Real-time adaptive estimation of decoherence timescales for a single qubit

Abstract

Characterizing the time over which quantum coherence survives is critical for any implementation of quantum bits, memories, and sensors. The usual method for determining a quantum system’s decoherence rate involves a suite of experiments probing the entire expected range of this parameter, and extracting the resulting estimation in postprocessing. Here we present an adaptive multiparameter Bayesian approach, based on a simple analytical update rule, to estimate the key decoherence timescales (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><a:msub><a:mi>T</a:mi><a:mn>1</a:mn></a:msub></a:math>, <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><d:msubsup><d:mi>T</d:mi><d:mn>2</d:mn><d:mo>∗</d:mo></d:msubsup></d:math>, and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><g:msub><g:mi>T</g:mi><g:mn>2</g:mn></g:msub></g:math>) and the corresponding decay exponent of a quantum system in real time, using information gained in preceding experiments. This approach reduces the time required to reach a given uncertainty by a factor up to an order of magnitude, depending on the specific experiment, compared to the standard protocol of curve fitting. A further speedup of a factor approximately <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><j:mn>2</j:mn></j:math> can be realized by performing our optimization with respect to sensitivity as opposed to variance. Published by the American Physical Society 2024