  Quantum information science harnesses the principles of quantum mechanics to
realize computational algorithms with complexities vastly intractable by
current computer platforms. Typical applications range from quantum chemistry
to optimization problems and also include simulations for high energy physics.
The recent maturing of quantum hardware has triggered preliminary explorations
by several institutions (including Fermilab) of quantum hardware capable of
demonstrating quantum advantage in multiple domains, from quantum computing to
communications, to sensing. The Superconducting Quantum Materials and Systems
(SQMS) Center, led by Fermilab, is dedicated to providing breakthroughs in
quantum computing and sensing, mediating quantum engineering and HEP based
material science. The main goal of the Center is to deploy quantum systems with
superior performance tailored to the algorithms used in high energy physics. In
this Snowmass paper, we discuss the two most promising superconducting quantum
architectures for HEP algorithms, i.e. three-level systems (qutrits) supported
by transmon devices coupled to planar devices and multi-level systems (qudits
with arbitrary N energy levels) supported by superconducting 3D cavities. For
each architecture, we demonstrate exemplary HEP algorithms and identify the
current challenges, ongoing work and future opportunities. Furthermore, we
discuss the prospects and complexities of interconnecting the different
architectures and individual computational nodes. Finally, we review several
different strategies of error protection and correction and discuss their
potential to improve the performance of the two architectures. This whitepaper
seeks to reach out to the HEP community and drive progress in both HEP research
and QIS hardware.
