# Duke Physics Colloquium - Quantum Simulation of Condensed Matter Using Trotterized Entanglement Renormalization

Emergent phenomena in strongly-correlated quantum materials have tremendous potential for technological advancements. Significant challenges are, for example, the understanding and design of high-temperature superconductors and systems with topological order. Strong correlations render mean-field and perturbative approaches inapplicable, and, for some of the most interesting systems, quantum Monte Carlo is hampered by the notorious sign problem. However, the investigation of entanglement properties shows that typical many-body systems in equilibrium and after local perturbations do not explore the entirety of the exponentially big Hilbert space. This led us to techniques that approximate strongly correlated states by networks of tensors - so-called tensor network states. We apply them in studies of condensed matter physics to investigate quantum phase transitions, dynamic response, equilibration and thermalization, quantum transport, as well as decoherence phenomena and nonequilibrium transitions in driven-dissipative systems.

While computation costs of tensor network methods scale polynomially instead of exponentially in the system size, classical computation has its limits and it is still difficult to assess certain phenomena in 2d and 3d systems with sufficient accuracy. I will discuss our recent efforts to investigate quantum materials using quantum computers. A hybrid quantum-classical solver based on a multi-scale entanglement renormalization ansatz (MERA) allows us to study condensed matter groundstate problems. Due to causal-cone structures of the MERA tensor network, one can simulate large systems on noisy intermediate-scale quantum (NISQ) devices. 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. Our benchmark simulations have established a quantum advantage for this approach. I will report on first experimental implementations, demonstrating a quantum phase transition on ion-trap devices of the Duke Quantum Center, and shortly comment on the question of barren plateaus.