Optimizing two-dimensional isometric tensor networks with quantum computers

TL;DR

This paper introduces a hybrid quantum-classical algorithm for efficiently approximating ground states of 2D quantum systems using isometric tensor networks, leveraging quantum computers to overcome classical contraction limitations.

Contribution

It presents a novel method combining tensor network optimization with quantum computing, enabling scalable ground state approximations for 2D systems without exponential classical complexity.

Findings

Successfully optimized 2D transverse-field Ising model on up to 25 qubits

Achieved accurate ground states with modest quantum resources

Outperformed standard variational quantum eigensolvers in efficiency

Abstract

We propose a hybrid quantum-classical algorithm for approximating the ground state of two-dimensional quantum systems using an isometric tensor network ansatz, which maps naturally to quantum circuits. Inspired by the density matrix renormalization group, we optimize tensors sequentially by diagonalizing a series of effective Hamiltonians. These are constructed using a tomography-inspired method on a qubit subset whose size depends only on the bond dimension. Our approach leverages quantum computers to enable accurate solutions without relying on approximate contractions, circumventing the exponential complexity faced by classical techniques. We demonstrate our method on the two-dimensional (2D) transverse-field Ising model, achieving ground-state optimization on up to 25 qubits with modest quantum overhead -- significantly less than standard solutions based on variational quantum eigensolvers. Overall, our results offer a path towards scalable variational quantum algorithms in both noisy and fault-tolerant regimes.