Holographic Quantum Simulation of Entanglement Renormalization Circuits

While standard approaches to quantum simulation require a number of qubits proportional to the number of simulated particles, current noisy quantum computers are limited to tens of qubits. With the technique of holographic quantum simulation, a D-dimensional system can be simulated with a (D - 1)-dimensional subset of qubits, enabling the study of systems significantly larger than current quantum computers. Using circuits derived from the multiscale entanglement renormalization ansatz (MERA), we accurately prepare the ground state of an L = 32 critical, nonintegrable perturbed Ising model and measure long-range correlations on the ten-qubit Quantinuum trapped-ion computer. We introduce generalized MERA networks that interpolate between MERA and matrix product state networks and demonstrate that generalized MERA can capture far longer correlations than a MERA with the same number of qubits, at the expense of greater circuit depth. Finally, we perform noisy simulations of these two network ansatzes and find that the optimal choice of network depends on the noise level, available qubits, and the state to be represented.

Automated summary

Traditional approaches to quantum simulation are limited by the number of qubits needed, but holographic quantum simulation allows for the simulation of larger systems using a subset of qubits. We utilized the multiscale entanglement renormalization ansatz (MERA) and the Quantinuum trapped-ion computer to accurately prepare the ground state and measure correlations of a perturbed Ising model. Generalized MERA networks were introduced to capture longer correlations than traditional MERA networks.