  Scalability of today's superconducting quantum computers is limited due to
the huge costs of generating/routing microwave control pulses per qubit from
room temperature. One active research area in both industry and academia is to
push the classical controllers to the dilution refrigerator in order to
increase the scalability of quantum computers. Superconducting Single Flux
Quantum (SFQ) is a classical logic technology with low power consumption and
ultra-high speed, and thus is a promising candidate for in-fridge classical
controllers with maximized scalability. Prior work has demonstrated
high-fidelity SFQ-based single-qubit gates. However, little research has been
done on SFQ-based multi-qubit gates, which are necessary to realize SFQ-based
universal quantum computing.
  In this paper, we present the first thorough analysis of SFQ-based two-qubit
gates. Our observations show that SFQ-based two-qubit gates tend to have high
leakage to qubit non-computational subspace, which presents severe design
challenges. We show that despite these challenges, we can realize gates with
high fidelity by carefully designing optimal control methods and qubit
architectures. We develop optimal control methods that suppress leakage, and
also investigate various qubit architectures that reduce the leakage. After
carefully engineering our SFQ-friendly quantum system, we show that it can
achieve similar gate fidelity and gate time to microwave-based quantum systems.
The promising results of this paper show that (1) SFQ-based universal quantum
computation is both feasible and effective; and (2) SFQ is a promising approach
in designing classical controller for quantum machines because it can increase
the scalability while preserving gate fidelity and performance.
