Impact of time-retarded noise on dynamical decoupling schemes for qubits

One of the simplest and least resource-intensive methods to suppress decoherence for qubit operations, namely, dynamical decoupling (DD), is investigated for a broad range of realistic noise sources with time-retarded feedback. By way of example, the Carr-Purcell-Meiboom-Gill sequence is analyzed in a numerically rigorous manner accounting also for correlations between qubits and environments. Since experimentally noise sources are characterized through spectral densities, we adopt the spin-boson model as a suitable framework to describe the qubit dynamics under DD for a given spectral density <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>J</a:mi><a:mrow><a:mo>(</a:mo><a:mi>ω</a:mi><a:mo>)</a:mo></a:mrow><a:mo>∝</a:mo><a:msup><a:mi>ω</a:mi><a:mi>s</a:mi></a:msup></a:mrow></a:math>. Motivated by the situation for superconducting qubits, the spectral exponent <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>s</b:mi></b:math> is varied from <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mi>s</c:mi><c:mo>=</c:mo><c:mn>1</c:mn></c:mrow></c:math> (Ohmic bath) to a substantially small value <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mn>0</d:mn><d:mo>&lt;</d:mo><d:mi>s</d:mi><d:mo>≪</d:mo><d:mn>1</d:mn></d:mrow></d:math> (deep sub-Ohmic bath), in order to investigate the impact of time-nonlocal back action on DD performances for enhanced coherence times. As reference to the DD schemes, dynamics of a single qubit subject to Ramsey sequences without any pules and Hahn echo sequences are also investigated.