Sampling Problems on a Quantum Computer
arXiv:2402.16341 · doi:10.1109/QCE57702.2023.00062
Abstract
Due to the advances in the manufacturing of quantum hardware in the recent years, significant research efforts have been directed towards employing quantum methods to solving problems in various areas of interest. Thus a plethora of novel quantum methods have been developed in recent years. In this paper, we provide a survey of quantum sampling methods alongside needed theory and applications of those sampling methods as a starting point for research in this area. This work focuses in particular on Gaussian Boson sampling, quantum Monte Carlo methods, quantum variational Monte Carlo, quantum Boltzmann Machines and quantum Bayesian networks. We strive to provide a self-contained overview over the mathematical background, technical feasibility, applicability for other problems and point out potential areas of future research.
arXiv comment11 pages, 4 figures. Accepted at QCE 2023
References in corpus (39)
- The density-matrix renormalization group in the age of matrix product states
- Area laws for the entanglement entropy - a review
- Quantum computational advantage using photons
- Solving the Quantum Many-Body Problem with Artificial Neural Networks
- A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
- A Quantum Approximate Optimization Algorithm
- Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
- The Variational Quantum Eigensolver: a review of methods and best practices
- Quantum Random Number Generators
- From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz
- Gaussian Boson Sampling
- Quantum Natural Gradient
- Quantum Boltzmann Machine
- Boson Sampling from Gaussian States
- Green Function Monte Carlo with Stochastic Reconfiguration
- Study of the Two-Dimensional Frustrated J1-J2 Model with Neural Network Quantum States
- Weak binding between two aromatic rings: feeling the van der Waals attraction by quantum Monte Carlo methods
- Estimation of effective temperatures in quantum annealers for sampling applications: A case study with possible applications in deep learning
- A detailed study of Gaussian Boson Sampling
- Application of Quantum Annealing to Training of Deep Neural Networks
- Linear growth of quantum circuit complexity
- Searching for quantum speedup in quasistatic quantum annealers
- A Cluster Monte Carlo Algorithm for 2-Dimensional Spin Glasses
- Quantum Machine Learning for Electronic Structure Calculations
- Neural Quantum States of frustrated magnets: generalization and sign structure
- Quantum-Assisted Learning of Hardware-Embedded Probabilistic Graphical Models
- Sign-Problem-Free Fermionic Quantum Monte Carlo: Developments and Applications
- Quantum Neural Network States: A Brief Review of Methods and Applications
- Variational Quantum Boltzmann Machines
- The Boundary for Quantum Advantage in Gaussian Boson Sampling
- QIRAL: A High Level Language for Lattice QCD Code Generation
- Enhancing Generative Models via Quantum Correlations
- Quantum-enhanced Markov chain Monte Carlo
- Experimental Gaussian Boson Sampling
- Learning the ground state of a non-stoquastic quantum Hamiltonian in a rugged neural network landscape
- Quantum Machine-Learning for Eigenstate Filtration in Two-Dimensional Materials
- Grammar-aware sentence classification on quantum computers
- Expressive power of complex-valued restricted Boltzmann machines for solving non-stoquastic Hamiltonians
- Clever Design, Unexpected Obstacles: Insights on Implementing a Quantum Boltzmann Machine