Demonstration of a parity-time symmetry breaking phase transition using superconducting and trapped-ion qutrits

Scalable quantum computers hold the promise to solve hard computational problems, such as prime factorization, combinatorial optimization, simulation of many-body physics, and quantum chemistry. While being key to understanding many real-world phenomena, simulation of non-conservative quantum dynamics presents a challenge for unitary quantum computation. In this work, we focus on simulating non-unitary parity-time symmetric systems, which exhibit a distinctive symmetry-breaking phase transition as well as other unique features that have no counterpart in closed systems. We show that a qutrit, a three-level quantum system, is capable of realizing this non-equilibrium phase transition. By using two physical platforms - an array of trapped ions and a superconducting transmon - and by controlling their three energy levels in a digital manner, we experimentally simulate the parity-time symmetry-breaking phase transition. Our results indicate the potential advantage of multi-level (qudit) processors in simulating physical effects, where additional accessible levels can play the role of a controlled environment.Comment: 14 pages, 9 figure

Continuous dynamical decoupling of optical 171^{171}Yb+^{+} qudits with radiofrequency fields

The use of multilevel quantum information carriers, also known as qudits, attracts a significant deal of interest as a way for further scalability of quantum computing devices. However, a nontrivial task is to experimentally achieve a gain in the efficiency of realizing quantum algorithms with qudits since higher qudit levels typically have relatively short coherence times compared to qubit states. Here we propose and experimentally demonstrate two approaches for the realization of continuous dynamical decoupling of magnetic-sensitive states with $m_F=\pm1$ for qudits encoded in optical transition of trapped $^{171}$Yb$^{+}$ ions. We achieve improvement in qudit levels coherence time by the order of magnitude (more than 9 ms) without any magnetic shielding, which reveals the potential advantage of the symmetry of the $^{171}$Yb$^{+}$ ion energy structure for counteracting the magnetic field noise. Our results are a step towards the realization of qudit-based algorithms using trapped ions.Comment: 12 pages, 5 figure