  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.
