise affecting the quantum system satisfies certainwell-defined theoretical conditions. However, existing methods for noisecharacterisation have become intractable already for the systems that arecontrolled in today's labs. In this paper we introduce a technique based onsymmetrisation that enables direct experimental characterisation of keyproperties of the decoherence affecting a multi-body quantum system. Our methodreduces the number of experiments required by existing methods from exponentialto polynomial in the number of subsystems. We demonstrate the application ofthis technique to the optimisation of control over nuclear spins in the solidstate.

Symmetrised Characterisation of Noisy Quantum Processes