Probing critical states of matter on a digital quantum computer

TL;DR

This paper demonstrates the use of a quantum computer to simulate and analyze critical quantum states in a many-body system, overcoming classical simulation limitations through hierarchical tensor-network techniques.

Contribution

It introduces a method to encode and analyze quantum critical states on a quantum computer using tensor networks, enabling the study of larger systems than classical methods.

Findings

Successfully created a 128-site ground state of the transverse-field Ising model

Extracted critical properties with high fidelity

Showed potential for quantum-assisted tensor network contraction

Abstract

Although quantum mechanics underpins the microscopic behavior of all materials, its effects are often obscured at the macroscopic level by thermal fluctuations. A notable exception is a zero-temperature phase transition, where scaling laws emerge entirely due to quantum correlations over a diverging length scale. The accurate description of such transitions is challenging for classical simulation methods of quantum systems, and is a natural application space for quantum simulation. These quantum simulations are, however, not without their own challenges \textemdash~representing quantum critical states on a quantum computer requires encoding entanglement of a large number of degrees of freedom, placing strict demands on the coherence and fidelity of the computer's operations. Using Quantinuum's H1-1 quantum computer, we address these challenges by employing hierarchical quantum tensor-network techniques, creating the ground state of the critical transverse-field Ising chain on 128-sites with sufficient fidelity to extract accurate critical properties of the model. Our results suggest a viable path to quantum-assisted tensor network contraction beyond the limits of classical methods.