Quantum convolutional neural networks

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.Machine learning based on neural networks has recently provided significant advances for many practical applications 1 . In physics, one natural application involves the study of quantum many-body systems, where the extreme complexity of many-body states often makes theoretical analysis intractable. This has led to a number of recent works using machine learning to study properties of quantum systems 2-7 , using physical concepts to interpret machine learning 8,9 , or using quantum computers to enhance conventional machine learning tasks 10-13 .In this work, motivated by the progress towards realizing quantum information processors 14-17 , we bridge these approaches by proposing a quantum circuit model inspired by machine learning and illustrating its success for two important classes of quantum many-body problems. The first class of problems we consider is quantum phase recognition (QPR), which asks whether a given input quantum state ρ in belongs to a particular quantum phase of matter. Critically, in contrast to many existing schemes based on tensor network descriptions 18-20 , we assume ρ in is prepared in a physical system without direct access to its classical description. The second class, quantum error correction (QEC) optimization, asks for an optimal QEC code for a given, a priori unknown error model such as dephasing or potentially correlated depolarization in realistic experimental settings.The highly complex and intrinsically quantum nature of these problems makes them particularly difficult to solve using existing classical and quantum machine learning techniques. While conventional machine learning with large-scale neural networks can successfully solve analogous classical problems such as image recognition or improving classical error correction 1 , the exponentially large many-body...

Quantum supremacy using a programmable superconducting processor

“…Quantum supremacy also heralds the era of noisy intermediatescale quantum (NISQ) technologies 15 . The benchmark task we demonstrate has an immediate application in generating certifiable random numbers (S. Aaronson, manuscript in preparation); other initial uses for this new computational capability may include optimization 16,17 , machine learning [18][19][20][21] , materials science and chemistry [22][23][24] . However, realizing the full promise of quantum computing (using Shor's algorithm for factoring, for example) still requires technical leaps to engineer fault-tolerant logical qubits [25][26][27][28][29] .…”

Entanglement-based quantum deep learning

“…This is because efficient computation by exponentially reducing the number of parameters can be implemented using the quantum convolutional neural network as described in Ref. [42].…”

“…Now, some quantum machine learning algorithms have been proposed and demonstrated [23][24][25][26][27][28][29][30][31][32][33], such as quantum support vector machine [25], supervised and unsupervised machine learning [23], quantum-enhanced machine learning [27], and distributed quantum learning [33]. Based on these algorithms, some schemes of quantum deep learning (QDL) have been discussed [34][35][36][37][38][39][40][41][42][43][44]. Quantum…”

“…Quantum Hopfield neural network based on the simulation of sparse Hamiltonian and the solution of linear systems of equations has been discussed to realize exponential speed up in computation and training [39]. Quantum convolutional neural network based on the reverse-direction correspondence of the multi-scale entanglement renormalization ansatz has been analyzed to realize efficient computation by exponentially reducing the number of parameters [42].…”

Rapid Classification of Quantum Sources Enabled by Machine Learning

“…[22][23][24][25][26][27] Recently, ML algorithms have also been applied to quantum photonics. [28][29][30][31][32][33][34] Combining the Bayesian phase estimation with Hamiltonian Learning techniques for analyzing large datasets www.advancedsciencenews.com www.advquantumtech.com from nitrogen vacancy (NV) centers in bulk diamond allowed for magnetic field measurements with extreme sensitivity at room temperature. [35] Hamiltonian Learning was adopted for the characterization of different quantum systems, [36] including the characterization of electron spin states in diamond NV centers.…”