Diamond-shaped quantum circuit for real-time quantum dynamics in one dimension

Abstract: In recent years, quantum computing has evolved as an exciting frontier, with the development of numerous algorithms dedicated to constructing quantum circuits that adeptly represent quantum many-body states. However, this domain remains in its early stages and requires further refinement to understand better the effective construction of highly-entangled quantum states within quantum circuits. Here, we demonstrate that quantum many-body states can be universally represented using a quantum circuit comprising multi-qubit gates. Furthermore, we evaluate the efficiency of a quantum circuit constructed with two-qubit gates in quench dynamics for the transverse-field Ising model. In this specific model, despite the initial state being classical without entanglement, it undergoes long-time evolution, eventually leading to a highly-entangled quantum state. Our results reveal that a diamond-shaped quantum circuit, designed to approximate the multi-qubit gate-based quantum circuit, remarkably excels in accurately representing the long-time dynamics of the system. Moreover, the diamond-shaped circuit follows the volume law behavior in entanglement entropy, offering a significant advantage over alternative quantum circuit constructions employing two-qubit gates.