Information-driven Nonlinear Quantum Neuron

The promising performance increase offered by quantum computing has led to the idea of applying it to neural networks. Studies in this regard can be divided into two main categories: simulating quantum neural networks with the standard quantum circuit model, and implementing them based on hardware. However, the ability to capture the non-linear behavior in neural networks using a computation process that usually involves linear quantum mechanics principles remains a major challenge in both categories. In this study, a hardware-efficient quantum neural network operating as an open quantum system is proposed, which presents non-linear behaviour. The model's compatibility with learning processes is tested through the obtained analytical results. In other words, we show that this dissipative model based on repeated interactions, which allows for easy parametrization of input quantum information, exhibits differentiable, non-linear activation functions.

[1]  Ufuk Korkmaz,et al.  Quantum collisional classifier driven by information reservoirs , 2022, Physical Review A.

[2]  A. Chiesa,et al.  High cooperativity coupling to nuclear spins on a circuit quantum electrodynamics architecture , 2022, Communications Physics.

[3]  T. Monz,et al.  A universal qudit quantum processor with trapped ions , 2021, Nature Physics.

[4]  Wilson Rosa de Oliveira,et al.  Quantum neuron with real weights , 2021, Neural Networks.

[5]  F. V. Massoli,et al.  A Leap among Quantum Computing and Quantum Neural Networks: A Survey , 2021, ACM Comput. Surv..

[6]  V. Giovannetti,et al.  Quantum collision models: Open system dynamics from repeated interactions , 2021, Physics Reports.

[7]  W S McCulloch,et al.  A logical calculus of the ideas immanent in nervous activity , 1990, The Philosophy of Artificial Intelligence.

[8]  J. P. Pascual,et al.  Analysis and Performance of Lumped-Element Kinetic Inductance Detectors for W-Band , 2021, IEEE Transactions on Microwave Theory and Techniques.

[9]  W. Cui,et al.  Nonlinear Quantum Neuron: A Fundamental Building Block for Quantum Neural Networks , 2020, Physical Review A.

[10]  M. Cattaneo,et al.  Collision Models Can Efficiently Simulate Any Multipartite Markovian Quantum Dynamics. , 2020, Physical review letters.

[11]  Fernando M de Paula Neto,et al.  Implementing Any Nonlinear Quantum Neuron , 2020, IEEE Transactions on Neural Networks and Learning Systems.

[12]  Roberto Prevete,et al.  A survey on modern trainable activation functions , 2020, Neural Networks.

[13]  Hsuan-Hao Lu,et al.  Quantum Phase Estimation with Time‐Frequency Qudits in a Single Photon , 2019, Advanced Quantum Technologies.

[14]  G. Guo,et al.  Building quantum neural networks based on a swap test , 2019, Physical Review A.

[15]  Fei Yan,et al.  A quantum engineer's guide to superconducting qubits , 2019, Applied Physics Reviews.

[16]  Soonwon Choi,et al.  Quantum convolutional neural networks , 2018, Nature Physics.

[17]  H. Riemann,et al.  Engineering long spin coherence times of spin–orbit qubits in silicon , 2018, Nature Materials.

[18]  John Preskill,et al.  Quantum Computing in the NISQ era and beyond , 2018, Quantum.

[19]  Amir Hussain,et al.  Applications of Deep Learning and Reinforcement Learning to Biological Data , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[20]  Marc Peter Deisenroth,et al.  Deep Reinforcement Learning: A Brief Survey , 2017, IEEE Signal Processing Magazine.

[21]  R. Rom'an-Ancheyta,et al.  Tailoring the thermalization time of a cavity field using distinct atomic reservoirs , 2017, Journal of the Optical Society of America B.

[22]  Nei Kato,et al.  State-of-the-Art Deep Learning: Evolving Machine Intelligence Toward Tomorrow’s Intelligent Network Traffic Control Systems , 2017, IEEE Communications Surveys & Tutorials.

[23]  Sophia E. Economou,et al.  Robustness of error-suppressing entangling gates in cavity-coupled transmon qubits , 2017, 1703.03514.

[24]  J. García-Ripoll,et al.  Coherent manipulation of three-qubit states in a molecular single-ion magnet , 2017 .

[25]  Cristian Romero García,et al.  Quantum Machine Learning , 2017, Encyclopedia of Machine Learning and Data Mining.

[26]  Robert Gardner,et al.  Quantum generalisation of feedforward neural networks , 2016, npj Quantum Information.

[27]  Demis Hassabis,et al.  Mastering the game of Go with deep neural networks and tree search , 2016, Nature.

[28]  Anmer Daskin Quantum Principal Component Analysis , 2015 .

[29]  Maria Schuld,et al.  The quest for a Quantum Neural Network , 2014, Quantum Information Processing.

[30]  Igor L. Markov,et al.  Limits on fundamental limits to computation , 2014, Nature.

[31]  Franco Scarselli,et al.  On the Complexity of Neural Network Classifiers: A Comparison Between Shallow and Deep Architectures , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[32]  Sebastian Deffner Information-driven current in a quantum Maxwell demon. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  S. Fei,et al.  Geometry of Quantum Computation with Qutrits , 2013, Scientific Reports.

[34]  C. Jarzynski,et al.  Information Processing and the Second Law of Thermodynamics: An Inclusive Hamiltonian Approach. , 2013, 1308.5001.

[35]  Franco Nori,et al.  QuTiP 2: A Python framework for the dynamics of open quantum systems , 2012, Comput. Phys. Commun..

[36]  T. Umeda,et al.  Hybrid quantum circuit with a superconducting qubit coupled to a spin ensemble. , 2011, Physical review letters.

[37]  J. Schmiedmayer,et al.  Cavity QED with magnetically coupled collective spin states. , 2011, Physical review letters.

[38]  Isaac L. Chuang,et al.  Quantum Computation and Quantum Information (10th Anniversary edition) , 2011 .

[39]  L. Bishop Circuit quantum electrodynamics , 2010, 1007.3520.

[40]  L Frunzio,et al.  High-cooperativity coupling of electron-spin ensembles to superconducting cavities. , 2010, Physical review letters.

[41]  F. Verstraete,et al.  Quantum computation and quantum-state engineering driven by dissipation , 2009 .

[42]  Erik Lucero,et al.  Emulation of a Quantum Spin with a Superconducting Phase Qudit , 2009, Science.

[43]  A. Harrow,et al.  Quantum algorithm for linear systems of equations. , 2008, Physical review letters.

[44]  R. Bertlmann,et al.  Bloch vectors for qudits , 2008, 0806.1174.

[45]  Jens Koch,et al.  Coupling superconducting qubits via a cavity bus , 2007, Nature.

[46]  Sean Hallgren Polynomial-time quantum algorithms for Pell's equation and the principal ideal problem , 2007, JACM.

[47]  W. V. Dam,et al.  Quantum algorithms for some hidden shift problems , 2002, SODA '03.

[48]  Mário Ziman,et al.  Diluting quantum information: An analysis of information transfer in system-reservoir interactions , 2002 .

[49]  V. Scarani,et al.  Thermalizing quantum machines: dissipation and entanglement. , 2001, Physical review letters.

[50]  Peter W. Shor,et al.  Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer , 1995, SIAM Rev..

[51]  F ROSENBLATT,et al.  The perceptron: a probabilistic model for information storage and organization in the brain. , 1958, Psychological review.

[52]  M. Levitt Spin Dynamics: Basics of Nuclear Magnetic Resonance , 2001 .