Frame-Based Filter-Function Formalism for Quantum Characterization and Control

Abstract

We introduce a theoretical framework for resource-efficient characterization and control of non-Markovian open quantum systems, which naturally allows for the integration of given, experimentally motivated, control capabilities and constraints. This is achieved by developing a transfer filter-function formalism based on the general notion of a frame and by appropriately tying the choice of frame to the available control. While recovering the standard frequency-based filter-function formalism as a special instance, this control-adapted generalization affords intrinsic flexibility and allows us to overcome important limitations of existing approaches. In particular, we show how to implement quantum noise spectroscopy in the presence of non-stationary noise sources, and how to effectively achieve control-driven model reduction for noise-tailored optimized quantum gate design.

Path integral framework for characterizing and controlling decoherence induced by non-stationary environments on a quantum probe

“…This sets a paradigmatic model of typical environments that can be suddenly quenched to put them out of equilibrium, where excitations start spreading over a large number of degrees of freedom [13,50,56,64,74]. The environment dynamics sensed by the qubit-probe can be represented with a generalized diffusion process, and possible examples can be encountered in spin ensembles coupled to single NV centers in diamond [94,128,129], macromolecular dynamics [130][131][132][133], spin diffusion on environments that becomes out of equilibrium [13,35,86,134,135], dynamics of spin and current fluctuations in a material at the nanoscale probed by magnetic noise sensors [136,137], and molecular diffusion out of equilibrium [63,[138][139][140][141].…”

“…Most of the approaches for controlling and characterizing the decoherence effects are developed for stationary noise fluctuations [19,20,28,29,32,35,40,[45][46][47][48]. Developing methods for controlling and characterizing non-stationary environmental fluctuations is a prerequisite to exploit the full extent of quantum technologies at atomic-and nano-scales, where the environmental systems are intrinsically of the many-body type and are * Electronic address: gonzalo.alvarez@cab.cnea.gov.ar out-of-equilibrium [13,16,[49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64].…”

“…However, it remains open how to interpret the extracted noise spectrum probed by a quantum sensor when it is coupled to a complex and unknown environment [44,61,72,73]. More importantly, there are no universal methods for determining the properties of the natural, out-of-equilibrium environments that lead to non-stationary, non-markovian noise fluctuation processes [49,51,55,61,63,64,67,74].…”

Quantum Control Noise Spectroscopy with Optimal Suppression of Dephasing

“…Approaches such as dynamical decoupling (DD) or dynamically corrected quantum gates (DCGs) are capable of refocusing both control and environmental noise sources, as long as the temporal correlations of the noise decay on timescales that are slow compared to the control [7][8][9]. While CPs, DD and DCGs are powerful in that they can increase gate fidelities without detailed knowledge of the control noise, further gains can be realized by taking into account specific features of the noise affecting a quantum device and leveraging optimal control to design robust, customized gates [3,[10][11][12].…”

Extracting Quantum Dynamical Resources: Consumption of Non-Markovianity for Noise Reduction

“…Reduced noise will also significantly enhance the performance of current generation devices [10]. These facts have lead to a flurry of techniques for noise characterisation and control [11,12]. While many different approaches exist, the general goal is to maximise the retained information between an input and the final output of the dynamics, for an arbitrary underlying noise process, by means of active experimental interventions.…”