As we continue to find applications where the currently available noisy devices exhibit an advantage over their classical counterparts, the efficient use of quantum resources is highly desirable. The notion of quantum autoencoders was proposed as a way for the compression of quantum information to reduce resource requirements. Here, we present a strategy to design quantum autoencoders using evolutionary algorithms for transforming quantum information into lower-dimensional representations. We successfully demonstrate the initial applications of the algorithm for compressing different families of quantum states. In particular, we point out that using a restricted gate set in the algorithm allows for efficient simulation of the generated circuits. This approach opens the possibility of using classical logic to find low representations of quantum data, using fewer computational resources.
As we continue to find applications where the currently available noisy devices exhibit an advantage over their classical counterparts, the efficient use of quantum resources is highly desirable. The notion of quantum autoencoders was proposed as a way for the compression of quantum information to reduce resource requirements. Here, we present a strategy to design quantum autoencoders using evolutionary algorithms for transforming quantum information into lower-dimensional representations. We successfully demonstrate the initial applications of the algorithm for compressing different families of quantum states. In particular, we point out that using a restricted gate set in the algorithm allows for efficient simulation of the generated circuits. This approach opens the possibility of using classical logic to find low representations of quantum data, using fewer computational resources.
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.
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 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.
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.
Variational quantum algorithms (VQAs) have emerged as the leading strategy for using these noisy devices to achieve an advantage over their classical counterparts.VQAs use a hybrid quantum-classical framework, in which one employs the quantum computer to prepare a parameterized quantum state and outsource the optimization to a classical subroutine. VQAs have been proposed for applications in various fields, including physics, quantum chemistry, machine learning, and optimization. Nevertheless, many challenges must be addressed before we can use them for practical tasks. In this dissertation, we propose strategies to overcome some challenges in implementing VQAs. We first look at the issue of trainability for VQAs and propose three methods for optimizing them.The first method is based on natural evolutionary strategies (NES) and can alleviate the issue of vanishing gradients for randomly initialized parameterized quantum circuits (PQCs). The second method is based on the notion of information flow in PQCs and uses a mutual information-based distance metric to define paths for stochastic optimization of VQAs. Finally, we develop gradient evaluation procedures for optimizing objectives with the unitary coupled-cluster ansatz. Next, we study the issue of expressibility of PQCs used in variational algorithms.First, using the theory of quantum optimal control we define a notion of reachability of general ans\"atze used in VQAs. Next, using a variational autoencoder (VAE) coupled with a regression model, we try to gain a better understanding of the parameterization of PQCs. Finally, we attempt to remedy the inefficient usage of quantum resources for storing quantum data using evolutionary strategies to design quantum circuits for compressing quantum data. We present numerical evidence that the work presented here can increase trainability, efficiency, and understanding of VQAs.We believe our work is of interest to the quantum computing community as we continue to push the limits of NISQ devices for solving practical problems.
- 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.