A new method of constructing adversarial examplesfor quantum variational circuits

A quantum variational circuit is a quantum machine learning model similar to a neural network.A crafted adversarial example can lead to incorrect results for the model.Using adversarial examples to train the model will greatly improve its robustness.The existing method is to use automatic differentials or finite difference to obtain a gradient and use it to construct adversarial examples.This paper proposes an innovative method for constructing adversarial examples of quantum variational circuits.In this method,the gradient can be obtained by measuring the expected value of a quantum bit respectively in a series quantum circuit.This method can be used to construct the adversarial examples for a quantum variational circuit classifier.The implementation results prove the effectiveness of the proposed method.Compared with the existing method,our method requires fewer resources and is more efficient.

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 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.

A backdoor attack against quantum neural networks with limited information

Backdoor attacks are emerging security threats to deep neural networks.In these attacks,adversaries manipulate the network by constructing training samples embedded with backdoor triggers.The backdoored model performs as expected on clean test samples but consistently misclassifies samples containing the backdoor trigger as a specific target label.While quantum neural networks(QNNs)have shown promise in surpassing their classical counterparts in certain machine learning tasks,they are also susceptible to backdoor attacks.However,current attacks on QNNs are constrained by the adversary's understanding of the model structure and specific encoding methods.Given the diversity of encoding methods and model structures in QNNs,the effectiveness of such backdoor attacks remains uncertain.In this paper,we propose an algorithm that leverages dataset-based optimization to initiate backdoor attacks.A malicious adversary can embed backdoor triggers into a QNN model by poisoning only a small portion of the data.The victim QNN maintains high accuracy on clean test samples without the trigger but outputs the target label set by the adversary when predicting samples with the trigger.Furthermore,our proposed attack cannot be easily resisted by existing backdoor detection methods.

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.

Solving the subset sum problem by the quantum Ising model with variational quantum optimization based on conditional values at risk

The subset sum problem is a combinatorial optimization problem,and its complexity belongs to the nondeterministic polynomial time complete(NP-Complete)class.This problem is widely used in encryption,planning or scheduling,and integer partitions.An accurate search algorithm with polynomial time complexity has not been found,which makes it challenging to be solved on classical computers.To effectively solve this problem,we translate it into the quantum Ising model and solve it with a variational quantum optimization method based on conditional values at risk.The proposed model needs only n qubits to encode 2ndimensional search space,which can effectively save the encoding quantum resources.The model inherits the advantages of variational quantum algorithms and can obtain good performance at shallow circuit depths while being robust to noise,and it is convenient to be deployed in the Noisy Intermediate Scale Quantum era.We investigate the effects of the scalability,the variational ansatz type,the variational depth,and noise on the model.Moreover,we also discuss the performance of the model under different conditional values at risk.Through computer simulation,the scale can reach more than nine qubits.By selecting the noise type,we construct simulators with different QVs and study the performance of the model with them.In addition,we deploy the model on a superconducting quantum computer of the Origin Quantum Technology Company and successfully solve the subset sum problem.This model provides a new perspective for solving the subset sum problem.

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.

Diabetic Retinopathy Detection Using Classical-Quantum Transfer Learning Approach and Probability Model

Diabetic Retinopathy(DR)is a common complication of diabetes mellitus that causes lesions on the retina that affect vision.Late detection of DR can lead to irreversible blindness.The manual diagnosis process of DR retina fundus images by ophthalmologists is time consuming and costly.While,Classical Transfer learning models are extensively used for computer aided detection of DR;however,their maintenance costs limits detection performance rate.Therefore,Quantum Transfer learning is a better option to address this problem in an optimized manner.The significance of Hybrid quantum transfer learning approach includes that it performs heuristically.Thus,our proposed methodology aims to detect DR using a hybrid quantum transfer learning approach.To build our model we extract the APTOS 2019 Blindness Detection dataset from Kaggle and used inception-V3 pre-trained classical neural network for feature extraction and Variational Quantum classifier for stratification and trained our model on Penny Lane default device,IBM Qiskit BasicAer device and Google Cirq Simulator device.Both models are built based on PyTorch machine learning library.We bring about a contrast performance rate between classical and quantum models.Our proposed model achieves an accuracy of 93%–96%on the quantum hybrid model and 85%accuracy rate on the classical model.So,quantum computing can harness quantum machine learning to do work with power and efficiency that is not possible for classical computers.

Formulation of the Social Workers’ Problem in Quadratic Unconstrained Binary Optimization Form and Solve It on a Quantum Computer

The problem of social workers visiting their patients at home is a class of combinatorial optimization problems and belongs to the class of problems known as NP-Hard. These problems require heuristic techniques to provide an efficient solution in the best of cases. In this article, in addition to providing a detailed resolution of the social workers’ problem using the Quadratic Unconstrained Binary Optimization Problems (QUBO) formulation, an approach to mapping the inequality constraints in the QUBO form is given. Finally, we map it in the Hamiltonian of the Ising model to solve it with the Quantum Exact Solver and Variational Quantum Eigensolvers (VQE). The quantum feasibility of the algorithm will be tested on IBMQ computers.

Quantum Computational Techniques for Prediction of Cognitive State of Human Mind from EEG Signals

The utilization of quantum states for the representation of information and the advances in machine learning is considered as an efficient way of modeling the working of complex systems.The states of mind or judgment outcomes are highly complex phenomena that happen inside the human body.Decoding these states is significant for improving the quality of technology and providing an impetus to scientific research aimed at understanding the functioning of the human mind.One of the key advantages of quantum wave-functions over conventional classical models is the existence of configurable hidden variables,which provide more data density due to its exponential state-space growth.These hidden variables correspond to the amplitudes of each probable state of the system and allow for the modeling of various intricate aspects of measurable and observable physical quantities.This makes the quantum wave-functions powerful and felicitous to model cognitive states of the human mind,as it inherits the ability to efficiently couple the current context with past experiences temporally and spatially to approach an appropriate future cognitive state.This paper implements and compares some techniques like Variational Quantum Classifiers(VQC),quantum annealing classifiers,and hybrid quantum-classical neural networks,to harness the power of quantum computing for processing cognitive states of the mind by making use of EEG data.It also introduces a novel pipeline by logically combining some of the aforementioned techniques,to predict future cognitive responses.The preliminary results of these approaches are presented and are very encouraging with upto 61.53%validation accuracy.

Properties of strong-coupling magneto-bipolaron qubit in quantum dot under magnetic field

Based on the variational method of Pekar type, we study the energies and the wave-functions of the ground and the first-excited states of magneto-bipolaron, which is strongly coupled to the LO phonon in a parabolic potential quantum dot under an applied magnetic field, thus built up a quantum dot magneto-bipolaron qubit. The results show that the oscillation period of the probability density of the two electrons in the qubit decreases with increasing electron–phonon coupling strength α, resonant frequency of the magnetic field ωc, confinement strength of the quantum dot ω0, and dielectric constant ratio of the medium η; the probability density of the two electrons in the qubit oscillates periodically with increasing time t, angular coordinate φ2, and dielectric constant ratio of the medium η; the probability of electron appearing near the center of the quantum dot is larger, and the probability of electron appearing away from the center of the quantum dot is much smaller.

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.

Algorithm for simulating ocean circulation on a quantum computer

The accurate and efficient simulation of ocean circulation is a fundamental topic in marine science;however,it is also a well-known and dauntingly difficult problem that requires solving nonlinear partial differential equations with multiple variables.In this paper,we present for the first time an algorithm for simulating ocean circulation on a quantum computer to achieve a computational speedup.Our approach begins with using primitive equations describing the ocean dynamics and then discretizing these equations in time and space.It results in several linear system of equations(LSE)with sparse coefficient matrices.We solve these sparse LSE using the variational quantum linear solver that enables the present algorithm to run easily on near-term quantum computers.Additionally,we develop a scheme for manipulating the data flow in the algorithm based on the quantum random access memory and l∞norm tomography technique.The efficiency of our algorithm is verified using multiple platforms,including MATLAB,a quantum virtual simulator,and a real quantum computer.The impact of the number of shots and the noise of quantum gates on the solution accuracy is also discussed.Our findings demonstrate that error mitigation techniques can efficiently improve the solution accuracy.With the rapid advancements in quantum computing,this work represents an important first step toward solving the challenging problem of simulating ocean circulation using quantum computers.

Variational algorithms for linear algebra

Quantum algorithms have been developed for efficiently solving linear algebra tasks.However,they generally require deep circuits and hence universal fault-tolerant quantum computers.In this work,we propose variational algorithms for linear algebra tasks that are compatible with noisy intermediate-scale quantum devices.We show that the solutions of linear systems of equations and matrix–vector multiplications can be translated as the ground states of the constructed Hamiltonians.Based on the variational quantum algorithms,we introduce Hamiltonian morphing together with an adaptive ans?tz for efficiently finding the ground state,and show the solution verification.Our algorithms are especially suitable for linear algebra problems with sparse matrices,and have wide applications in machine learning and optimisation problems.The algorithm for matrix multiplications can be also used for Hamiltonian simulation and open system simulation.We evaluate the cost and effectiveness of our algorithm through numerical simulations for solving linear systems of equations.We implement the algorithm on the IBM quantum cloud device with a high solution fidelity of 99.95%.

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 computing for the Lipkin model with unitary coupled cluster and structure learning ansatz

We report a benchmark calculation for the Lipkin model in nuclear physics with a variational quantum eigensolver in quantum computing.Special attention is paid to the unitary coupled cluster(UCC)ansatz and structure learning(SL)ansatz for the trial wave function.Calculations with both the UCC and SL ansatz can reproduce the ground-state energy well;however,it is found that the calculation with the SL ansatz performs better than thatwith the UCC ansatz,and the SL ansatz has even fewer quantum gates than the UCC ansatz.

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.