Quantum Machine Learning For Classical Data
arXiv:2105.03684
Abstract
In this dissertation, we study the intersection of quantum computing and supervised machine learning algorithms, which means that we investigate quantum algorithms for supervised machine learning that operate on classical data. This area of research falls under the umbrella of quantum machine learning, a research area of computer science which has recently received wide attention. In particular, we investigate to what extent quantum computers can be used to accelerate supervised machine learning algorithms. The aim of this is to develop a clear understanding of the promises and limitations of the current state of the art of quantum algorithms for supervised machine learning, but also to define directions for future research in this exciting field. We start by looking at supervised quantum machine learning (QML) algorithms through the lens of statistical learning theory. In this framework, we derive novel bounds on the computational complexities of a large set of supervised QML algorithms under the requirement of optimal learning rates. Next, we give a new bound for Hamiltonian simulation of dense Hamiltonians, a major subroutine of most known supervised QML algorithms, and then derive a classical algorithm with nearly the same complexity. We then draw the parallels to recent "quantum-inspired" results, and will explain the implications of these results for quantum machine learning applications. Looking for areas which might bear larger advantages for QML algorithms, we finally propose a novel algorithm for Quantum Boltzmann machines, and argue that quantum algorithms for quantum data are one of the most promising applications for QML with potentially exponential advantage over classical approaches.
arXiv commentPhD thesis. arXiv admin note: text overlap with arXiv:1905.09902
References in corpus (60)
- Playing Atari with Deep Reinforcement Learning
- Quantum Machine Learning
- Quantum algorithm for solving linear systems of equations
- Barren plateaus in quantum neural network training landscapes
- Solving the Quantum Many-Body Problem with Artificial Neural Networks
- Quantum support vector machine for big data classification
- Quantum machine learning in feature Hilbert spaces
- Quantum principal component analysis
- Quantum random access memory
- Optimal Hamiltonian Simulation by Quantum Signal Processing
- Quantum algorithm for systems of linear equations with exponentially improved dependence on precision
- Quantum algorithms for supervised and unsupervised machine learning
- Quantum Data Fitting
- Quantum machine learning: a classical perspective
- Limits on Fundamental Limits to Computation
- On the relationship between continuous- and discrete-time quantum walk
- Hamiltonian simulation with nearly optimal dependence on all parameters
- Simulating chemistry using quantum computers
- Restricted-Boltzmann-Machine Learning for Solving Strongly Correlated Quantum Systems
- Architectures for a quantum random access memory
- Preconditioned quantum linear system algorithm
- Prediction by linear regression on a quantum computer
- Quantum simulation of time-dependent Hamiltonians and the convenient illusion of Hilbert space
- Learning Thermodynamics with Boltzmann Machines
- A quantum linear system algorithm for dense matrices
- Sampling from the thermal quantum Gibbs state and evaluating partition functions with a quantum computer
- Tomography and Generative Data Modeling via Quantum Boltzmann Training
- A Quantum-Quantum Metropolis Algorithm
- Quantum Algorithm for Linear Regression
- Quantum principal component analysis only achieves an exponential speedup because of its state preparation assumptions
- Improving CUR Matrix Decomposition and the Nyström Approximation via Adaptive Sampling
- Quantum-inspired algorithms in practice
- Sampling-based sublinear low-rank matrix arithmetic framework for dequantizing quantum machine learning
- Quantum assisted Gaussian process regression
- Fast inversion, preconditioned quantum linear system solvers, and fast evaluation of matrix functions
- Universal discriminative quantum neural networks
- Hamiltonian Simulation with Optimal Sample Complexity
- Adversarial quantum circuit learning for pure state approximation
- Operator Lipschitz Functions
- Quantum linear systems algorithms: a primer
- Quantum-inspired low-rank stochastic regression with logarithmic dependence on the dimension
- Learning with Errors is easy with quantum samples
- Dynamical mean field theory algorithm and experiment on quantum computers
- Hamiltonian Simulation by Uniform Spectral Amplification
- Computation of molecular excited states on IBM quantum computers using a discriminative variational quantum eigensolver
- Advances in quantum machine learning
- Efficient quantum circuits for arbitrary sparse unitaries
- Generative training of quantum Boltzmann machines with hidden units
- Diving into the shallows: a computational perspective on large-scale shallow learning
- Cost function embedding and dataset encoding for machine learning with parameterized quantum circuits
- Sublinear quantum algorithms for training linear and kernel-based classifiers
- Lecture Notes on Randomized Linear Algebra
- Quantum Language Processing
- Quantum Inspired Training for Boltzmann Machines
- Towards More Efficient SPSD Matrix Approximation and CUR Matrix Decomposition
- On sparse representations of linear operators and the approximation of matrix products
- Quantum algorithms for topological and geometric analysis of big data
- Explicit lower bounds on strong quantum simulation
- Nonlinear regression based on a hybrid quantum computer
- Weighted sampling of outer products