Convergence and Quantum Advantage of Trotterized MERA for Strongly-Correlated Systems

Understand

Strongly-correlated quantum many-body systems are difficult to study and simulate classically.

• We recently proposed a variational quantum eigensolver (VQE) based on the multiscale entanglement renormalization ansatz (MERA) with tensors constrained to certain Trotter circuits.
• Here, we determine the scaling of computation costs for various critical spin chains which substantiates a polynomial quantum advantage in comparison to classical MERA simulations based on exact energy gradients or variational Monte Carlo.
• Algorithmic phase diagrams suggest an even greater separation for higher-dimensional systems.