Quentin Oschatz

In the current era of noisy intermediate-scale quantum (NISQ) computing, the intersection of useful problems and computational tractability is narrow but no longer empty. Minor optimizations to quantum circuits can spell the difference between the possible and the impossible, especially with short coherence times starkly limiting the depth (i.e. number of successive gates) of feasible quantum circuits. Our collaborators at Cleveland Clinic are using quantum hardware to simulate large protein molecules, and scaling that approach requires more efficient circuits.

I am developing a similar approach to jointly optimize quantum circuits at multiple levels of abstraction, going end-to-end from the mathematical specification of the computation to highly optimized quantum circuit, all while remaining hardware-aware. Using SPIRAL's symbolic engine, which has support for complex roots of unity, algebraic extension fields, and transcendental functions, and a formalized specification, construction of aggressively optimized circuits can be automated. Machine-learning based reward models can also be trained to help guide the symbolic search for better circuits, which can encapsulate the highly non-linear relationships present in the problem without sacrificing the benefits and guarantees of symbolic reasoning.

Cerebus aims to verify the correctness of scientific code, especially when generated by LLMs. Here, mere syntactic correctness is insufficient, as scientific code can easily be plagued with hard-to-diagnose numerical errors despite compiling fine. Leveraging symbolic execution and semantic lifting, we can construct chains-of-reasoning that verify the numerical properties and error bounds of an implementation compared to the mathematical specifications.

This DARPA project aims to improve the basic scaling factor behind the processing of certain radar data, specifically when performing beamforming. Here, the clasical O(n³) Minimum Variance Distortionless Response (MVDR) beamforming algorithm is to be improved, ideally to yield a O(n log n) algorithm.

I helped develop and test several ML-based approaches, specifically CNNs acting on complex numbers. Additionally, I built a large part of the radar infrastructure, and helped implement a novel solver algorithm that took advantage of the data structure to reduce the scaling factor to O(n log n).