Dense outputs from quantum simulations

• URL: http://arxiv.org/abs/2307.14441v2
• Date: Wed, 19 Jun 2024 22:54:34 GMT
• Title: Dense outputs from quantum simulations
• Authors: Jin-Peng Liu, Lin Lin,
• Abstract summary: The quantum dense output problem is the process of evaluating time-accumulated observables from time-dependent quantum dynamics. This problem arises frequently in applications such as quantum control and spectroscopic computation. We present a range of algorithms designed to operate on both early and fully fault-tolerant quantum platforms.
• Score: 5.295277584890625
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The quantum dense output problem is the process of evaluating time-accumulated observables from time-dependent quantum dynamics using quantum computers. This problem arises frequently in applications such as quantum control and spectroscopic computation. We present a range of algorithms designed to operate on both early and fully fault-tolerant quantum platforms. These methodologies draw upon techniques like amplitude estimation, Hamiltonian simulation, quantum linear Ordinary Differential Equation (ODE) solvers, and quantum Carleman linearization. We provide a comprehensive complexity analysis with respect to the evolution time $T$ and error tolerance $\epsilon$. Our results demonstrate that the linearization approach can nearly achieve optimal complexity $\mathcal{O}(T/\epsilon)$ for a certain type of low-rank dense outputs. Moreover, we provide a linearization of the dense output problem that yields an exact and finite-dimensional closure which encompasses the original states. This formulation is related to the Koopman Invariant Subspace theory and may be of independent interest in nonlinear control and scientific machine learning.

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