I will describe a variational quantum eigensolver for the simulation of strongly-correlated quantum matter based on a multi-scale entanglement renormalization ansatz (MERA) and gradient-based optimization. Due to its narrow causal cone, the algorithm can be implemented on noisy intermediate-scale (NISQ) devices and still describe large systems. The number of required qubits is system-size independent and increases only to a logarithmic scaling when using quantum amplitude estimation to speed up gradient evaluations. Translation invariance can be used to make computation costs square-logarithmic in the system size and describe the thermodynamic limit. For the practical implementation, the MERA disentanglers and isometries are Trotterized, i.e., implemented as brickwall circuits. With a few Trotter steps, one recovers the accuracy of the full MERA. Results of benchmark simulations for various critical spin models establish a quantum advantage, and I will report on first experimental tests on ion-trap devices. For systems with finite-range interactions, one can also show that, in contrast to quantum neural networks, the variational energy optimization of isometric tensor networks like MERA is free of barren plateaus.
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