Entangling operations are among the most important primitive gates employed in quantum computing and it is crucial to ensure high-fidelity implementations as systems are scaled up. We experimentally realize and characterize a simple scheme to minimize errors in entangling operations related to the residual excitation of mediating bosonic oscillator modes that both improves gate-robustness and provides scaling benefits in larger systems. The technique employs discrete phase shifts in the control field driving the gate operation, determined either analytically or numerically, to ensure all modes are de-excited at arbitrary user-defined times. We demonstrate an average gate fidelity of 99.4(2)% across a wide range of parameters in a system of 171 Yb + trapped ion qubits, and observe a reduction of gate error in the presence of common experimental error sources. Our approach provides a unified framework to achieve robustness against both static and time-varying laser amplitude and frequency detuning errors. We verify these capabilities through systemidentification experiments revealing improvements in error-susceptibility achieved in phase-modulated gates.The ability to perform robust, high fidelity entangling gates in multi-qubit systems is a key requirement for realizing scalable quantum information processing 1 . In several hardware architectures, qubits are entangled through shared bosonic oscillator modes via an interaction that is moderated by an external driving field. The Mølmer-Sørensen (MS) gate in trapped ions 2-4 and the resonator-induced phase gate in superconducting circuits 5-7 are both of this type. In addition, interactions simultaneously employing multiple bosonic modes have been explored to improve gate fidelities 8 and probe novel types of interactions 9 in superconducting circuits.A major source of error for oscillator-mediated gates is residual qubit-oscillator entanglement at the end of the operation 10 . This detrimental effect can arise due to the presence of quasi-static or time-varying noise on the driving field, slow drifts in experimental parameters such as the qubit and oscillator frequencies, or the presence of spectator modes that are not properly accounted for in the gate construction. In trapped ion systems, various schemes have been demonstrated that minimize this residual coupling 11-15 , with some also incorporating the ability to simultaneously decouple from multiple modes 16-21 . Their common feature is a temporal modulation of the driving field, modifying the trajectories of the joint qubit-oscillator states in each oscillator's phase space.In this work, we experimentally demonstrate a new class of phase-modulated (ΦM) entangling gates using trapped ions in the presence of multi-mode motional spectra. Specifically, we implement an MS-type interaca) These three authors contributed equally to this work. b) Current address: Fachrichtung Physik, Universität des Saarlandes, tion and employ discrete phase shifts of the driving field to suppress dominant gate errors. Using both an ana...

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.

Magnetic field topologies between the Sun and Earth are important for the connectivity to Earth of solar suprathermal particles, e.g., solar energetic particles and beam electrons in type III solar radio bursts. An approach is developed for mapping large‐scale magnetic field lines near the solar equatorial plane, using near‐Earth observations and a solar wind model with nonzero azimuthal magnetic field at the source surface. Unlike Parker's spiral model, which restricts the in‐ecliptic angle ΦB in the Geocentric Solar Ecliptic coordinates to (90°–180°, 270°–360°) and so is unable to predict field configurations for the other ΦB values frequently observed in the solar wind, our approach can account for all the observed ΦB values. A set of predicted maps shows that near both minimal and maximal solar activity the field lines are typically open and that loops with both ends either connected to or disconnected from the Sun are relatively rare. The open field lines, nonetheless, often do not closely follow the Parker spiral, being less or more tightly wound, or strongly azimuthally or radially oriented, or inverted. The time‐varying classes, e.g., bidirectional electrons, of suprathermal electron pitch angle distributions (PADs) at 1 AU are predicted from the mapped field line configurations and compared with Wind observations for two solar rotations, one each near solar minimum and solar maximum. PAD predictions by our approach agree quantitatively (≈90%) with the PAD observations and outperform (by ≈20%) PAD predictions using Parker's model.

Quantum harmonic oscillators are central to many modern quantum technologies. We introduce a method to determine the frequency noise spectrum of oscillator modes through coupling them to a qubit with continuously driven qubit-state-dependent displacements. We reconstruct the noise spectrum using a series of different drive phase and amplitude modulation patterns in conjunction with a data-fusion routine based on convex optimization. We apply the technique to the identification of intrinsic noise in the motional frequency of a single trapped ion with sensitivity to fluctuations at the sub-Hz level in a spectral range from quasi-dc up to 50 kHz.