The accurate detection of small deviations in given density matrices is important for quantum information processing. Here we propose a method based on the concept of data mining. We demonstrate that the proposed method can more accurately detect small erroneous deviations in reconstructed density matrices, which contain intrinsic fluctuations due to the limited number of samples, than a naive method of checking the trace distance from the average of the given density matrices. This method has the potential to be a key tool in broad areas of physics where the detection of small deviations of quantum states reconstructed using a limited number of samples is essential.
The accurate detection of small deviations in given density matrices is important for quantum information processing. Here we propose a method based on the concept of data mining. We demonstrate that the proposed method can more accurately detect small erroneous deviations in reconstructed density matrices, which contain intrinsic fluctuations due to the limited number of samples, than a naive method of checking the trace distance from the average of the given density matrices. This method has the potential to be a key tool in broad areas of physics where the detection of small deviations of quantum states reconstructed using a limited number of samples is essential.
The accurate detection of small deviations in given density matrice is important for quantum information processing, which is a difficult task because of the intrinsic fluctuation in density matrices reconstructed using a limited number of experiments. We previously proposed a method for decoherence error detection using a machine-learning technique [S. Hara, T. Ono, R. Okamoto, T. Washio, and S. Takeuchi, Phys. Rev. A 89, 022104 (2014)]. However, the previous method is not valid when the errors are just changes in phase. Here, we propose a method that is valid for arbitrary errors in density matrices. The performance of the proposed method is verified using both numerical simulation data and real experimental data.
Anomaly detection is used for identifying data that deviate from ``normal'' data patterns. Its usage on classical data finds diverse applications in many important areas such as finance, fraud detection, medical diagnoses, data cleaning, and surveillance. With the advent of quantum technologies, anomaly detection of quantum data, in the form of quantum states, may become an important component of quantum applications. Machine-learning algorithms are playing pivotal roles in anomaly detection using classical data. Two widely used algorithms are the kernel principal component analysis and the one-class support vector machine. We find corresponding quantum algorithms to detect anomalies in quantum states. We show that these two quantum algorithms can be performed using resources that are logarithmic in the dimensionality of quantum states. For pure quantum states, these resources can also be logarithmic in the number of quantum states used for training the machine-learning algorithm. This makes these algorithms potentially applicable to big quantum data applications.
Quantum state estimation and discrimination are important tasks not only for many quantum information protocols but also precise measurements. In this paper, we report our recent efforts on this issue. In the first part, we report adoptive quantum state estimation, which provides the most accurate estimation using an optimal measurement basis for each measurement. In the second part, we introduce quantum state data mining where the erroneous states (density matrices) are discriminated from the normal ones efficiently using machine learning method.
Quantum autoencoder (QAE) is a key tool in quantum machine learning and can be applied to areas such as dimensionality reduction and feature extraction [1]. Anomaly detection identifies deviations from normal patterns, which is crucial yet challenging due to the need to detect risks while minimizing false positives [2]. We propose a QAE-based anomaly detection scheme using an optical quantum neural network. Figure 1 (A) shows the basic structure of the QAE: the encoder compresses the input quantum state into a low-dimensional latent space, and the decoder reconstructs the original quantum state from the latent space. QAE-based anomaly detection works by learning the low-dimensional features of normal data and minimizing its reconstruction error. Normal data can be well reconstructed, while anomalous data exhibits a larger reconstruction error. When the reconstruction error of test data exceeds a set threshold, it is classified as anomalous. We constructed the QAE using an optical quantum neural network consisting of 50:50 beam splitters and controllable phase shifters [3]. Due to the unitary matrix property, only the encoder needs to be trained, and the decoder is simply the conjugate transpose of the encoder. To compress an N-dimensional quantum stateρintoKdimensions, efficient compression can be achieved by minimizing the expectation value of the projection onto the trash state, given byC(θ,ϕ)=Tr(PU(θ,ϕ)ρU+(θ,ϕ))[4]. Here,P=(IK⊕∣0⟩⊗N−K⟨0∣⊗(N−K))represents the projection onto the trash state,IKis the K-dimensional identity matrix,∣0⟩⊗(N−K)isthe trash state,Trdenotes the trace,U(θ,ϕ)is the encoder with adjustable parameters, andU†(θ,ϕ)is the decoder. We only need to train the encoder during the training process, and the decoder is simply its conjugate transpose.
The advent of quantum computers has justified the development of quantum machine learning algorithms , based on the adaptation of the principles of machine learning to the formalism of qubits. Among such quantum algorithms, anomaly detection represents an important problem crossing several disciplines from cybersecurity, to fraud detection to particle physics. We summarize the key concepts involved in quantum computing, introducing the formal concept of quantum speed up. The review provides a structured map of anomaly detection based on quantum machine learning. We have grouped existing algorithms according to the different learning methods, namely quantum supervised, quantum unsupervised and quantum reinforcement learning, respectively. We provide an estimate of the hardware resources to provide sufficient computational power in the future. The review provides a systematic and compact understanding of the techniques belonging to each category. We eventually provide a discussion on the computational complexity of the learning methods in real application domains.
Abstract In the processing of quantum computation, analyzing and learning the pattern of the quantum data are essential for many tasks. Quantum machine learning algorithms cannot only deal with the quantum states generated in the preceding quantum procedures, but also the quantum registers encoding classical problems. In this work, the anomaly detection of quantum states encoding audio samples with a three‐qubit quantum processor consisting of solid‐state spins in diamond is experimentally demonstrated. By training the quantum machine with a few normal samples, the quantum machine can detect the anomaly samples with a minimum error rate of 15.4%. These results show the power of quantum anomaly detection in dealing with machine learning tasks and the potential to detect abnormal output of quantum devices.