Supervised learning of random quantum circuits via scalable neural networks

Abstract

Predicting the output of quantum circuits is a hard computational task that plays a pivotal role in the development of universal quantum computers. Here we investigate the supervised learning of output expectation values of random quantum circuits. Deep convolutional neural networks (CNNs) are trained to predict single-qubit and two-qubit expectation values using databases of classically simulated circuits. These circuits are represented via an appropriately designed one-hot encoding of the constituent gates. The prediction accuracy for previously unseen circuits is analyzed, also making comparisons with small-scale quantum computers available from the free IBM Quantum program. The CNNs often outperform the quantum devices, depending on the circuit depth, on the network depth, and on the training set size. Notably, our CNNs are designed to be scalable. This allows us exploiting transfer learning and performing extrapolations to circuits larger than those included in the training set. These CNNs also demonstrate remarkable resilience against noise, namely, they remain accurate even when trained on (simulated) expectation values averaged over very few measurements.

arXiv comment17+ pages, 18 figures

References in corpus (44)

• Adam: A Method for Stochastic Optimization
• Very Deep Convolutional Networks for Large-Scale Image Recognition
• Quantum Computing in the NISQ era and beyond
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Quantum Computing
• An introduction to quantum machine learning
• Predicting Many Properties of a Quantum System from Very Few Measurements
• Strong quantum computational advantage using a superconducting quantum processor
• Quantum annealing with more than one hundred qubits
• Power of data in quantum machine learning
• Theory of Quantum Annealing of an Ising Spin Glass
• Machine learning prediction errors better than DFT accuracy
• Defining and detecting quantum speedup
• How to represent crystal structures for machine learning: towards fast prediction of electronic properties
• ProjectQ: An Open Source Software Framework for Quantum Computing
• Deep Learning Scaling is Predictable, Empirically
• Deep Learning is Robust to Massive Label Noise
• Improved classical simulation of quantum circuits dominated by Clifford gates
• Experimental signature of programmable quantum annealing
• QuEST and High Performance Simulation of Quantum Computers
• Provably efficient machine learning for quantum many-body problems
• Improving Variational Quantum Optimization using CVaR
• Quantum versus Classical Annealing of Ising Spin Glasses
• Integrating Neural Networks with a Quantum Simulator for State Reconstruction
• Establishing the Quantum Supremacy Frontier with a 281 Pflop/s Simulation
• Intel Quantum Simulator: A cloud-ready high-performance simulator of quantum circuits
• Understanding Quantum Tunneling through Quantum Monte Carlo Simulations
• Neural Predictor based Quantum Architecture Search
• Precise measurement of quantum observables with neural-network estimators
• Efficient Tensor Network ansatz for high-dimensional quantum many-body problems
• Extensive deep neural networks for transferring small scale learning to large scale systems
• Convolutional neural networks for atomistic systems
• Machine learning assisted readout of trapped-ion qubits
• Going Beyond Bell's Theorem
• Quantum Monte Carlo tunneling from quantum chemistry to quantum annealing
• Quantum Monte Carlo Simulations of Tunneling in Quantum Adiabatic Optimization
• Supervised machine learning of ultracold atoms with speckle disorder
• Scalable neural networks for the efficient learning of disordered quantum systems
• A deep learning model for noise prediction on near-term quantum devices
• Understanding Quantum Tunneling using Diffusion Monte Carlo Simulations
• Supervised learning of few dirty bosons with variable particle number
• Tunneling in projective quantum Monte Carlo simulations with guiding wave functions
• Deep learning density functionals for gradient descent optimization
• Deep learning of spatial densities in inhomogeneous correlated quantum systems

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