Hierarchical quantum circuit representations for neural architecture search

TL;DR

This work proposes a framework for representing quantum circuit architectures using techniques from NAS, which enables search space design and architecture search and uses a genetic algorithm to perform Quantum Phase Recognition as an example of architecture search with this representation.

Abstract

Machine learning with hierarchical quantum circuits, usually referred to as Quantum Convolutional Neural Networks (QCNNs), is a promising prospect for near-term quantum computing. The QCNN is a circuit model inspired by the architecture of Convolutional Neural Networks (CNNs). CNNs are successful because they do not need manual feature design and can learn high-level features from raw data. Neural Architecture Search (NAS) builds on this success by learning network architecture and achieves state-of-the-art performance. However, applying NAS to QCNNs presents unique challenges due to the lack of a well-defined search space. In this work, we propose a novel framework for representing QCNN architectures using techniques from NAS, which enables search space design and architecture search. Using this framework, we generate a family of popular QCNNs, those resembling reverse binary trees. We then evaluate this family of models on a music genre classification dataset, GTZAN, to justify the importance of circuit architecture. Furthermore, we employ a genetic algorithm to perform Quantum Phase Recognition (QPR) as an example of architecture search with our representation. This work provides a way to improve model performance without increasing complexity and to jump around the cost landscape to avoid barren plateaus. Finally, we implement the framework as an open-source Python package to enable dynamic QCNN creation and facilitate QCNN search space design for NAS.

Figures (13)

• Figure 1: The machine learning pipeline we implemented for music genre classification. Given an audio signal of a song (a), we generate two forms of data: tabular (b) and image (c). Each form has data preprocessing applied before being encoded into a quantum state (d). The QCNN circuit shown in (d) favours Principal Component Analysis (PCA) because qubits are pooled from bottom to top, and principal components are encoded from top to bottom. This architecture is an instance of the reverse binary tree family that we generated with our framework.
• Figure 2: An overview of our architectural representation for QCNNs. From a given set of gates, we build two-qubit unitary ansatzes. The representation then captures design motifs $M^l_k$ on different levels $l$ of the hierarchy. On the lowest level $l=1$, we define primitives which act as building blocks for the architecture. For example, a convolution operation with stride one is encoded as the directed graph $M_1^1$. The directed graph $M^1_3$ is a pooling operation that measures the bottom half of the circuit. Combined, they form the level two motif (e): a convolution-pooling unit $M^2_1$. Higher-level motifs consist of combinations of lower-level motifs up until the final level $l=L$, which contains only one motif $M^L_1$, the complete QCNN architecture. $M^L_1$ is a hierarchy of directed graphs fully specifying how to spread the unitary ansatzes across the circuit. The two lines of code $(e)$ and $(f)$ show the power of this representation as it is all that is required to create the entire QCNN circuit from Figure \ref{['fig:qcnn_pipeline']} (d). The code comes from the Python package we implemented based on the work of this paper. It facilitates dynamic QCNN creation and search space design.
• Figure 3: QCNN with the $F_m^{\rm{right}}$ pooling filter using low resolution image data. The accuracies for all genre pairs are provided.
• Figure 4: QCNN with the $F_m^{\rm{even}}$ pooling filter using low resolution image data. The accuracies for all genre pairs are provided.
• Figure 5: Expectation values for the circuit found via evolutionary search for a system of $N=15$ spins. Points represent a test set of $64\times64$ ground states for various $h_1$ and $h_2$ values of the Hamiltonian, $J=1$. The inside, middle and outside points were used to evaluate an architecture's fitness during search. The same color scale as in cong_quantum_2019 is used to facilitate comparison.