# Quantum-inspired algorithms in practice

@article{Arrazola2019QuantuminspiredAI, title={Quantum-inspired algorithms in practice}, author={Juan Miguel Arrazola and Alain Delgado and Bhaskar Roy Bardhan and Seth Lloyd}, journal={Quantum}, year={2019}, volume={4}, pages={307} }

We study the practical performance of quantum-inspired algorithms for recommendation systems and linear systems of equations. These algorithms were shown to have an exponential asymptotic speedup compared to previously known classical methods for problems involving low-rank matrices, but with complexity bounds that exhibit a hefty polynomial overhead compared to quantum algorithms. This raised the question of whether these methods were actually useful in practice. We conduct a theoretical…

## 76 Citations

### Quantum-Inspired Classical Algorithms for Singular Value Transformation

- Computer ScienceMFCS
- 2020

This paper develops quantum-inspired algorithms for a large class of matrix transformations that are defined via the singular value decomposition of the matrix and obtains classical algorithms with complexity polynomially related to the complexity of the best quantum algorithms for singular value transformation recently developed.

### Sampling-based sublinear low-rank matrix arithmetic framework for dequantizing Quantum machine learning

- Computer ScienceSTOC
- 2020

This work develops classical algorithms for SVT that run in time independent of input dimension, under suitable quantum-inspired sampling assumptions, and gives compelling evidence that in the corresponding QRAM data structure input model, quantum SVT does not yield exponential quantum speedups.

### Quantum-Inspired Algorithms for Solving Low-Rank Linear Equation Systems with Logarithmic Dependence on the Dimension

- Computer Science, MathematicsISAAC
- 2020

The pseudoinverse of a low-rank matrix is implemented allowing us to sample from the solution to the problem Ax = b using fast sampling techniques, indicating that more low- rank quantum algorithms can be “dequantised” into classical length-square sampling algorithms.

### Quantum-Inspired Sublinear Algorithm for Solving Low-Rank Semidefinite Programming

- Computer ScienceMFCS
- 2020

A proof-of-principle sublinear-time algorithm for solving SDPs with low-rank constraints; specifically, given an SDP with $m$ constraint matrices, each of dimension n and rank r, this algorithm can compute any entry and efficient descriptions of the spectral decomposition of the solution matrix.

### Quantum-inspired algorithm applied to extreme learning

- Computer Science
- 2022

The quantum-inspired singular value decomposition technique is applied to extreme learning which is a machine learning framework that performs linear regression using random feature vectors generated through a random neural network and it is observed that the algorithm works order-of-magnitude faster than the exact SVD when the authors use high-dimensional feature vectors.

### Quantum-Inspired Classical Algorithm for Slow Feature Analysis

- Computer ScienceArXiv
- 2020

This work proposed an algorithm for slow feature analysis, a machine learning algorithm that extracts the slow-varying features, with a run time O(polylog(n)poly(d)).

### A Survey of Quantum Computing for Finance

- Computer Science
- 2022

A comprehensive summary of the state of the art of quantum computing for financial applications, with particular emphasis on stochastic modeling, optimization, and machine learning, describing how these solutions, adapted to work on a quantum computer, can potentially help to solve financial problems more efficiently and accurately.

### A quantum interior-point predictor–corrector algorithm for linear programming

- Computer ScienceJournal of Physics A: Mathematical and Theoretical
- 2020

We introduce a new quantum optimization algorithm for dense linear programming problems, which can be seen as the quantization of the interior point predictor–corrector algorithm [] using a quantum…

### Quantum algorithms for SVD-based data representation and analysis

- Computer ScienceQuantum Mach. Intell.
- 2022

This paper formalizes quantum procedures that speed-up the solution of eigenproblems for data representations in machine learning through new quantum algorithms, sublinear in the input matrix’s size, for principal component analysis, correspondence analysis, and latent semantic analysis.

### Enhancing the Quantum Linear Systems Algorithm Using Richardson Extrapolation

- Computer ScienceACM Transactions on Quantum Computing
- 2022

This work shows how to use Richardson extrapolation to enhance Hamiltonian simulation, resulting in an implementation of Quantum Phase Estimation (QPE) within the algorithm with 1/√ε circuits that can be run in parallel each with circuit complexity 1/ ∼√ ε instead of 1/ε.

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