Hybrid Continuous-Discrete-Variable Quantum Signal Processing: Algorithms and Applications

Quantum computing with discrete variable (DV, qubit) hardware is approaching the large scales necessary for computations beyond the reach of classical computers. Separately, hardware containing native continuous-variable (CV, oscillator) systems has received attention as an alternative approach, yet the universal control of such systems is non-trivial. In this talk, I will highlight novel quantum algorithms, control protocols, and applications developed for hybrid CV-DV quantum systems, which offer powerful new computational paradigms that inherit the strengths of both DV and CV quantum processors. I will start by a pedagogical introduction to CV-DV systems and instruct sets for universal programmability. I will then present a variety of new hybrid CV-DV compilation techniques and algorithms, including the extension of quantum signal processing to CV-DV systems. This is followed by several applications including state transfer, quantum sensing, and simulation of interacting spins and bosons. To facilitate the development of hybrid CV-DV processor systems, I will also introduce formal Abstract Machine Models and Instruction Set Architectures — essential abstractions that enable developers to formulate applications, compile algorithms, and explore the potential of current and future hardware for realizing fault-tolerant circuits, modules, and processors. I will conclude the talk with open questions and future opportunities of hybrid CV-DV quantum computation in broader areas of science and engineering.