Using the MERA tensor network ansatz on Honeywell's QCCD chips

One of the main applications for quantum computers will be the simulation of other strongly correlated quantum many-body systems. Tensor networks ansatz states are well established for simulations of such systems on classical hardware, where they drastically reduce the computational cost. Here, we show one example where a tensor network helps to reduce the required number of qubits on quantum hardware. The multiscale entanglement renormalization ansatz (MERA) is a tensor network specifically designed to accurately capture the long-range correlations in the ground states of critical spin chains. The ability of Honeywell's quantum charge coupled devices (QCCD) to measure and reset a qubit mid-circuit, in combination with the MERA ansatz, allows to obtain expectation values of an $N$ site spin chain with only $O(log(N))$ qubits, at the price of a larger depth of the circuit. We demonstrate the measurement of long-range correlation functions on the quantum hardware. Further, we discuss the tradeoff how a larger depth of the MERA network leads to a more accurate wave function representation, but also more statistical noise due to the larger circuit depth.