2024/10/08 by Claudio Sanavio, Sanavio, Claudio, Enea Mauri +3 · 4 citations
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Quantum and electron transport phenomena #Spectroscopy and Quantum Chemical Studies
paper · pdf · doi:10.48550/arxiv.2410.05876
openalex publication_date 2024/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We assess the convergence of the Carleman linearization of advection-diffusion-reaction (ADR) equations with a logistic nonlinearity. It is shown that five Carleman iterates provide a satisfactory approximation of the original ADR across a broad range of parameters and strength of nonlinearity. To assess the feasibility of a quantum algorithm based on this linearization, we analyze the projection of the Carleman ADR matrix onto the tensor Pauli basis. It is found that the Carleman ADR matrix requires an exponential number of Pauli gates as a function of the number of qubits. This prevents the practical implementation of the Carleman approach to the quantum simulation of ADR problems on current hardware. We propose to address this limitation by resorting to block-encoding techniques for sparse matrix employing oracles. Such quantum ADR oracles are presented in explicit form and shown to turn the exponential complexity into a polynomial one. However, due to the low probability of successfully implementing the nonunitary Carleman operator, further research is needed to implement the multi-timestep version of the present circuit.