Digital Simulation of Projective Non-Abelian Anyons with 68 Superconducting Qubits

Non-Abelian anyons are exotic quasiparticle excitations hosted by certain topological phases of matter.They break the fermion-boson dichotomy and obey non-Abelian braiding statistics:their interchanges yield unitary operations,rather than merely a phase factor,in a space spanned by topologically degenerate wavefunctions.They are the building blocks of topological quantum computing.However,experimental observation of non-Abelian anyons and their characterizing braiding statistics is notoriously challenging and has remained elusive hitherto,in spite of various theoretical proposals.Here,we report an experimental quantum digital simulation of projective non-Abelian anyons and their braiding statistics with up to 68 programmable superconducting qubits arranged on a two-dimensional lattice.By implementing the ground states of the toric-code model with twists through quantum circuits,we demonstrate that twists exchange electric and magnetic charges and behave as a particular type of non-Abelian anyons,i.e.,the Ising anyons.In particular,we show experimentally that these twists follow the fusion rules and non-Abelian braiding statistics of the Ising type,and can be explored to encode topological logical qubits.Furthermore,we demonstrate how to implement both single-and two-qubit logic gates through applying a sequence of elementary Pauli gates on the underlying physical qubits.Our results demonstrate a versatile quantum digital approach for simulating non-Abelian anyons,offering a new lens into the study of such peculiar quasiparticles.

Quantum Continual Learning Overcoming Catastrophic Forgetting

Catastrophic forgetting describes the fact that machine learning models will likely forget the knowledge of previously learned tasks after the learning process of a new one.It is a vital problem in the continual learning scenario and recently has attracted tremendous concern across different communities.We explore the catastrophic forgetting phenomena in the context of quantum machine learning.It is found that,similar to those classical learning models based on neural networks,quantum learning systems likewise suffer from such forgetting problem in classification tasks emerging from various application scenes.We show that based on the local geometrical information in the loss function landscape of the trained model,a uniform strategy can be adapted to overcome the forgetting problem in the incremental learning setting.Our results uncover the catastrophic forgetting phenomena in quantum machine learning and offer a practical method to overcome this problem,which opens a new avenue for exploring potential quantum advantages towards continual learning.

Probe Knots and Hopf Insulators with Ultracold Atoms

Knots and links are fascinating and intricate topological objects.Their influence spans from DNA and molecular chemistry to vortices in superfluid helium,defects in liquid crystals and cosmic strings in the early universe.Here we find that knotted structures also exist in a peculiar class of three-dimensional topological insulators—the Hopf insulators.In particular,we demonstrate that the momentum-space spin textures of Hopf insulators are twisted in a nontrivial way,which implies the presence of various knot and link structures.We further illustrate that the knots and nontrivial spin textures can be probed via standard time-of-flight images in cold atoms as preimage contours of spin orientations in stereographic coordinates.The extracted Hopf invariants,knots,and links are validated to be robust to typical experimental imperfections.Our work establishes the existence of knotted structures in Hopf insulators,which may have potential applications in spintronics and quantum information processing.

Unsupervised learning of interacting topological phases from experimental observables

Classifying topological phases of matter with strong interactions is a notoriously challenging task and has attracted considerable attention in recent years.In this paper,we propose an unsupervised machine learning approach that can classify a wide range of symmetry-protected interacting topological phases directly from the experimental observables and without a priori knowledge.We analytically show that Green’s functions,which can be derived from spectral functions that can be measured directly in an experiment,are suitable for serving as the input data for our learning proposal based on the diffusion map.As a concrete example,we consider a one-dimensional interacting topological insulators model and show that,through extensive numerical simulations,our diffusion map approach works as desired.In addition,we put forward a generic scheme to measure the spectral functions in ultracold atomic systems through momentum-resolved Raman spectroscopy.Our work circumvents the costly diagonalization of the system Hamiltonian,and provides a versatile protocol for the straightforward and autonomous identification of interacting topological phases from experimental observables in an unsupervised manner.

Recent advances for quantum classifiers

Machine learning has achieved dramatic success in a broad spectrum of applications.Its interplay with quantum physics may lead to unprecedented perspectives for both fundamental research and commercial applications,giving rise to an emergent research frontier of quantum machine learning.Along this line,quantum classifiers,which are quantum devices that aim to solve classification problems in machine learning,have attracted tremendous attention recently.In this review,we give a relatively comprehensive overview for the studies of quantum classifiers,with a focus on recent advances.First,we will review a number of quantum classification algorithms,including quantum support vector machines,quantum kernel methods,quantum decision tree classifiers,quantum nearest neighbor algorithms,and quantum annealing based classifiers.Then,we move on to introduce the variational quantum classifiers,which are essentially variational quantum circuits for classifications.We will review different architectures for constructing variational quantum classifiers and introduce the barren plateau problem,where the training of quantum classifiers might be hindered by the exponentially vanishing gradient.In addition,the vulnerability aspect of quantum classifiers in the setting of adversarial learning and the recent experimental progress on different quantum classifiers will also be discussed.

Quantum federated learning through blind quantum computing

Private distributed learning studies the problem of how multiple distributed entities collaboratively train a shared deep network with their private data unrevealed. With the security provided by the protocols of blind quantum computation, the cooperation between quantum physics and machine learning may lead to unparalleled prospect for solving private distributed learning tasks.In this paper, we introduce a quantum protocol for distributed learning that is able to utilize the computational power of the remote quantum servers while keeping the private data safe. For concreteness, we first introduce a protocol for private single-party delegated training of variational quantum classifiers based on blind quantum computing and then extend this protocol to multiparty private distributed learning incorporated with diferential privacy. We carry out extensive numerical simulations with diferent real-life datasets and encoding strategies to benchmark the efectiveness of our protocol. We find that our protocol is robust to experimental imperfections and is secure under the gradient attack after the incorporation of diferential privacy. Our results show the potential for handling computationally expensive distributed learning tasks with privacy guarantees, thus providing a valuable guide for exploring quantum advantages from the security perspective in the field of machine learning with real-life applications.

自适应量子储层计算与多任务学习

随着实验技术的快速发展,含噪声的中等规模量子(NISQ)设备的可编程性越来越高,人们能够更好地利用量子计算的优势.本文利用可编程的NISQ设备的复杂动力学来进行量子储层计算,并通过使用遗传算法来优化该过程.令人惊讶的是,单个自适应量子储层可以同时学习多个任务,包括振荡型基因网络、混沌型基因网络和分数阶蔡氏电路.通过自适应量子储层计算,这些任务的学习性能得到了显著提升,远远超过了经典储层计算的表现.此外,本文还将自适应量子储层计算应用于外汇市场,相较于经典储层计算,它能更准确地捕捉汇率的随机演化.通过与经典储层计算的比较,本文突出了量子相干性在量子储层计算中的重要性,并验证了量子相干性是实现卓越学习性能的关键.研究结果表明,自适应量子储层计算能够充分发挥NISQ设备的量子计算能力,并在通用人工智能的发展方面具有巨大潜力.

Quantum enhanced convolutional neural networks for NISQ computers

The interplay between quantum physics and machine learning may lead to unprecedented perspectives for both fields [1]. On the one hand, ideas and techniques from machine learning, or more broadly artificial intelligence, can be exploited to tackle challenging problems in the quantum domain.