Deep recurrent networks predicting the gap evolution in adiabatic quantum computing

Abstract

In adiabatic quantum computing finding the dependence of the gap of the Hamiltonian as a function of the parameter varied during the adiabatic sweep is crucial in order to optimize the speed of the computation. Inspired by this challenge, in this work, we explore the potential of deep learning for discovering a mapping from the parameters that fully identify a problem Hamiltonian to the aforementioned parametric dependence of the gap applying different network architectures. Through this example, we conjecture that a limiting factor for the learnability of such problems is the size of the input, that is, how the number of parameters needed to identify the Hamiltonian scales with the system size. We show that a long short-term memory network succeeds in predicting the gap when the parameter space scales linearly with system size. Remarkably, we show that once this architecture is combined with a convolutional neural network to deal with the spatial structure of the model, the gap evolution can even be predicted for system sizes larger than the ones seen by the neural network during training. This provides a significant speedup in comparison with the existing exact and approximate algorithms in calculating the gap.

References in corpus (36)

• Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Machine learning phases of matter
• Many-body quantum state tomography with neural networks
• Learning phase transitions by confusion
• Quantum Search by Local Adiabatic Evolution
• Discovering Phase Transitions with Unsupervised Learning
• Quantum Computation by Adiabatic Evolution
• Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders
• Reinforcement Learning in Different Phases of Quantum Control
• Information-theoretic bounds on quantum advantage in machine learning
• Anderson localization casts clouds over adiabatic quantum optimization
• Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines
• Provably efficient machine learning for quantum many-body problems
• Quantum many-body dynamics in two dimensions with artificial neural networks
• Neural-Network Quantum States, String-Bond States, and Chiral Topological States
• Demonstration of a scaling advantage for a quantum annealer over simulated annealing
• Machine learning vortices at the Kosterlitz-Thouless transition
• Adiabatic approximation with exponential accuracy for many-body systems and quantum computation
• Size dependence of the minimum excitation gap in the Quantum Adiabatic Algorithm
• First Order Quantum Phase Transition in Adiabatic Quantum Computation
• Classical variational simulation of the Quantum Approximate Optimization Algorithm
• Exponential complexity of an adiabatic algorithm for an NP-complete problem
• Evaluating energy differences on a quantum computer with robust phase estimation
• Expectation Values from the Single-Layer Quantum Approximate Optimization Algorithm on Ising Problems
• Adiabatic preparation without Quantum Phase Transitions
• Scalable neural networks for the efficient learning of disordered quantum systems
• Deep Learning of Quantum Many-Body Dynamics via Random Driving
• Policy Guided Monte Carlo: Reinforcement Learning Markov Chain Dynamics
• Error suppression in adiabatic quantum computing with qubit ensembles
• Solving Quadratic Unconstrained Binary Optimization with divide-and-conquer and quantum algorithms
• Dynamical quantum phase transitions
• Neural networks in quantum many-body physics: a hands-on tutorial
• Divide and Conquer for Combinatorial Optimization and Distributed Quantum Computation
• Learnability and Complexity of Quantum Samples
• Deep learning of spatial densities in inhomogeneous correlated quantum systems

Cited by in corpus (7)

• Challenges and Opportunities in Quantum Optimization
• Deep learning of many-body observables and quantum information scrambling
• Deep learning optimal quantum annealing schedules for random Ising models
• Hybrid quantum-classical unsupervised data clustering based on the self-organizing feature map
• Synergy between noisy quantum computers and scalable classical deep learning
• Challenges and opportunities in the supervised learning of quantum circuit outputs
• Adiabatic Dynamics of Entanglement