Topological properties of quantum systems are among the most intriguing emerging phenomena in condensed matter physics. A crucial property of topological systems is the symmetry-protected robustness towards local noise. Experiments have demonstrated topological phases of matter in various quantum systems. However, using the robustness of such modes to stabilize quantum correlations is still a highly sought-after milestone. In this work, we put forward a concept of using topological modes to stabilize fully entangled quantum states, and we demonstrate the stability of the entanglement with respect to parameter fluctuations. Specifically, we see that entanglement remains stable against parameter fluctuations in the topologically nontrivial regime, while entanglement in the trivial regime is highly susceptible to local noise. We supplement our scheme with an experimentally realistic and detailed proposal based on coupled superconducting resonators and qubits. Our proposal sets an approach for generating long-lived quantum modes with robustness towards disorder in the circuit parameters via a bottom-up experimental approach relying on easy-to-engineer building blocks.
Topological properties of quantum systems are among the most intriguing emerging phenomena in condensed matter physics. A crucial property of topological systems is the symmetry-protected robustness towards local noise. Experiments have demonstrated topological phases of matter in various quantum systems. However, using the robustness of such modes to stabilize quantum correlations is still a highly sought-after milestone. In this work, we put forward a concept of using topological modes to stabilize fully entangled quantum states, and we demonstrate the stability of the entanglement with respect to parameter fluctuations. Specifically, we see that entanglement remains stable against parameter fluctuations in the topologically nontrivial regime, while entanglement in the trivial regime is highly susceptible to local noise. We supplement our scheme with an experimentally realistic and detailed proposal based on coupled superconducting resonators and qubits. Our proposal sets an approach for generating long-lived quantum modes with robustness towards disorder in the circuit parameters via a bottom-up experimental approach relying on easy-to-engineer building blocks.
The quantum dynamics of chains of superconducting qubits is analyzed under realistic experimental conditions. Electromagnetic fluctuations due to the background circuitry, finite temperature in the external environment, and disorder in the initial preparation and the control parameters are taken into account. It is shown that the amount of disorder that is typically present in current experiments does not affect the entanglement dynamics significantly. However, the effect of the environmental noise can modify entanglement generation and propagation across the chain. We study the persistence of coherent effects in the presence of noise and possible ways to efficiently detect the presence of quantum entanglement. We also discuss under which circumstances the system exhibits steady state entanglement for both short (N<10) and long (N>30) chains and show that there are parameter regimes where the steady state entanglement is strictly non-monotonic as a function of the noise strength. We present optimized schemes for entanglement verification and quantification based on simple correlation measurements that are experimentally more economic than state tomography.
Quantum decoherence poses a significant challenge to the development of practical quantum computers. The inherent sensitivity of quantum states to environmental interactions leads to rapid loss of quantum information. This work proposes a novel strategy for mitigating decoherence effects by leveraging topological protection. Specifically, we investigate the construction of quantum device arrays utilizing topologically protected states, combined with non-Abelian entanglement, to create a robust barrier against external noise. The core concept relies on isolating quantum bits (qubits) from environmental interactions through the unique properties of topological insulators and engineered topological structures. This approach aims to dramatically improve the fidelity and stability of quantum computations. Mathematical formulations detail the theoretical framework, demonstrating the potential of this method to achieve significantly reduced decoherence rates and enhanced quantum coherence times. The proposed architecture offers a pathway toward building more reliable and scalable quantum computing platforms.
Abstract Topological phases of matter are an exotic phenomenon in modern condensed matter physics, which has attracted much attention due to the unique boundary states and transport properties. Recently, this topological concept in electronic materials has been exploited in many other fields of physics. Motivated by designing and controlling the behavior of electromagnetic waves in optical, microwave, and sound frequencies, topological photonics emerges as a rapid growing research field. Due to the flexibility and diversity of superconducting quantum circuits system, it is a promising platform to realize exotic topological phases of matter and to probe and explore topologically‐protected effects in new ways. Here, theoretical and experimental advances of topological photonics on superconducting quantum circuits—via the experimentally demonstrated parametric tunable coupling techniques, including using of the superconducting transmission line resonator, superconducting qubits, and their coupled system—are reviewed. On superconducting circuits, the flexible interactions and intrinsic nonlinearity make topological photonics in this system not only a simple photonic analog of topological effects for novel devices, but also a realm of exotic but less‐explored fundamental physics.
During the past decades, the exploration of new topological material and the study of their novel physical properties have become a hot topic in condensed matter physics. However, it is hard to realize various topological materials and observe their physical properties that have been predicted theoretically due to the limitation of experimental techniques, such as fabrication, parameter control, and measurement. This situation makes quantum simulation a way alternative to simulating large quantum systems. In general, quantum simulation can be implemented by some controllable quantum systems. As a kind of all-solid state device, superconducting quantum circuit is an artificial quantum system that has great advantage in scalability, integration, and controllability, which provides an important scheme to realize the quantum simulator. In this paper, we review our recent results of quantum simulation in the space-time inversion symmetry protected topological semimetal bands, Hopf-link semimetal bands, and topological Maxwell metal bands with superconducting quantum circuits. These results show that the superconducting circuit is a promising system for simulating the quantum many-body system in condensed matter physics.
This paper proposes a novel quantum error correction code leveraging the inherent entanglement preservation properties of topological quantum states. Traditional quantum error correction schemes rely on creating and maintaining fragile quantum entanglement, which is highly susceptible to environmental noise. Our approach utilizes the topologically protected nature of certain quantum states to provide a robust mechanism for error detection and correction. We formulate a code based on the controlled-Z operation within a topological qubit architecture, demonstrating a significant improvement in error correction capabilities compared to conventional approaches. Specifically, we define the code parameters, including the code rate, minimum distance, and the required number of physical qubits. We analyze the code's performance under various noise models, highlighting the enhanced resilience due to topological protection. The key innovation lies in harnessing the natural, robust entanglement provided by topological states, offering a pathway to more practical and reliable quantum computation. The theoretical framework presented here provides a foundation for future research and development in topological quantum error correction.
Superconducting quantum devices have drawn the attention of physicists greatly in recent years, not only because they are one of the most favorable candidates for developing a solid state quantum computer, but also because they can be employed as test systems for understanding quantum mechanics at nearly macro scale. Superconducting quantum devices can be divided into two groups: the superconducting resonators (linear devices), which have equally spaced discrete energy levels, and the artificial atoms (non-linear devices) consisting of Josephson junctions which have unequally spaced discrete energy levels. By combining these two kinds of devices together, a solid state counterpart of optical cavity quantum electrodynamics (QED) known as circuit QED emerges. Experiments of cavity QED and quantum optics can be reproduced in either circuit QED systems or in bare superconducting artificial atoms. As an example, we have observed the Autler-Townes effect in a three-level artificial atom called phase qutrit. \nMore than one decade has passed since the first experimental demonstration of superconducting two-level artificial atom (qubit). However, to build a practical quantum computer with thousands of superconducting qubits there is still a long way to go (we are at the stage of three qubits now). One of the main obstacles preventing us from scaling up a superconducting quantum computer, as well as some other kinds of quantum computers, has been decoherence, which is believed to be dominated by the low frequency noise due to the two-level system (TLS) fluctuators located inside the Josephson junction barrier. We have experimentally simulated the dynamics of a qubit longitudinally coupled to a randomly fluctuating TLS. A phenomenon known as motional averaging has been observed. \nIn this thesis, theoretical models for decoherence in both resonator and artificial atoms have been established and used for explaining phenomena observed in the experiments performed in our laboratory. The phenomenon of decoherence in coupled bipartite systems has been also studied, and besides the already known entanglement sudden death phenomenon, stable entanglement (robust under decoherence) generated from an arbitrary initial state has been found in these systems.