A quantum-classical eigensolver using multiscale entanglement renormalization

Strongly-correlated quantum many-body systems are very hard to study and simulate classically. Based on the multi-scale entanglement renormalization ansatz (MERA) and gradient-based optimization, we propose a variational quantum eigensolver (VQE) for the simulation of strongly correlated quantum matter. Compared to corresponding classical algorithms with large tensor contraction costs, this MERA quantum eigensolver has significantly lower computation costs. This algorithm is capable of being implemented on NISQ devices while still describing very large systems because of its narrow causal cone. This feature is particularly attractive for ion-trap devices with ion-shuttling capabilities. As the size of the simulated system grows, the total number of qubits required grows logarithmically, but the number of qubits needed in the interaction region is system-size independent. Translation invariance of the simulated systems can be used to make computation costs square-logarithmic in the system size and describe the thermodynamic limit. We demonstrate the approach numerically for a MERA with Trotterized disentanglers and isometries. With a few Trotter steps, one recovers the accuracy of the full MERA.