Probing critical states of matter on a digital quantum computer

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.

8 pages, 6 figures

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Cited by in corpus (8)

• Tensor networks for quantum computing
• Absence of barren plateaus and scaling of gradients in the energy optimization of isometric tensor network states
• Convergence and Quantum Advantage of Trotterized MERA for Strongly-Correlated Systems
• Tomonaga-Luttinger Liquid Behavior in a Rydberg-encoded Spin Chain
• Exploring nontrivial topology at quantum criticality in a superconducting processor
• Scaling of contraction costs for entanglement renormalization algorithms including tensor Trotterization and variational Monte Carlo
• Fractal decompositions and tensor network representations of Bethe wavefunctions
• Revealing emergent many-body phenomena by analyzing large-scale space-time records of monitored quantum systems