Based on superconducting lines, CAS team successfully simulates critical quantum phase transition

Quantum simulation provides an effective way to study many-body physics, promising to solve many-body problems that may be difficult for classical computers to handle. The simulation and measurement of a large class of Hamiltonian quantities can be achieved by manipulating artificially controllable quantum systems, such as superconducting quantum bits. And the Aubry-André-Harper (AAH) model, as a theoretical basis for the study of localization and topological states, has attracted wide interest at the experimental and theoretical levels in recent years. A class of extended AAH (GAAH) models evolved from the AAH model, whose Hamiltonian contains both on-site and off-diagonal quasi-periodic modulations, is analytically shown to contain three phases with different topological and localization properties: extended phase, localized phase and critical phase. Since the simulation of their Hamiltonian quantities requires both diagonal and off-diagonal quasi-periodic modulations, superconducting quantum bit devices with direct coupling between bits are difficult to realize such modulations; moreover, the GAAH model, although realized in the synthetic dimension of momentum space in cold atomic systems, only observes the dynamical behavior at the single-particle (mean-field) level.

Recently, Hao Li, a joint Ph.D. student from Northwestern University, and Yongyi Wang, a Ph.D. student from Q03 group of Institute of Physics, Chinese Academy of Sciences/Beijing National Research Center for Condensed Matter Physics, under the guidance of Research Fellow Jiao Fan and Associate Research Fellow Kai Xu, have collaborated with Research Fellow Dongning Zheng and Deputy Chief Engineer Loyal Xiang from SC5 group, Associate Research Fellow Xiaohui Song from Q02 group, and Research Fellow Shu Chen from T01 group to achieve the first GAAH model on a tunable coupled superconducting quantum The first simulation and tuning of GAAH Hamiltonian quantities on a chip was achieved, and the different kinetic properties of the three phases and the phase transitions between them were observed at the multi-particle dynamics level, and the results have been published in npj Quantum Information 9, 40 (2023).

The experiment was done in a superconducting quantum chip with a one-dimensional array of 10 quantum bits and 9 couplers (couplers). By precisely controlling the frequencies of the quantum bits and couplers, quasi-periodic modulation of the bit frequencies and the intensity of the near-neighbor jumps was achieved to realize the Hamiltonian quantities of the GAAH model, changing the parameters to drive the system in three different phases: extended phase, local phase, and critical phase. quantum phases. The spin transport behaviors of different phases in single and multi-excitation states are observed experimentally, and the multi-excitation kinetic participation entropy is measured using the multi-bit simultaneous readout capability of the superconducting device to demonstrate the multi-particle fractal wave function properties in different phases and to characterize the transitions between the three phases, thus enabling the simulation of the critical phase transition. The tunable coupling structure of the superconducting quantum processor greatly extends the simulation range of the superconducting quantum processor to realize many types of Hamiltonian quantities, thus opening the way to study different quantum and topological phenomena.

This work was recently published under the title "Observation of critical phase transitions based on superconducting lines in the extended AAH model", and is also authored by researcher Shiping Zhao and associate researcher Tian Ye in the Q03 group, as well as by Professor Zhanying Yang, a PhD student and postdoctoral fellow at Northwestern University. This work was supported by the National Natural Science Foundation of China, the Ministry of Science and Technology, the Beijing Natural Science Foundation, and the CAS Pioneer Project.