# Noisy intermediate-scale quantum (NISQ) algorithms

arXiv: https://arxiv.org/abs/2101.08448 · HTML: https://mlsanity.com/paper/2101.08448/

## Key facts

- Cited by 79 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 275 references that are in the map.
- First posted on arXiv 21 Jan 2021.

## Builds on (most cited first, 22 of 22)

- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Ising formulations of many NP problems](https://mlsanity.com/paper/1302.5843/) (2013)
- [Quantum Natural Gradient](https://mlsanity.com/paper/1909.02108/) (2019)
- [Quantum machine learning: a classical perspective](https://mlsanity.com/paper/1707.08561/) (2017)
- [The Born Supremacy: Quantum Advantage and Training of an Ising Born Machine](https://mlsanity.com/paper/1904.02214/) (2019)
- [Stochastic gradient descent for hybrid quantum-classical optimization](https://mlsanity.com/paper/1910.01155/) (2019)
- [Machine learning & artificial intelligence in the quantum domain](https://mlsanity.com/paper/1709.02779/) (2017)
- [Information Perspective to Probabilistic Modeling: Boltzmann Machines versus Born Machines](https://mlsanity.com/paper/1712.04144/) (2017)
- [Quantum versus Classical Generative Modelling in Finance](https://mlsanity.com/paper/2008.00691/) (2020)
- [Graph-theoretic Simplification of Quantum Circuits with the ZX-calculus](https://mlsanity.com/paper/1902.03178/) (2019)
- [Quantum autoencoders via quantum adders with genetic algorithms](https://mlsanity.com/paper/1709.07409/) (2017)
- [Computer-inspired Quantum Experiments](https://mlsanity.com/paper/2002.09970/) (2020)
- [Optimizing quantum heuristics with meta-learning](https://mlsanity.com/paper/1908.03185/) (2019)
- [Multiqubit and multilevel quantum reinforcement learning with quantum technologies](https://mlsanity.com/paper/1709.07848/) (2017)
- [Extracting Success from IBM's 20-Qubit Machines Using Error-Aware Compilation](https://mlsanity.com/paper/1903.10963/) (2019)
- [Bayesian Network Structure Learning Using Quantum Annealing](https://mlsanity.com/paper/1407.3897/) (2014)
- [Optimization of Quantum Circuit Mapping using Gate Transformation and Commutation](https://mlsanity.com/paper/1907.02686/) (2019)

## Built on by (most cited first, 30 of 79)

- [Theory of overparametrization in quantum neural networks](https://mlsanity.com/paper/2109.11676/) (2021)
- [Quantum machine learning beyond kernel methods](https://mlsanity.com/paper/2110.13162/) (2021)
- [The Inductive Bias of Quantum Kernels](https://mlsanity.com/paper/2106.03747/) (2021)
- [Parametrized quantum policies for reinforcement learning](https://mlsanity.com/paper/2103.05577/) (2021)
- [Federated Quantum Machine Learning](https://mlsanity.com/paper/2103.12010/) (2021)
- [Encoding-dependent generalization bounds for parametrized quantum circuits](https://mlsanity.com/paper/2106.03880/) (2021)
- [Training Quantum Embedding Kernels on Near-Term Quantum Computers](https://mlsanity.com/paper/2105.02276/) (2021)
- [Equivalence of quantum barren plateaus to cost concentration and narrow gorges](https://mlsanity.com/paper/2104.05868/) (2021)
- [Variational Quantum Reinforcement Learning via Evolutionary Optimization](https://mlsanity.com/paper/2109.00540/) (2021)
- [Quantum Vision Transformers](https://mlsanity.com/paper/2209.08167/) (2022)
- [Quantum Self-Attention Neural Networks for Text Classification](https://mlsanity.com/paper/2205.05625/) (2022)
- [Recent advances for quantum classifiers](https://mlsanity.com/paper/2108.13421/) (2021)
- [On Circuit-based Hybrid Quantum Neural Networks for Remote Sensing Imagery Classification](https://mlsanity.com/paper/2109.09484/) (2021)
- [A comprehensive review of Quantum Machine Learning: from NISQ to Fault Tolerance](https://mlsanity.com/paper/2401.11351/) (2024)
- [Quantum machine learning with differential privacy](https://mlsanity.com/paper/2103.06232/) (2021)
- [Quantum Recurrent Neural Networks for Sequential Learning](https://mlsanity.com/paper/2302.03244/) (2023)
- [Quantum Architecture Search via Continual Reinforcement Learning](https://mlsanity.com/paper/2112.05779/) (2021)
- [Asynchronous training of quantum reinforcement learning](https://mlsanity.com/paper/2301.05096/) (2023)
- [Power and limitations of single-qubit native quantum neural networks](https://mlsanity.com/paper/2205.07848/) (2022)
- [Classical-to-quantum convolutional neural network transfer learning](https://mlsanity.com/paper/2208.14708/) (2022)
- [Optimal training of variational quantum algorithms without barren plateaus](https://mlsanity.com/paper/2104.14543/) (2021)
- [Multiclass classification using quantum convolutional neural networks with hybrid quantum-classical learning](https://mlsanity.com/paper/2203.15368/) (2022)
- [Stochastic noise can be helpful for variational quantum algorithms](https://mlsanity.com/paper/2210.06723/) (2022)
- [Neural Error Mitigation of Near-Term Quantum Simulations](https://mlsanity.com/paper/2105.08086/) (2021)
- [Policy Gradients using Variational Quantum Circuits](https://mlsanity.com/paper/2203.10591/) (2022)
- [Adaptive shot allocation for fast convergence in variational quantum algorithms](https://mlsanity.com/paper/2108.10434/) (2021)
- [Learning Interpretable Representations of Entanglement in Quantum Optics Experiments using Deep Generative Models](https://mlsanity.com/paper/2109.02490/) (2021)
- [Learning the noise fingerprint of quantum devices](https://mlsanity.com/paper/2109.11405/) (2021)
- [Effects of quantum resources on the statistical complexity of quantum circuits](https://mlsanity.com/paper/2102.03282/) (2021)
- [Quantum Pufferfish Privacy: A Flexible Privacy Framework for Quantum Systems](https://mlsanity.com/paper/2306.13054/) (2023)

## Abstract (arXiv)

A universal fault-tolerant quantum computer that can solve efficiently problems such as integer factorization and unstructured database search requires millions of qubits with low error rates and long coherence times. While the experimental advancement towards realizing such devices will potentially take decades of research, noisy intermediate-scale quantum (NISQ) computers already exist. These computers are composed of hundreds of noisy qubits, i.e. qubits that are not error-corrected, and therefore perform imperfect operations in a limited coherence time. In the search for quantum advantage with these devices, algorithms have been proposed for applications in various disciplines spanning physics, machine learning, quantum chemistry and combinatorial optimization. The goal of such algorithms is to leverage the limited available resources to perform classically challenging tasks. In this review, we provide a thorough summary of NISQ computational paradigms and algorithms. We discuss the key structure of these algorithms, their limitations, and advantages. We additionally provide a comprehensive overview of various benchmarking and software tools useful for programming and testing NISQ devices.