We describe an approach to the integrated control and measurement of a large-scale superconducting multiqubit circuit using a proximal coprocessor based on the Single Flux Quantum (SFQ) digital logic family. Coherent control is realized by irradiating the qubits directly with classical bitstreams derived from optimal control theory. Qubit measurement is performed by a Josephson photon counter, which provides access to the classical result of projective quantum measurement at the millikelvin stage. We analyze the power budget and physical footprint of the SFQ coprocessor and discuss challenges and opportunities associated with this approach.

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.

Single flux quantum pulses are a natural candidate for on-chip control of superconducting qubits. We show that they can drive high-fidelity single-qubit rotations---even in leaky transmon qubits---if the pulse sequence is suitably optimized. We achieve this objective by showing that, for these restricted all-digital pulses, genetic algorithms can be made to converge to arbitrarily low error, verified up to a reduction in gate error by 2 orders of magnitude compared to an evenly spaced pulse train. Timing jitter of the pulses is taken into account, exploring the robustness of our optimized sequence. This approach takes us one step further towards on-chip qubit controls.Comment: 4 pages, 6 figure

The cross-resonance (CR) gate is an entangling gate for fixed frequency superconducting qubits. While being simple and extensible, it is comparatively slow, at 160 ns and thus of limited fidelity due to on-going incoherent processes. Using two different optimal control algorithms, we estimate the quantum speed limit for a controlled-NOT (CNOT) gate in this system to be 10 ns, indicating a potential for great improvements. We show that the ability to approach this limit depends strongly on the choice of ansatz used to describe optimized control pulses and limitations placed on their complexity. Using a piecewise-constant ansatz, with a single carrier and bandwidth constraints, we identify an experimentally feasible 70-ns pulse shape. Further, an ansatz based on the two dominant frequencies involved in the optimal control problem allows for an optimal solution more than twice as fast again, at under 30 ns, with smooth features and limited complexity. This is twice as fast as gate realizations using tunable-frequency, resonantly coupled qubits. Compared to current CR-gate implementations, we project our scheme will provide a sixfold speed-up and thus a sixfold reduction in fidelity loss due to incoherent effects.

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