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Optimal digital dynamical decoupling for general decoherence via Walsh modulation. (English) Zbl 1387.81076
Summary: We provide a general framework for constructing digital dynamical decoupling sequences based on Walsh modulation – applicable to arbitrary qubit decoherence scenarios. By establishing equivalence between decoupling design based on Walsh functions and on concatenated projections, we identify a family of optimal Walsh sequences, which can be exponentially more efficient, in terms of the required total pulse number, for fixed cancellation order, than known digital sequences based on concatenated design. Optimal sequences for a given cancellation order are highly non-unique – their performance depending sensitively on the control path. We provide an analytic upper bound to the achievable decoupling error and show how sequences within the optimal Walsh family can substantially outperform concatenated decoupling in principle, while respecting realistic timing constraints.
MSC:
81P40 Quantum coherence, entanglement, quantum correlations
81S22 Open systems, reduced dynamics, master equations, decoherence
42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
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