Tensor Network States for Vibrational Spectroscopy

First-Principles Calculations of Excited-State Decay Rate Constants in Organic Fluorophores

“…83 More recently, Reiher's group has proposed the vibrational DMRG method 84 at a lower computational cost that was also extended to treat strongly anharmonic cases. 85 3.4. Specific Rates.…”

Flexible DMRG-Based Framework for Anharmonic Vibrational Calculations

“…On-the-fly PES construction and the corresponding VSCF calculation were implemented and performed in the Colibri program . Currently, our framework supports n -mode expansions, including up to third-order mode couplings.…”

“…Taylor series expansions are the prevalent functional format to efficiently approximate many-body potential energy surfaces since they have the innate benefit to be automatically encoded in a sum-over-products form, which is a convenient parametrization for various vibrational structure approaches. This is also the case for vDMRG, as the Taylor expansion naturally provides a second-quantization framework in which to express the vibrational Hamiltonian in matrix product operator (MPO) form . The resulting so-called canonical quantization spans the Hilbert space generated by the harmonic oscillator eigenfunction basis.…”

Synthesis of Hidden Subgroup Quantum Algorithms and Quantum Chemical Dynamics

“…To alleviate this rather catastrophic situation, tensor networks (TNs) , have recently become popular. Tensor networks have roots in the tensor decomposition field of multilinear algebra, , are a general framework for data compression, − and have proven to be effective for efficient representation of many-body quantum states in strongly correlated systems. ,− While a tensor network treatment adaptively truncates the Hilbert space based on the intrinsic entanglement within the problem, given the advent of novel quantum computing algorithms, tensor networks have also proved to be a natural resource for developing new quantum algorithms. − The approach has been shown to have applications for low-energy states of local, gapped Hamiltonians, which are characterized by satisfying a so-called area law of entanglement. ,, The introduction of the density matrix renormalization group (DMRG) − was perhaps the catalyst for the excitement in the TN methodology, proving to be very useful for the simulation of one-dimensional quantum lattices, − electronic structure calculations, − approximations to vibrational states, − open-quantum systems ,, and image processing, − , and even machine learning applications. − …”