Quantum autoencoders for efficient compression of quantum data (1612.02806v2)

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 $x$, is 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 dataset 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 paper proposes Quantum Autoencoders, a quantum analog of classical autoencoders, designed to compress quantum states by learning unitary evolutions that map them into a lower-dimensional subspace.
• The research demonstrates that Quantum Autoencoders can achieve significant compression with high fidelity reconstruction for quantum states, exemplified using data from molecular hydrogen and Hubbard models.
• Quantum Autoencoders could significantly reduce resource requirements for storing and manipulating quantum states, potentially enabling more efficient quantum simulations and advanced quantum machine learning applications.

Summary of "Quantum Autoencoders for Efficient Compression of Quantum Data"

The paper presents the development and analysis of a quantum analog to classical autoencoders, specifically termed "Quantum Autoencoders." This model seeks to compress quantum states similarly to how classical autoencoders reduce dimensionality by training neural networks to learn efficient representations of input data. In this work, the quantum autoencoder model is proposed for processing data inherent to quantum systems, such as those encountered in quantum simulations and quantum computing.

The primary goal of a quantum autoencoder is to learn a unitary evolution that maps input quantum states into a lower-dimensional subspace while still capturing the essential features necessary for accurately reconstructing the original state. Classical optimization algorithms are employed to train the quantum autoencoder, in particular, adjusting the parameters defining these unitary evolutions to optimize performance based on training data sets.

Results and Claims

The paper demonstrates the applicability of the quantum autoencoder by considering the compression of quantum data in quantum simulations. It provides examples using quantum states from systems like the molecular hydrogen Hamiltonian and the Hubbard model. The results indicate that significant compression is achievable while maintaining high fidelity in the reconstructed states. The authors report mean absolute errors in fidelity reaching levels that ensure the preservation of quantum information with high accuracy.

The research claims that the quantum autoencoder could significantly reduce the resources required to store quantum states, especially those obeying particular symmetries or constraints such as particle number conservation in fermionic systems.

Implications and Future Directions

The introduction of quantum autoencoders holds implications for quantum computing resource optimization, potentially reducing the qubit overhead for state storage and manipulation. This resource reduction is particularly relevant as quantum systems increase in complexity and as practical quantum technologies emerge. For practical applications, such as quantum simulations of electronic structures or simulating larger molecule systems, quantum autoencoders could facilitate more efficient handling of quantum data. Furthermore, the quantum autoencoder framework presents a pathway toward developing more advanced quantum machine learning tools that can recognize and exploit quantum mechanical properties like entanglement more effectively than classical methods.

Moving forward, further refinement of the model, including hybrid classical-quantum training algorithms, could enhance practical implementations. The paper also suggests future extensions of the quantum autoencoder model to encompass quantum channels, opening avenues for improved quantum communication protocols. Additionally, customizing the unitary evolution employed by the autoencoder to specific problem sets could yield further compression efficiencies.

Overall, while the paper describes the current landscape and capabilities of quantum autoencoders, continual research might explore diverse applications, including those beyond quantum simulations, like error-correcting codes and advanced quantum state preparation techniques.