Abstract
With quantum computers still in their infancy, simulating quantum manybody systems numerically on ordinary classical computers remains an important task in both physics and chemistry. This is a difficult problem in general since quantum states are described by tensors that scale exponentially with system size. Fortunately, some physically relevant states of one and twodimensional systems can be efficiently simulated using tensor network methods. The prototypical example being White's density matrix renormalisation group (DMRG) algorithm, which is based on a tensor decomposition called the tensor train or matrix product state.One way to improve the performance of classical simulations is to take advantage of modern supercomputers. However, this requires the use of efficient parallel algorithms, while most tensor network methods are inherently serial. In this thesis, I argue that the DMRG parallelisation scheme proposed by Stoudenmire and White in 2013 provides a unified framework for parallel matrix product state algorithms. To demonstrate this, I start by parallelising White and Feiguin's timedependent DMRG algorithm. I find strong scaling up to 512 processes with a parallel efficiency greater than 70% and show that the algorithm can be used to study manybody localisation in a onedimensional lattice comprising more than 50,000 spins (qubits). I then use the same framework to implement a parallel variant of the timedependent variational principle algorithm, thus introducing the first parallel tensor network method capable of time evolving systems with longrange interactions.
Alongside these algorithmic developments, I explore the benefits of tensornetwork parallelisation in two experimentally motivated case studies. In the first, I verify the results of a groundbreaking analogue dynamical quantum simulator in a matter of days rather than weeks. In the second, I use parallel DMRG to map out a zerotemperature phase diagram of the numericallychallenging spin1 extended BoseHubbard model.
Date of Award  26 Jun 2024 

Original language  English 
Awarding Institution 

Supervisor  Sergey Dolgov (Supervisor), Stephen Clark (Supervisor) & Richard James (Supervisor) 
Keywords
 quantum
 physics
 tensor train
 tensor network
 matrix product state
 lattice
 spin
 boson
 parallel
 decomposition
 lowrank
 approximation
 parallelisation
 BoseHubbard model
 Heisenberg model
 model
 nonlocal
 longrange
 Hamiltonian
 matrix product operator
 time evolution
 dynamics
 relaxation
 simulation
 equilibration
 TEBD
 TDVP
 DMRG
 TDMRG
 pDMRG
 pTEBD
 pTDMRG
 pTDVP
 MPI
 OpenMP
 MPS
 MPO
 TT
 timeevolving
 renormalisation
 ALS
 chemistry
 numerical methods
 numerical simulations
 tensor
 manybody
 localisation
 correlation
 strongly correlated
 spin chain
 Ising model
 computational methods
 computational simulation