Adiabatic Optimization of Tensor Networks

Mike Espig, Wolfgang Hackbusch, Stefan Handschuh +1 more

Hyeongjin Kim, Matthew Fishman, Dries Sels

We discuss a tensor network method for constructing the adiabatic gauge potential—the generator of adiabatic transformations—as a matrix product operator, which allows us to adiabatically transport matrix product states. Adiabatic evolution of tensor networks offers a wide range of applications, of which two are explored in this paper: improving tensor network optimization and scanning phase diagrams. By efficiently transporting eigenstates to quantum criticality and performing intermediary density-matrix renormalization group (DMRG) optimizations along the way, we demonstrate that we can compute ground and low-lying excited states faster and more reliably than a standard DMRG method at or near quantum criticality. We demonstrate a simple automated step size adjustment and detection of the critical point based on the norm of the adiabatic gauge potential. Remarkably, we are able to reliably transport states through the critical point of the models we study. Published by the American Physical Society 2024

Samuel Desrosiers, Glen Evenbly, Thomas E. Baker

Kshiti Sneh Rai, Jin-Fu Chen, Patrick Emonts +1 more

The preparation of nontrivial states is crucial to the study of quantum many-body physics. Such states can be prepared with adiabatic quantum algorithms, which are restricted by the minimum spectral gap along the path. In this Letter, we propose an efficient method to adiabatically prepare tensor network states (TNSs). We maximize the spectral gap leveraging degrees of freedom in the parent Hamiltonian construction. We demonstrate this efficient adiabatic algorithm for preparing TNSs, through examples of random TNSs in one dimension, AKLT (Affleck-Kennedy-Lieb-Tasaki), and GHZ states. The Hamiltonian optimization applies to both injective and non-injective tensors, in the latter case by exploiting symmetries present in the tensors.

Guglielmo Lami, Pietro Torta, Giuseppe E. Santoro +1 more

Here, we focus on the problem of minimizing complex classical cost functions associated with prototypical discrete neural networks, specifically the paradigmatic Hopfield model and binary perceptron. We show that the adiabatic time evolution of QA can be efficiently represented as a suitable Tensor Network. This representation allows for simple classical simulations, well-beyond small sizes amenable to exact diagonalization techniques. We show that the optimized state, expressed as a Matrix Product State (MPS), can be recast into a Quantum Circuit, whose depth scales only linearly with the system size and quadratically with the MPS bond dimension. This may represent a valuable starting point allowing for further circuit optimization on near-term quantum devices.

Aaron C. Hoyt, Jonathan S. Bersson, Sean Garner +2 more

Large-scale tensor network simulations are crucial for developing robust complexity-theoretic bounds on classical quantum simulation, enabling circuit cutting approaches, and optimizing circuit compilation, all of which aid efficient quantum computation on limited quantum resources. Modern exascale high-performance computing platforms offer significant potential for advancing tensor network quantum circuit simulation capabilities. We implement TN-Sim, a tensor network simulator backend within the NWQ-Sim software package that utilizes the Tensor Algebra for Many-body Methods (TAMM) framework to support both distributed HPC-scale computations and local simulations with ITensor. To optimize the scale up in computation across multiple nodes we implement a task based parallelization scheme to demonstrate parallelized gate contraction for wide quantum circuits with many gates per layer. Through the integration of the TAMM framework with Matrix Product State (MPS) tensor network approaches, we deliver a simulation environment that can scale from local systems to HPC clusters. We demonstrate an MPS tensor network simulator running on the state-of-the-art Perlmutter (NVIDIA) supercomputer and discuss the potential portability of this software to HPC clusters such as Frontier (AMD) and Aurora (Intel). We also discuss future improvements including support for different tensor network topologies and enhanced computational efficiency.