Approximate Quantum Compiling for Quantum Simulation: A Tensor Network based approach

Abstract

The simulation of quantum spin chains is a promising candidate for the demonstration of quantum advantage. One of the main obstacles to achieving this is the noise that arises from implementing the deep circuits that appear in standard quantum time evolution algorithms. Compiling these deep circuits into shallower ones is thus a key issue that we address in this work. We use a Tensor Network based approach to Approximate Quantum Compiling to produce short depth quantum circuits that simulate the time evolution of the Heisenberg spin chain on up to 100 qubits. Furthermore, we run these short depth circuits on a ibmq-mumbai -a 27 qubit device -and show that the accuracy of the measured observables is significantly improved after applying our Tensor Network compilation scheme.