Variational quantum simulation of thermal statistical states on a superconducting quantum processer

Quantum computers promise to solve finite-temperature properties of quantum many-body systems,which is generally challenging for classical computers due to high computational complexities.Here,we report experimental preparations of Gibbs states and excited states of Heisenberg X X and X X Z models by using a 5-qubit programmable superconducting processor.In the experiments,we apply a hybrid quantum–classical algorithm to generate finite temperature states with classical probability models and variational quantum circuits.We reveal that the Hamiltonians can be fully diagonalized with optimized quantum circuits,which enable us to prepare excited states at arbitrary energy density.We demonstrate that the approach has a self-verifying feature and can estimate fundamental thermal observables with a small statistical error.Based on numerical results,we further show that the time complexity of our approach scales polynomially in the number of qubits,revealing its potential in solving large-scale problems.

Variational quantum semi-supervised classifier based on label propagation

Label propagation is an essential semi-supervised learning method based on graphs,which has a broad spectrum of applications in pattern recognition and data mining.This paper proposes a quantum semi-supervised classifier based on label propagation.Considering the difficulty of graph construction,we develop a variational quantum label propagation(VQLP)method.In this method,a locally parameterized quantum circuit is created to reduce the parameters required in the optimization.Furthermore,we design a quantum semi-supervised binary classifier based on hybrid Bell and Z bases measurement,which has a shallower circuit depth and is more suitable for implementation on near-term quantum devices.We demonstrate the performance of the quantum semi-supervised classifier on the Iris data set,and the simulation results show that the quantum semi-supervised classifier has higher classification accuracy than the swap test classifier.This work opens a new path to quantum machine learning based on graphs.

Towards an efficient variational quantum algorithm for solving linear equations

Variational quantum algorithms are promising methods with the greatest potential to achieve quantum advantage,widely employed in the era of noisy intermediate-scale quantum computing.This study presents an advanced variational hybrid algorithm(EVQLSE)that leverages both quantum and classical computing paradigms to address the solution of linear equation systems.Initially,an innovative loss function is proposed,drawing inspiration from the similarity measure between two quantum states.This function exhibits a substantial improvement in computational complexity when benchmarked against the variational quantum linear solver.Subsequently,a specialized parameterized quantum circuit structure is presented for small-scale linear systems,which exhibits powerful expressive capabilities.Through rigorous numerical analysis,the expressiveness of this circuit structure is quantitatively assessed using a variational quantum regression algorithm,and it obtained the best score compared to the others.Moreover,the expansion in system size is accompanied by an increase in the number of parameters,placing considerable strain on the training process for the algorithm.To address this challenge,an optimization strategy known as quantum parameter sharing is introduced,which proficiently minimizes parameter volume while adhering to exacting precision standards.Finally,EVQLSE is successfully implemented on a quantum computing platform provided by IBM for the resolution of large-scale problems characterized by a dimensionality of 220.

Pure quantum gradient descent algorithm and full quantum variational eigensolver

Optimization problems are prevalent in various fields,and the gradient-based gradient descent algorithm is a widely adopted optimization method.However,in classical computing,computing the numerical gradient for a function with variables necessitates at least d+1 function evaluations,resulting in a computational complexity of O(d).As the number of variables increases,the classical gradient estimation methods require substantial resources,ultimately surpassing the capabilities of classical computers.Fortunately,leveraging the principles of superposition and entanglement in quantum mechanics,quantum computers can achieve genuine parallel computing,leading to exponential acceleration over classical algorithms in some cases.In this paper,we propose a novel quantum-based gradient calculation method that requires only a single oracle calculation to obtain the numerical gradient result for a multivariate function.The complexity of this algorithm is just O(1).Building upon this approach,we successfully implemented the quantum gradient descent algorithm and applied it to the variational quantum eigensolver(VQE),creating a pure quantum variational optimization algorithm.Compared with classical gradient-based optimization algorithm,this quantum optimization algorithm has remarkable complexity advantages,providing an efficient solution to optimization problems.The proposed quantum-based method shows promise in enhancing the performance of optimization algorithms,highlighting the potential of quantum computing in this field.

Variational quantum algorithm for node embedding

Quantum machine learning has made remarkable progress in many important tasks.However,the gate complexity of the initial state preparation is seldom considered in lots of quantum machine learning algorithms,making them non-end-to-end.Herein,we propose a quantum algorithm for the node embedding problem that maps a node graph's topological structure to embedding vectors.The resulting quantum embedding state can be used as an input for other quantum machine learning algorithms.With O(log(N))qubits to store the information of N nodes,our algorithm will not lose quantum advantage for the subsequent quantum information processing.Moreover,owing to the use of a parameterized quantum circuit with O(poly(log(N)))depth,the resulting state can serve as an efficient quantum database.In addition,we explored the measurement complexity of the quantum node embedding algorithm,which is the main issue in training parameters,and extended the algorithm to capture high-order neighborhood information between nodes.Finally,we experimentally demonstrated our algorithm on an nuclear magnetic resonance quantum processor to solve a graph model.

Quantum computing in power systems

Electric power systems provide the backbone of modern industrial societies.Enabling scalable grid analytics is the keystone to successfully operating large transmission and distribution systems.However,today’s power systems are suffering from ever-increasing computational burdens in sustaining the expanding communities and deep integration of renewable energy resources,as well as managing huge volumes of data accordingly.These unprecedented challenges call for transformative analytics to support the resilient operations of power systems.Recently,the explosive growth of quantum computing techniques has ignited new hopes of revolutionizing power system computations.Quantum computing harnesses quantum mechanisms to solve traditionally intractable computational problems,which may lead to ultra-scalable and efficient power grid analytics.This paper reviews the newly emerging application of quantum computing techniques in power systems.We present a comprehensive overview of existing quantum-engineered power analytics from different operation perspectives,including static analysis,transient analysis,stochastic analysis,optimization,stability,and control.We thoroughly discuss the related quantum algorithms,their benefits and limitations,hardware implementations,and recommended practices.We also review the quantum networking techniques to ensure secure communication of power systems in the quantum era.Finally,we discuss challenges and future research directions.This paper will hopefully stimulate increasing attention to the development of quantum-engineered smart grids.

Near-term quantum computing techniques: Variational quantum algorithms, error mitigation, circuit compilation, benchmarking and classical simulation

Quantum computing is a game-changing technology for global academia,research centers and industries including computational science,mathematics,finance,pharmaceutical,materials science,chemistry and cryptography.Although it has seen a major boost in the last decade,we are still a long way from reaching the maturity of a full-fledged quantum computer.That said,we will be in the noisy-intermediate scale quantum(NISQ)era for a long time,working on dozens or even thousands of qubits quantum computing systems.An outstanding challenge,then,is to come up with an application that can reliably carry out a nontrivial task of interest on the near-term quantum devices with non-negligible quantum noise.To address this challenge,several near-term quantum computing techniques,including variational quantum algorithms,error mitigation,quantum circuit compilation and benchmarking protocols,have been proposed to characterize and mitigate errors,and to implement algorithms with a certain resistance to noise,so as to enhance the capabilities of near-term quantum devices and explore the boundaries of their ability to realize useful applications.Besides,the development of near-term quantum devices is inseparable from the efficient classical sim-ulation,which plays a vital role in quantum algorithm design and verification,error-tolerant verification and other applications.This review will provide a thorough introduction of these near-term quantum computing techniques,report on their progress,and finally discuss the future prospect of these techniques,which we hope will motivate researchers to undertake additional studies in this field.

Variational quantum support vector machine based on Hadamard test

Classical machine learning algorithms seem to be totally incapable of processing tremendous amounts of data,while quantum machine learning algorithms could deal with big data with ease and provide exponential acceleration over classical counterparts.Meanwhile,variational quantum algorithms are widely proposed to solve relevant computational problems on noisy,intermediate-scale quantum devices.In this paper,we apply variational quantum algorithms to quantum support vector machines and demonstrate a proof-of-principle numerical experiment of this algorithm.In addition,in the classification stage,fewer qubits,shorter circuit depth,and simpler measurement requirements show its superiority over the former algorithms.

Reconstructing unknown quantum states using variational layerwise method

In order to gain comprehensive knowledge of an arbitrary unknown quantum state,one feasible way is to reconstruct it,which can be realized by finding a series of quantum operations that can refactor the unitary evolution producing the unknown state.We design an adaptive framework that can reconstruct unknown quantum states at high fidelities,which utilizes SWAP test,parameterized quantum circuits(PQCs)and layerwise learning strategy.We conduct benchmarking on the framework using numerical simulations and reproduce states of up to six qubits at more than 96%overlaps with original states on average using PQCs trained by our framework,revealing its high applicability to quantum systems of different scales theoretically.Moreover,we perform experiments on a five-qubit IBM Quantum hardware to reconstruct random unknown single qubit states,illustrating the practical performance of our framework.For a certain reconstructing fidelity,our method can effectively construct a PQC of suitable length,avoiding barren plateaus of shadow circuits and overuse of quantum resources by deep circuits,which is of much significance when the scale of the target state is large and there is no a priori information on it.This advantage indicates that it can learn credible information of unknown states with limited quantum resources,giving a boost to quantum algorithms based on parameterized circuits on near-term quantum processors.

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.

量子计算机辅助设计先进的超导量子比特:Plasmonium

复杂的超导量子电路可以用来设计对噪声免疫的量子比特,但其复杂性可能会超出经典计算机所具备的模拟能力.在这种情况下,可以借助量子计算机来对其进行高效的模拟.在这项工作中,作者展示了在基于transmon比特的量子计算机上,利用变分量子算法模拟一种超导量子电路,并且基于此设计了一种新的量子比特“Plasmonium”,它工作在等离子体跃迁区域.文中展示的Plasmonium量子比特展示出了较高的两比特门保真度99.58(3)%.相比于transmon比特,它具有更小的物理尺寸和更大的非谐性.这些特征使得Plasmonium可以成为制造多比特量子处理器强有力的候选者.这项研究结果证实了利用量子计算机辅助设计更先进的量子处理器的可能性.