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Quantum Information Processing

An efficient quantum algorithm for simulating polynomial dynamical systems

Amit Surana, Abeynaya Gnanasekaran, Tuhin Sahai

Published Mar 13, 2024• 6 citations
Publisher
DOI
10.1007/s11128-024-04311-2

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An efficient numerical method is developed using the matrix product formalism for computing the properties at finite energy densities in one-dimensional (1D) many-body localized (MBL) systems. Arguing that any efficient (possibly quantum) algorithm can only have a polynomially small energy resolution, we propose a (rigorous) polynomial-time (classical) algorithm that outputs a diagonal density operator supported on a microcanonical ensemble of an inverse polynomial bandwidth. The proof uses no other conditions for MBL but assumes that the effect of any local perturbation (e.g., injecting conserved charges) is restricted to a region whose radius grows logarithmically with time. A non-optimal version of this algorithm efficiently simulates the quantum phase estimation algorithm in 1D MBL systems; a heuristic version of the algorithm can be easily coded and used to, e.g., detect energy-tuned dynamical quantum phase transitions between MBL phases. We extend the algorithm to two and higher spatial dimensions using the projected entangled pair formalism.
Multi-component quantum systems that interact strongly with their environments are difficult to simulate numerically. This challenge is approached by introducing the numerically exact Time Evolving Density Matrix with Orthogonal Polynomial Algorithm (TEDOPA). The application of this algorithm allows for the efficient simulation of open quantum system dynamics, including spin-boson models and generalizations of it to multi-component systems. In this thesis, TEDOPA is introduced and applied to pigment-protein complexes that play a key role in the photosynthetic process and that have been studied extensively in the last years. Further methodical and numerical improvements of TEDOPA are developed, resulting in major speed-ups for certain parameter regimes.