Completely Quantum Neural Networks

Artificial neural networks are at the heart of modern deep learning algorithms. We describe how to embed and train a general neural network in a quantum annealer without introducing any classical el-ement in training. To implement the network on a state-of-the-art quantum annealer, we develop three crucial ingredi-ents: binary encoding the free parameters of the network, polynomial approximation of the activation function, and reduction of binary higher-order polynomials into quadratic ones. Together, these ideas allow encoding the loss function as an Ising model Hamiltonian. The quantum annealer then trains the network by finding the ground state. We implement this for an elementary network and illustrate the advantages of quantum training: its consistency in finding the global minimum of the loss function and the fact that the network training converges in a single annealing step, which leads to short training times while maintaining a high classification performance. Our approach opens a novel avenue for the quantum training of general machine learning models.

[1]  Jack Y. Araz,et al.  Classical versus Quantum: comparing Tensor Network-based Quantum Circuits on LHC data , 2022, Physical Review A.

[2]  M. Spannowsky,et al.  Anomaly detection in high-energy physics using a quantum autoencoder , 2021, Physical Review D.

[3]  Tat-Jun Chin,et al.  Quantum Annealing Formulation for Binary Neural Networks , 2021, 2021 Digital Image Computing: Techniques and Applications (DICTA).

[4]  M. Spannowsky,et al.  Quantum Optimisation of Complex Systems with a Quantum Annealer , 2021, Physical Review A.

[5]  M. Spannowsky,et al.  Unsupervised event classification with graphs on classical and photonic quantum computers , 2021, Journal of High Energy Physics.

[6]  T. Kanao,et al.  Quantum annealing using vacuum states as effective excited states of driven systems , 2020 .

[7]  Daniel A. Lidar,et al.  Quantum adiabatic machine learning by zooming into a region of the energy surface , 2020, Physical Review A.

[8]  M. Spannowsky,et al.  Quantum machine learning for particle physics using a variational quantum classifier , 2020, Journal of High Energy Physics.

[9]  Daniel A. Lidar,et al.  Prospects for quantum enhancement with diabatic quantum annealing , 2020, Nature Reviews Physics.

[10]  Jens Eisert,et al.  On the Quantum versus Classical Learnability of Discrete Distributions , 2020, Quantum.

[11]  J. Tanaka,et al.  Event Classification with Quantum Machine Learning in High-Energy Physics , 2020, Computing and Software for Big Science.

[12]  Nathan Killoran,et al.  Transfer learning in hybrid classical-quantum neural networks , 2019, Quantum.

[13]  Bruce Yabsley,et al.  Search for heavy particles decaying into a top-quark pair in the fully hadronic final state in pp collisions at √s = 13 TeV with the ATLAS detector , 2019 .

[14]  Alba Cervera-Lierta Exact Ising model simulation on a quantum computer , 2018, Quantum.

[15]  Seth Lloyd,et al.  Continuous-variable quantum neural networks , 2018, Physical Review Research.

[16]  J. Caudron,et al.  Search for heavy particles decaying into top-quark pairs using lepton-plus-jets events in proton-proton collisions at $\sqrt{s} = 13$ TeV with the ATLAS detector , 2018, 1804.10823.

[17]  M. Schuld,et al.  Circuit-centric quantum classifiers , 2018, Physical Review A.

[18]  Hartmut Neven,et al.  Classification with Quantum Neural Networks on Near Term Processors , 2018, 1802.06002.

[19]  Daniel A. Lidar,et al.  Solving a Higgs optimization problem with quantum annealing for machine learning , 2017, Nature.

[20]  Liwei Wang,et al.  The Expressive Power of Neural Networks: A View from the Width , 2017, NIPS.

[21]  G. Santoro,et al.  Dissipation in adiabatic quantum computers: lessons from an exactly solvable model , 2017, 1704.03183.

[22]  Vasil S. Denchev,et al.  Computational multiqubit tunnelling in programmable quantum annealers , 2015, Nature Communications.

[23]  Daniel A. Lidar,et al.  Tunneling and speedup in quantum optimization for permutation-symmetric problems , 2015, 1511.03910.

[24]  M. Benedetti,et al.  Estimation of effective temperatures in quantum annealers for sampling applications: A case study with possible applications in deep learning , 2015, 1510.07611.

[25]  Ryan Babbush,et al.  The theory of variational hybrid quantum-classical algorithms , 2015, 1509.04279.

[26]  Walter Vinci,et al.  Maximum-Entropy Inference with a Programmable Annealer , 2015, Scientific Reports.

[27]  E. Farhi,et al.  A Quantum Approximate Optimization Algorithm , 2014, 1411.4028.

[28]  Alán Aspuru-Guzik,et al.  Bayesian network structure learning using quantum annealing , 2014, The European Physical Journal Special Topics.

[29]  Daniel A. Lidar,et al.  Consistency tests of classical and quantum models for a quantum annealer , 2014, 1403.4228.

[30]  J. Swanson Search for anomalous production in the highly-boosted all-hadronic final state , 2014 .

[31]  M. W. Johnson,et al.  Entanglement in a Quantum Annealing Processor , 2014, 1401.3500.

[32]  M. W. Johnson,et al.  Thermally assisted quantum annealing of a 16-qubit problem , 2013, Nature Communications.

[33]  Alán Aspuru-Guzik,et al.  A variational eigenvalue solver on a photonic quantum processor , 2013, Nature Communications.

[34]  S. D. Pinski,et al.  Adiabatic Quantum Computing , 2011, 1108.0560.

[35]  M. Sipser,et al.  Quantum Computation by Adiabatic Evolution , 2000, quant-ph/0001106.

[36]  Rosenbaum,et al.  Quantum annealing of a disordered magnet , 1999, Science.

[37]  H. Nishimori,et al.  Quantum annealing in the transverse Ising model , 1998, cond-mat/9804280.

[38]  J. D. Doll,et al.  Quantum annealing: A new method for minimizing multidimensional functions , 1994, chem-ph/9404003.

[39]  Kurt Hornik,et al.  Approximation capabilities of multilayer feedforward networks , 1991, Neural Networks.

[40]  George Cybenko,et al.  Approximation by superpositions of a sigmoidal function , 1989, Math. Control. Signals Syst..

[41]  S. Adachi,et al.  Search for heavy particles decaying into top-quark pairs using lepton-plus-jets events in proton-proton collisions at root s=13 TeV with the ATLAS detector , 2018 .

[42]  Alán Aspuru-Guzik,et al.  The theory of variational hybrid quantum-classical algorithms , 2015, 1509.04279.