Quantum-classical eigensolver using multiscale entanglement renormalization

Abstract

We propose a variational quantum eigensolver (VQE) for the simulation of strongly-correlated quantum matter based on a multi-scale entanglement renormalization ansatz (MERA) and gradient-based optimization. This MERA quantum eigensolver can have substantially lower computation costs than corresponding classical algorithms. Due to its narrow causal cone, the algorithm can be implemented on noisy intermediate-scale quantum (NISQ) devices and still describe large systems. It is particularly attractive for ion-trap devices with ion-shuttling capabilities. 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. 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.

14 pages, 9 figures; additional discussions of the computational complexity, layer-transition maps for homogeneous MERA, mid-circuit qubit resets, and data on the quantum advantage; further minor improvements; published version

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• Machine learning with tree tensor networks, CP rank constraints, and tensor dropout
• Equivalence of cost concentration and gradient vanishing for quantum circuits: An elementary proof in the Riemannian formulation
• 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
• Double-bracket quantum algorithms for quantum imaginary-time evolution
• Efficient preparation of the AKLT State with Measurement-based Imaginary Time Evolution
• Scaling of contraction costs for entanglement renormalization algorithms including tensor Trotterization and variational Monte Carlo
• A quantum eigenvalue solver based on tensor networks