Quantum Convolutional Neural Networks (1810.03787v2)

Abstract: We introduce and analyze a novel quantum machine learning model motivated by convolutional neural networks. Our quantum convolutional neural network (QCNN) makes use of only $O(\log(N))$ variational parameters for input sizes of $N$ qubits, allowing for its efficient training and implementation on realistic, near-term quantum devices. The QCNN architecture combines the multi-scale entanglement renormalization ansatz and quantum error correction. We explicitly illustrate its potential with two examples. First, QCNN is used to accurately recognize quantum states associated with 1D symmetry-protected topological phases. We numerically demonstrate that a QCNN trained on a small set of exactly solvable points can reproduce the phase diagram over the entire parameter regime and also provide an exact, analytical QCNN solution. As a second application, we utilize QCNNs to devise a quantum error correction scheme optimized for a given error model. We provide a generic framework to simultaneously optimize both encoding and decoding procedures and find that the resultant scheme significantly outperforms known quantum codes of comparable complexity. Finally, potential experimental realization and generalizations of QCNNs are discussed.

• The paper presents QCNNs that use logarithmic scaling of variational parameters to achieve efficient quantum phase recognition and error correction.
• QCNNs mimic classical CNN architectures with translationally invariant convolutional and pooling layers, ensuring performance independent of system size.
• The model outperforms classical methods in sample complexity and logical error rate reduction, paving the way for fault-tolerant quantum computation.

Quantum Convolutional Neural Networks: A Cutting-Edge Approach in Quantum Machine Learning

The paper "Quantum Convolutional Neural Networks" presents an innovative approach in the discipline of quantum machine learning by proposing Quantum Convolutional Neural Networks (QCNNs), motivated by the classical success of Convolutional Neural Networks (CNNs). Unlike classical approaches, this model is specifically designed for solving problems in quantum many-body systems, focusing on tasks like quantum phase recognition (QPR) and quantum error correction (QEC) optimization.

Structural Overview and Methodology

QCNNs draw inspiration from the layered architecture of traditional CNNs, featuring translationally invariant convolutional and pooling layers, each characterized by a constant number of parameters independent of system size, thus maintaining computational efficiency. A QCNN circuit is structurally similar to MERA (Multiscale Entanglement Renormalization Ansatz), but operates in the inverse direction, employing error-corrective techniques akin to those found in quantum error correction.

A compelling feature of QCNNs is their use of logarithmic scaling of variational parameters with respect to the number of qubits, making them feasible for near-term quantum devices. Among its applications, the QCNN is utilized for (1) recognizing quantum states corresponding to 1D symmetry-protected topological (SPT) phases, and (2) developing optimized quantum error correction schemes suited to specific error models.

Quantum Phase Recognition Application

In the QPR example, QCNNs are adept at identifying whether an input quantum state belongs to a particular SPT phase. The paper demonstrates the model's capability to efficiently learn from a small set of training examples from exactly solvable points and accurately predict phase boundaries across an extensive parameter range.

One significant result is QCNNs' superior performance in sample complexity over classical methods such as measuring string order parameters (SOP), especially near phase transitions where quantum projection noise hinders measurements. This efficiency is attributed to a multiscale string order parameter approach, which tests exponentially many SOP products to maintain sharp phase classification outputs even near criticality.

Quantum Error Correction Optimization

In the field of QEC optimization, QCNNs provide a framework that simultaneously optimizes the encoding and decoding processes, representing a step forward in designing codes for unknown error models. Notably, in example models with complex correlated errors, QCNNs surpass traditional codes such as the Shor code, demonstrating significant reduction in logical error rates. The QCNN's architecture provides potential pathways for further research into fault-tolerant quantum computation strategies.

Implications and Future Directions

The proposed QCNN model could open avenues for the exploration of higher-dimensional problems, including those involving topological order and complex quantum spin liquids. Furthermore, the methodology hints at possible enhancements to existing quantum learning algorithms, advocating adjustments like parameter initialization strategies inspired by known quantum circuit properties and error correction schemes.

The experimental feasibility of QCNNs on platforms like Rydberg atoms and superconducting qubits suggests near-term implementation possibilities, adding to their practical significance. Additionally, this work fuels further investigation into efficient quantum backpropagation strategies to optimize learning procedures beyond classical paradigms.

In summary, the introduction and analysis of QCNNs represent a substantive advancement in leveraging quantum resources to tackle otherwise intractable problems in quantum many-body science, setting the stage for practical applications in quantum computing and machine learning.