Essential to the functionality of qubit-based sensors are control protocols, which shape their response in frequency space. However, in common control routines out-of-band spectral leakage complicates interpretation of the sensor’s signal. In this work, we leverage discrete prolate spheroidal sequences (a.k.a. Slepian sequences) to synthesize provably optimal narrowband controls ideally suited to spectral estimation of a qubit’s noisy environment. Experiments with trapped ions demonstrate how spectral leakage may be reduced by orders of magnitude over conventional controls when a near resonant driving field is modulated by Slepians, and how the desired narrowband sensitivity may be tuned using concepts from RF engineering. We demonstrate that classical multitaper techniques for spectral analysis can be ported to the quantum domain and combined with Bayesian estimation tools to experimentally reconstruct complex noise spectra. We then deploy these techniques to identify previously immeasurable frequency-resolved amplitude noise in our qubit’s microwave synthesis chain.

Effectively manipulating quantum computing hardware in the presence of imperfect devices and control systems is a central challenge in realizing useful quantum computers. Susceptibility to noise in particular limits the performance and algorithmic capabilities experienced by end users. Fortunately, in both the NISQ era and beyond, quantum control enables the efficient execution of quantum logic operations and quantum algorithms exhibiting robustness to errors, without the need for complex logical encoding. In this manuscript we introduce the first commercial-grade software tools for the application and integration of quantum control in quantum computing research from Q-CTRL, serving the needs of hardware R&D teams, algorithm developers, and end users. We survey quantum control and its role in combating noise and instability in near-term devices; our primary focus is on quantum firmware, the low-level software solutions designed to enhance the stability of quantum computational hardware at the physical layer. We explain the benefits of quantum firmware not only in error suppression, but also in simplifying higher-level compilation protocols and enhancing the efficiency of quantum error correction. Following this exposition, we provide an overview of Q-CTRL's classical software tools for creating and deploying optimized quantum control solutions at various layers of the quantum computing software stack. We describe our software architecture leveraging both high-performance distributed cloud computation and local custom integration into hardware systems, and explain how key functionality is integrable with other software packages and quantum programming languages. Our presentation includes a detailed technical overview of central product features including a multidimensional control-optimization engine, engineering-inspired filter functions for high-dimensional Hilbert spaces, and a new approach to noise characterization. Finally, we present a series of case studies demonstrating the utility of quantum control solutions derived from these tools in improving the performance of trapped-ion and superconducting quantum computer hardware.

Classical control noise is ubiquitous in qubit devices, making its accurate spectral characterization essential for designing optimized error suppression strategies at the physical level. Here, we focus on multiplicative Gaussian amplitude control noise on a driven qubit sensor and show that sensing protocols using optimally band-limited Slepian modulation offer substantial benefit in realistic scenarios. Special emphasis is given to laying out the theoretical framework necessary for extending non-parametric multitaper spectral estimation to the quantum setting by highlighting key points of contact and differences with respect to the classical formulation. In particular, we introduce and analyze two approaches (adaptive vs. single-setting) to quantum multitaper estimation, and show how they provide a practical means to both identify fine spectral features not otherwise detectable by existing protocols and to obtain reliable prior estimates for use in subsequent parametric estimation, including high-resolution Bayesian techniques. We quantitatively characterize the performance of both singleand multitaper Slepian estimation protocols by numerically reconstructing representative spectral densities, and demonstrate their advantage over dynamical-decoupling noise spectroscopy approaches in reducing bias from spectral leakage as well as in compensating for aliasing effects while maintaining a desired sampling resolution. arXiv:1803.05538v2 [quant-ph]