As a ubiquitous aspect of modern information technology, data compression has a wide range of applications. Therefore, a quantum autoencoder which can compress quantum information into a low-dimensional space is fundamentally important to achieve automatic data compression in the field of quantum information. Such a quantum autoencoder can be implemented through training the parameters of a quantum device using classical optimization algorithms. In this paper, we demonstrate the condition of achieving a perfect quantum autoencoder and theoretically prove that a quantum autoencoder can losslessly compress high-dimensional quantum information into a low-dimensional space (also called latent space) if the number of maximum linearly independent vectors from input states is no more than the dimension of the latent space. Also, we experimentally realize a universal two-qubit unitary gate and design a quantum autoencoder device by applying a machine learning method. Experimental results demonstrate that our quantum autoencoder is able to compress two two-qubit states into two one-qubit states. Besides compressing quantum information, the quantum autoencoder is used to experimentally discriminate two groups of nonorthogonal states.
As a ubiquitous aspect of modern information technology, data compression has a wide range of applications. Therefore, a quantum autoencoder which can compress quantum information into a low-dimensional space is fundamentally important to achieve automatic data compression in the field of quantum information. Such a quantum autoencoder can be implemented through training the parameters of a quantum device using classical optimization algorithms. In this paper, we demonstrate the condition of achieving a perfect quantum autoencoder and theoretically prove that a quantum autoencoder can losslessly compress high-dimensional quantum information into a low-dimensional space (also called latent space) if the number of maximum linearly independent vectors from input states is no more than the dimension of the latent space. Also, we experimentally realize a universal two-qubit unitary gate and design a quantum autoencoder device by applying a machine learning method. Experimental results demonstrate that our quantum autoencoder is able to compress two two-qubit states into two one-qubit states. Besides compressing quantum information, the quantum autoencoder is used to experimentally discriminate two groups of nonorthogonal states.
With quantum resources a precious commodity, their efficient use is highly desirable. Quantum autoencoders have been proposed as a way to reduce quantum memory requirements. Generally, an autoencoder is a device that uses machine learning to compress inputs, that is, to represent the input data in a lower-dimensional space. Here, we experimentally realize a quantum autoencoder, which learns how to compress quantum data using a classical optimization routine. We demonstrate that when the inherent structure of the dataset allows lossless compression, our autoencoder reduces qutrits to qubits with low error levels. We also show that the device is able to perform with minimal prior information about the quantum data or physical system and is robust to perturbations during its optimization routine.
Abstract Classical autoencoders are neural networks that can learn efficient low-dimensional representations of data in higher-dimensional space. The task of an autoencoder is, given an input x , to map x to a lower dimensional point y such that x can likely be recovered from y . The structure of the underlying autoencoder network can be chosen to represent the data on a smaller dimension, effectively compressing the input. Inspired by this idea, we introduce the model of a quantum autoencoder to perform similar tasks on quantum data. The quantum autoencoder is trained to compress a particular data set of quantum states, where a classical compression algorithm cannot be employed. The parameters of the quantum autoencoder are trained using classical optimization algorithms. We show an example of a simple programmable circuit that can be trained as an efficient autoencoder. We apply our model in the context of quantum simulation to compress ground states of the Hubbard model and molecular Hamiltonians.
The concept of an autoencoder is a key element of modern machine learning methods. It is used, e.g., to compress the input data into a lower-dimensional representation, which is later employed in other machine learning algorithms. In the area of quantum computing application methods, quantum machine learning is also developing dynamically, with the concept of a quantum autoencoder also present. In the article, we discuss a variant of building a quantum autoencoder based on a quantum convolutional network. The proposed autoencoder is characterized by an architecture based on adjacent quantum gates, which is especially important for the near-future noisy intermediate-scale hardware implementation of such a type of quantum circuits. The proposed circuits are built with an elementary set of gates, i.e., controlled negation gates and rotation gates. The described architecture of a quantum autoencoder properly uses the quantum phenomenon called quantum exponential capacitys, i.e., a linear number of qubits which allow encoding an exponential amount of classical information. In our case, for n qubit, it is possible to encode a classical gray coloured image with dimensionality 2n × 2n. The conducted numerical experiments on a set image of handwritten characters and letters show that, for a small number of parameters, the quantum autoencoder offers a reconstruction quality comparable to the currently used classical autoencoders. An important assumption is the omission of additional dimensionality reduction techniques, e.g., PCA, for the preparation of classical data. In the discussed experiment, the data after reconstruction can be read directly from the quantum register, through a series of quantum register measurements.
- Classical data are often compressed by using simple procedure which allows a string of data to take up less space during a computer’s memory. But, In Quantum Computing Data Compression is different because Quantum data are different and it's impossible to decide the frequencies of 1’s and 0’s in quantum information. The structure of the underlying autoencoder network is often chosen to represent the information on a smaller dimension, effectively compressing the input. Inspired by this concept, we introduce the model of a quantum autoencoder to perform similar tasks on quantum data. The quantum autoencoder is trained to compress a specific dataset of quantum states, where a classical compression algorithm cannot be employed. Using classical optimization algorithms, the parameters of the quantum autoencoder are trained. We show an example of an easy programmable circuit which will be trained as an efficient autoencoder with and without using dummy swap gates are implemented in IBMQ.
A quantum autoencoder is a quantum neural network model for compressing information stored in quantum states. However, one needs to process information stored in quantum circuits for many tasks in the emerging quantum information technology. In this work, generalizing the ideas of classical and quantum autoencoders, we introduce the quantum circuit autoencoder (QCAE) model to compress and encode information within quantum circuits. We provide a comprehensive protocol for QCAE and design a variational quantum algorithm, varQCAE, for its implementation. We theoretically analyze this model by deriving conditions for lossless compression and establishing both upper and lower bounds on its recovery fidelity. Finally, we apply varQCAE to three practical tasks, and numerical results show that it can effectively (1) compress the information within quantum circuits, (2) detect anomalies in quantum circuits, and (3) mitigate the depolarizing noise in quantum circuits. These suggest that our algorithm is potentially applicable to other information processing tasks for quantum circuits.
Abstract We examine information loss, resource costs, and run time from practical application of quantum data compression. Compressing quantum data to fewer qubits enables efficient use of resources, as well as applications for quantum communication and denoising. In this context, we provide a description of the quantum and classical components of the hybrid quantum autoencoder algorithm, implemented using IBMs Qiskit language. Utilizing our own data sets, we encode bitmap images as quantum superposition states, which correspond to linearly independent vectors with density matrices of discrete values. We successfully compress this data with near-lossless compression using simulation, and then run our algorithm on an IBMQ quantum chip. We describe conditions and run times for training and compressing our data on quantum devices, and relate trainability to specific characteristics and performance metrics of our parametric quantum circuits.