Search for quantum advantage in condensed matter physics

Abstract

In the era of the rapid development of quantum devices, the next milestone to be achieved is to surpass the performance of classical computers with quantum computers in practical problems, that is, to achieve the quantum advantage. In this paper, we introduce recent studies that argue that the main field for this purpose is envisioned to be condensed matter physics. The main contributions of this paper are summarized in three points: (1) the proposal of a method for analyzing the execution time of classical computation algorithms based on the tensor network method, (2) the evaluation of the execution time of fault-tolerant quantum computation algorithms at the instruction level, and (3) the discovery of a quantum advantage region in two-dimensional strongly correlated quantum many-body systems. The lattice model discussed in this paper is expected to play a guiding role in the research and development of fault-tolerant quantum computers, as it requires fewer resources in terms of the number of qubits and execution time than other known platforms for the quantum advantage.