Abstract The field of quantum control and sensing encounters challenges due to various forms of time-dependent noise. We introduce a generalized filter-function framework that treats noise coupling strength as a tunable control parameter, enabling target noise suppression across user-defined frequency bands. By optimizing this generalized filter function, we design band-selective control pulses that achieve high fidelity of single- and two-qubit gates under strong noise with diverse spectral profiles. We further extend the method to selectively enhance the signal-to-noise ratio for quantum sensing of AC signals with an enhanced precision of up to 12.58 dB. The resulting control pulses are experimentally feasible, offering a practical pathway toward robust quantum operations and high-precision sensing under spectrally complex noises.
Abstract The field of quantum control and sensing encounters challenges due to various forms of time-dependent noise. We introduce a generalized filter-function framework that treats noise coupling strength as a tunable control parameter, enabling target noise suppression across user-defined frequency bands. By optimizing this generalized filter function, we design band-selective control pulses that achieve high fidelity of single- and two-qubit gates under strong noise with diverse spectral profiles. We further extend the method to selectively enhance the signal-to-noise ratio for quantum sensing of AC signals with an enhanced precision of up to 12.58 dB. The resulting control pulses are experimentally feasible, offering a practical pathway toward robust quantum operations and high-precision sensing under spectrally complex noises.
Quantum control protocols are typically devised in the time domain, leaving their spectral behavior to emerge only a posteriori. Here, we invert this paradigm. Starting from a target frequency-domain filter, we employ the dynamical-invariant framework to derive the continuous driving fields that enact the chosen spectral response on a qubit. This approach, Quantum Invariant Filtering (QIF), maps arbitrary finite-impulse responses, including multi-band and phase-sensitive profiles, into experimentally feasible Hamiltonian modulations. Implemented on a single nitrogen-vacancy center in diamond, the method realizes the prescribed passbands with high fidelity, suppresses noise, and preserves coherence for milliseconds, two orders of magnitude longer than Carr-Purcell-Meiboom-Gill sequences, while remaining robust to 50% drive-amplitude errors. Our results establish QIF as a broadly applicable framework for enhanced quantum control and sensing across diverse physical platforms, including superconducting qubits, trapped ions, and nuclear magnetic resonance systems.
We introduce a quantum control protocol that produces smooth, experimentally implementable control sequences optimized to combat temporally correlated noise for single-qubit systems. The control ansatz is specifically chosen to be a functional expansion of discrete prolate spheroidal sequences, a discrete time basis known to be optimally concentrated in time and frequency, and quite attractive when faced with experimental control hardware constraints. We leverage the filter function formalism to transform the control problem into a filter design problem, and show that the frequency response of a quantum system can be carefully tailored to avoid the most relevant dynamical contributions of noise processes. Using gradient ascent, we obtain optimized filter functions and exploit them to elucidate important details about the relationship between filter function design, control bandwidth, and noise characteristics. In particular, we identify regimes of optimal noise suppression and, in turn, optimal control bandwidth directly proportional to the size of the frequency bands where the noise power is large. In addition to providing guiding principles for filter design, our approach enables the development of controls that simultaneously yield robust noise filtering and high-fidelity single-qubit logic operations in a wide variety of complex noise environments.
The main obstacles to implementing ideal quantum operations are unwanted interactions of quantum systems with the environment and noise in control fields. This problem can be tackled by methods of quantum control. Among these methods are \ncomposite pulse (CP) sequences which have long been employed in nuclear magnetic resonance (NMR) to mitigate the effects of systematic errors in the control. CP sequences have been initially developed to correct for static but otherwise unknown \nerrors in the amplitude or frequency of the driving field. One of the challenges to the systematic incorporation of these control protocols into practical quantum information systems remains the limited understanding of CP performance in the presence \nof time-dependent noise. Treating the influence of time-dependent noise processes on quantum control operations has been facilitated by recent advances in dynamical \nerror suppression based on open-loop Hamiltonian engineering. These approaches provide a general framework for understanding and mitigating non-Markovian time- \ndependent noise in a finite-dimensional open quantum system. Particularly, arbitrary single-qubit control characteristics may be captured quantitatively in filter-transfer \nfunctions (FF) using methods of spectral overlap in the frequency domain. In this thesis work, we present a systematic study of control pulse sequences in the presence of time-dependent noise. We use a combination of analytic formulations based on FFs and numerical simulations to demonstrate that CPs are able to effectively suppress control errors caused by time-dependent processes possessing realistic noise \npower spectra. We provide a geometric interpretation of CP performance under time-dependent amplitude noise, further linking the FF formalism with known techniques in CP construction. We also develop new optimized pulse sequences that act as notch filters for time-dependent noise. These high-fidelity control protocols effectively sup- \npress errors from the noise sources with sharp features in spectral densities and can be used practically on various quantum architectures. We also present our work \non simulation of randomized benchmarking protocols and CPs that have been used experimentally by our collaborators to measure gate errors.
The performance of quantum processors in the noisy intermediate-scale quantum (NISQ) era is severely constrained by environmental noise and other uncertainties. While the recently proposed quantum control robustness landscape (QCRL) offers a powerful framework for generating robust control pulses for parametric gate families, its application has been practically restricted to quasi-static noise. To address the spectrally complex, time-varying noise prevalent in reality, we propose filter function-enhanced QCRL (FF-QCRL), which integrates filter function formalism into the QCRL framework. The resulting FF-QCRL algorithm minimizes a generalized robustness metric that faithfully encodes the impact of stochastic processes, enabling robust pulse-family generation for parametric gates under realistic time-varying noise. Numerical validation in a representative single-qubit setting confirms the effectiveness of the proposed method.
Abstract. We address the problem of deriving analytic expressions for calculating universal decoherence-induced errors in qubits undergoing arbitrary, unitary, time-dependent quantum-control protocols. We show that the fidelity of a control operation may be expressed in terms of experimentally relevant spectral characteristics of the noise and of the control, over all Cartesian directions. We formulate control matrices in the time domain to capture the effects of piecewise-constant control, and convert them to generalized Fourier-domain filter functions. These generalized filter functions may be derived for complex temporally modulated control protocols, accounting for susceptibility to rotations of the qubit state vector in three dimensions. Taken together, we show that this framework provides a computationally efficient means to calculate the effects of universal noise on arbitrary quantum control protocols, producing results comparable to those obtained via time-consuming simulations of Bloch vector evolution. As a concrete example, we apply our method to treating the problem of dynamical decoupling incorporating realistic control pulses of arbitrary duration or form, including the replacement of simple pi-pulses with complex dynamically corrected gates. ar
Mitigating noise-induced decoherence is the central challenge in controlling open quantum systems. While existing robust protocols often require precise noise models, we introduce a universal framework for noise-agnostic quantum control that achieves high-fidelity operations without prior environmental noise characterization. This framework capitalizes on the dynamical modification of the system-environment coupling through control drives, an effect rigorously encoded in the dynamical equation. Since the derived noise sensitivity metric remains independent of the coupling details between the system and the environment, our protocol demonstrates robustness against arbitrary Markovian noises within the first-order weak coupling approximation. Numerical validation through quantum state transfer and gate operations reveals near-unity fidelity across diverse noise regimes, achieving orders-of-magnitude error suppression compared to target-only approaches. This framework bridges critical gaps between theoretical control design and experimental constraints, establishing a broadly applicable strategy for high-fidelity quantum information processing across platforms such as superconducting circuits, trapped ions, and solid-state qubits.