Quantum convolutional neural networks

Iris Cong,Soonwon Choi,Mikhail D Lukin

doi:10.1038/s41567-019-0648-8

Iris Cong, Soonwon Choi + Show 1 more

Open Access

https://doi.org/10.1038/s41567-019-0648-8

Copy DOI

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.

Highlights

We introduce and analyze a novel quantum machine learning model motivated by convolutional neural networks
We introduce a quantum machine learning method for quantum phase recognition (QPR) and quantum error correction (QEC) optimization, provide both theoretical insight and numerical demonstrations for its success, and show its feasibility for near-term experimental implementation
The performance of a QPR solver can be quantified by sample complexity[21]: what is the expected number of copies of the input state required to identify its quantum phase? We demonstrate that the sample complexity of our exact quantum convolutional neural network (QCNN) circuit is significantly better than that of conventional methods

Summary

Z QEC X Z

To illustrate the potential of this procedure, we consider a two-layer QCNN with N = 9 physical qubits and 126 variational parameters (Figure 5a and Methods) This particular architecture includes the nested (classical) repetition codes and the 9-qubit Shor code[38]; in the following, we compare our performance to the better of the two. For a realistic effective coupling strength Ω ∼ 2π ×10−100 MHz and singlequbit coherence time τ ∼ 200 μs limited by the Rydberg state lifetime, approximately Ωτ ∼ 2π × 103 − 104 multiqubit operations can be performed, and a d = 4 QCNN on N ∼ 100 qubits feasible These estimates are reasonably conservative as we have not considered advanced control techniques such as pulse-shaping[46], or potentially parallelizing independent multi-qubit operations. While we have used a finite-difference scheme to compute gradients in our learning demonstrations, the structural similarity of QCNN with its classical counterpart motivates adoption of more efficient schemes such as backpropagation[1]

Methods

V1 V2X V1 V2 X V1 V2X V1 V2X V1 V2X V1 V2

Findings

QEC criterion