Quantum computing is in an era of limited resources. Current hardware lacks high fidelity gates, long coherence times, and the number of computational units required to perform meaningful computation. Contemporary quantum devices typically use a binary system, where each qubit exists in a superposition of the $\ket{0}$ and $\ket{1}$ states. However, it is often possible to access the $\ket{2}$ or even $\ket{3}$ states in the same physical unit by manipulating the system in different ways. In this work, we consider automatically encoding two qubits into one four-state qu\emph{quart} via a \emph{compression scheme}. We use quantum optimal control to design efficient proof-of-concept gates that fully replicate standard qubit computation on these encoded qubits. We extend qubit compilation schemes to efficiently route qubits on an arbitrary mixed-radix system consisting of both qubits and ququarts, reducing communication and minimizing excess circuit execution time introduced by longer-duration ququart gates. In conjunction with these compilation strategies, we introduce several methods to find beneficial compressions, reducing circuit error due to computation and communication by up to 50\%. These methods can increase the computational space available on a limited near-term machine by up to 2x while maintaining circuit fidelity.

翻译：量子计算正处于资源受限时代。当前硬件缺乏高保真门、长相干时间以及执行有意义计算所需数量的计算单元。现代量子设备通常使用二进制系统，其中每个量子比特存在于$\ket{0}$和$\ket{1}$态的叠加中。然而，通过不同方式操控系统，通常可以在同一物理单元中访问$\ket{2}$甚至$\ket{3}$态。在本工作中，我们考虑通过一种\emph{压缩方案}将两个量子比特自动编码为一个四态量子比特（qu\emph{quart}）。我们利用量子最优控制设计高效的概念验证门，以完全复制这些编码量子比特上的标准量子比特计算。我们将量子比特编译方案扩展到任意混合基数系统（同时包含量子比特和四态量子比特），实现高效路由，从而减少通信开销，并最小化由长持续时间的四态量子比特门引入的额外电路执行时间。结合这些编译策略，我们提出若干方法寻找有益压缩方案，将计算与通信导致的电路误差降低最多50%。这些方法可在保持电路保真度的同时，将受限近中期设备上的可用计算空间提升至2倍。