The Born Supremacy: Quantum Advantage and Training of an Ising Born Machine

Abstract

The search for an application of near-term quantum devices is widespread. Quantum Machine Learning is touted as a potential utilisation of such devices, particularly those which are out of the reach of the simulation capabilities of classical computers. In this work, we propose a generative Quantum Machine Learning Model, called the Ising Born Machine (IBM), which we show cannot, in the worst case, and up to suitable notions of error, be simulated efficiently by a classical device. We also show this holds for all the circuit families encountered during training. In particular, we explore quantum circuit learning using non-universal circuits derived from Ising Model Hamiltonians, which are implementable on near term quantum devices. We propose two novel training methods for the IBM by utilising the Stein Discrepancy and the Sinkhorn Divergence cost functions. We show numerically, both using a simulator within Rigetti's Forest platform and on the Aspen-1 16Q chip, that the cost functions we suggest outperform the more commonly used Maximum Mean Discrepancy (MMD) for differentiable training. We also propose an improvement to the MMD by proposing a novel utilisation of quantum kernels which we demonstrate provides improvements over its classical counterpart. We discuss the potential of these methods to learn `hard' quantum distributions, a feat which would demonstrate the advantage of quantum over classical computers, and provide the first formal definitions for what we call `Quantum Learning Supremacy'. Finally, we propose a novel view on the area of quantum circuit compilation by using the IBM to `mimic' target quantum circuits using classical output data only.

18 pages + supplementary material, 11 figures. Implementation at https://github.com/BrianCoyle/IsingBornMachine v4 : Close to journal published version - significant text structure change, split into main text & appendices. See v2 for unsplit version

References in corpus (28)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Generative Adversarial Networks
• Quantum algorithm for solving linear systems of equations
• A Quantum Approximate Optimization Algorithm
• Parameterized quantum circuits as machine learning models
• Evaluating analytic gradients on quantum hardware
• Quantum-assisted quantum compiling
• The Expressive Power of Parameterized Quantum Circuits
• A Kernel Method for the Two-Sample Problem
• A quantum-inspired classical algorithm for recommendation systems
• Concrete Categorical Model of a Quantum Circuit Description Language with Measurement
• Learning in Implicit Generative Models
• The Born Supremacy: Quantum Advantage and Training of an Ising Born Machine
• Quantum principal component analysis only achieves an exponential speedup because of its state preparation assumptions
• Sample Complexity of Sinkhorn divergences
• Interpolating between Optimal Transport and MMD using Sinkhorn Divergences
• Quantum Supremacy for Simulating A Translation-Invariant Ising Spin Model
• On integral probability metrics, ϕ-divergences and binary classification
• Learning and Inference on Generative Adversarial Quantum Circuits
• Universality, Characteristic Kernels and RKHS Embedding of Measures
• Learning to learn with quantum neural networks via classical neural networks
• Quantum-inspired low-rank stochastic regression with logarithmic dependence on the dimension
• Generative model benchmarks for superconducting qubits
• Sample complexity of device-independently certified "quantum supremacy"
• An efficient quantum algorithm for generative machine learning
• Robust Implementation of Generative Modeling with Parametrized Quantum Circuits
• Entanglement Entropy of Target Functions for Image Classification and Convolutional Neural Network
• On Solving Linear Systems in Sublinear Time

Cited by in corpus (85)

• Variational Quantum Algorithms
• Noisy intermediate-scale quantum (NISQ) algorithms
• Robust data encodings for quantum classifiers
• Barren Plateaus in Variational Quantum Computing
• Quantum Computing for High-Energy Physics: State of the Art and Challenges. Summary of the QC4HEP Working Group
• Quantum agents in the Gym: a variational quantum algorithm for deep Q-learning
• Solving nonlinear differential equations with differentiable quantum circuits
• The Born Supremacy: Quantum Advantage and Training of an Ising Born Machine
• Prospects for Quantum Enhancement with Diabatic Quantum Annealing
• Quantum computing models for artificial neural networks
• Quantum Machine Learning: from physics to software engineering
• On the Quantum versus Classical Learnability of Discrete Distributions
• Enhancing Generative Models via Quantum Correlations
• Does provable absence of barren plateaus imply classical simulability?
• Understanding quantum machine learning also requires rethinking generalization
• NISQ Computers: A Path to Quantum Supremacy
• Learning quantum data with the quantum Earth Mover's distance
• Synergy Between Quantum Circuits and Tensor Networks: Short-cutting the Race to Practical Quantum Advantage
• Generative quantum machine learning via denoising diffusion probabilistic models
• Markovian Quantum Neuroevolution for Machine Learning
• Generalized quantum circuit differentiation rules
• Quantum phase detection generalisation from marginal quantum neural network models
• Variational inference with a quantum computer
• Quantum Kernel Methods for Solving Differential Equations
• Quantum Machine Learning for Finance
• Style-based quantum generative adversarial networks for Monte Carlo events
• Generative Quantum Learning of Joint Probability Distribution Functions
• Application-Motivated, Holistic Benchmarking of a Full Quantum Computing Stack
• Qubit-efficient encoding schemes for binary optimisation problems
• Expressibility and trainability of parameterized analog quantum systems for machine learning applications
• Trainability barriers and opportunities in quantum generative modeling
• A Framework for Demonstrating Practical Quantum Advantage: Racing Quantum against Classical Generative Models
• Medical image classification via quantum neural networks
• Grover search revisited; application to image pattern matching
• Interpretable Quantum Advantage in Neural Sequence Learning
• Tree tensor network classifiers for machine learning: from quantum-inspired to quantum-assisted
• Generative machine learning with tensor networks: benchmarks on near-term quantum computers
• A single $T$-gate makes distribution learning hard
• A performance characterization of quantum generative models
• Tight and Efficient Gradient Bounds for Parameterized Quantum Circuits
• Quantum Natural Language Processing
• Generalization of Quantum Machine Learning Models Using Quantum Fisher Information Metric
• Approximate complex amplitude encoding algorithm and its application to data classification problems
• Quantum Quantile Mechanics: Solving Stochastic Differential Equations for Generating Time-Series
• A super-polynomial quantum-classical separation for density modelling
• Networked Quantum Services
• Comparing the effects of Boltzmann machines as associative memory in Generative Adversarial Networks between classical and quantum sampling
• Conditional Born machine for Monte Carlo event generation
• What can we learn from quantum convolutional neural networks?
• A Hyperparameter Study for Quantum Kernel Methods
• Variational Quantum Cloning: Improving Practicality for Quantum Cryptanalysis
• Mitigating errors by quantum verification and post-selection
• VQC-Based Reinforcement Learning with Data Re-uploading: Performance and Trainability
• Introducing Non-Linear Activations into Quantum Generative Models
• Opportunities and challenges of quantum computing for climate modelling
• Protocols for classically training quantum generative models on probability distributions
• A Continuous Variable Born Machine
• Parameterized quantum circuits as universal generative models for continuous multivariate distributions
• A Photonic Parameter-shift Rule: Enabling Gradient Computation for Photonic Quantum Computers
• Investigating the Effect of Noise on the Training Performance of Hybrid Quantum Neural Networks
• Generalization Error Bound for Quantum Machine Learning in NISQ Era -- A Survey
• F-Divergences and Cost Function Locality in Generative Modelling with Quantum Circuits
• Quantum supremacy and quantum phase transitions
• Generative model for learning quantum ensemble via optimal transport loss
• Protocols for Trainable and Differentiable Quantum Generative Modelling
• Application of quantum-inspired generative models to small molecular datasets
• Quantum self-learning Monte Carlo with quantum Fourier transform sampler
• Quantum Kernel Evaluation via Hong-Ou-Mandel Interference
• Quantum Computing for Data Centric Engineering and Science
• Error-mitigated photonic quantum circuit Born machine
• Quantum supremacy with analog quantum processors for material science and machine learning
• Tensor tree learns hidden relational structures in data to construct generative models
• On the average-case complexity of learning output distributions of quantum circuits
• Cross-platform hardware benchmark of style-based quantum GANs for data augmentation on superconducting and trapped-ion processors
• Multidimensional Quantum Generative Modeling by Quantum Hartley Transform
• On the learning abilities of photonic continuous-variable Born machines
• Building Continuous Quantum-Classical Bayesian Neural Networks for a Classical Clinical Dataset
• Quantum Algorithms for Unsupervised Machine Learning and Neural Networks
• Variational Quantum Generative Modeling by Sampling Expectation Values of Tunable Observables
• Quantum Model-Discovery
• Quantum community detection via deterministic elimination
• Quantum Chebyshev Probabilistic Models for Fragmentation Functions
• LArTPC hit-based topology classification with quantum machine learning and symmetry
• Multivariate unbounded quantum regression via log-ratio probabilities mitigating barren plateaus
• Quantum Machine Learning for Climate Modelling