Omer Gurevich

Omer Gurevich, Tal Mor, Ido Ram

Catalytic carbon fixation to formic acid is important for studying the reduction of carbon footprint and the emergence of life. Can discrete quantum exhaustive search merged with other methods help reduce the carbon footprint? We suggest merging quantum, quantum inspired, and classical tools for a better simulation of various relevant processes. Quantum tools are often used for analyzing the electronic structure of molecules, sometimes because this problem is not scalable (in the number of orbitals) on classical computers while it is potentially approximately scalable on (future) quantum computers. It is potentially even solvable in the near future using variational quantum eigensolvers (VQE) yet a major obstacle to such analysis is the appearance of barren plateaus in the Hilbert space describing the problem. Here we make use of the basic (standard) tools while also including a novel one -- the discrete quantum exhaustive search, which relies on mutually unbiased bases, for analyzing the simplest non-catalytic process involving carbon dioxide, hydrogen and formic acid.

Omer Gurevich, Maor Matityahu, Tal Mor

Ising formulation is important for many NP problems (Lucas, 2014). This formulation enables implementing novel quantum computing methods including Quantum Approximate Optimization Algorithm and Variational Quantum Eigensolver (VQE). Here, we investigate closely the traveling salesman problem (TSP). First, we present some non-trivial issues related to Ising model view versus a realistic salesman. Then, focusing on VQE we discuss and clarify the use of: a.-- Conventional VQE and how it is relevant as a novel SAT-solver; b.-- Qubit efficiency and its importance in the Noisy Intermediate Scale Quantum-era; and c.-- the relevance and importance of a novel approach named Discrete Quantum Exhaustive Search (Alfassi, Meirom, and Mor, 2024), for enhancing VQE and other methods using mutually unbiased bases. The approach we present here in details can potentially be extended for analyzing approximating and solving various other NP complete problems. Our approach can also be extended beyond the Ising model and beyond the class NP, for example to the class Quantum Merlin Arthur (QMA) of problems, relevant for quantum chemistry and for general spin problems.