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.

We show that measurements of finite duration performed on an open two-state system can protect the initial state from a phase-noisy environment, provided the measured observable does not commute with the perturbing interaction. When the measured observable commutes with the environmental interaction, the finite-duration measurement accelerates the rate of decoherence induced by the phase noise. For the description of the measurement of an observable that is incompatible with the interaction between system and environment, we have found an approximate analytical expression, valid at zero temperature and weak coupling with the measuring device. We have tested the validity of the analytical predictions against an exact numerical approach, based on the superoperator-splitting method, that confirms the protection of the initial state of the system. When the coupling between the system and the measuring apparatus increases beyond the range of validity of the analytical approximation, the initial state is still protected by the finite-time measurement, according with the exact numerical calculations.

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We consider the problem of measurement using the Lindblad equation, which allows the introduction of time in the interaction between the measured system and the measurement apparatus. We use analytic results, valid for weak system-environment coupling, obtained for a two-level system in contact with a measurer (Markovian interaction) and a thermal bath (non-Markovian interaction), where the measured observable may or may not commute with the system-environment interaction.Analysing the behavior of the coherence, which tends to a value asymptotically close to zero, we obtain an expression for the time of measurement which depends only on the system-measurer coupling, and which does not depend on whether the observable commutes with the system-bath interaction. The behavior of the coherences in the case of strong system-environment coupling, found numerically, indicates that an increase in this coupling decreases the measurement time, thus allowing our expression to be considered the upper limit for the duration of the process.