Corpus ID: 221703259

An improved quantum-inspired algorithm for linear regression

  title={An improved quantum-inspired algorithm for linear regression},
  author={Andr'as Gily'en and Zhao Song and Ewin Tang},
We give a classical algorithm for linear regression analogous to the quantum matrix inversion algorithm [Harrow, Hassidim, and Lloyd, Physical Review Letters'09] for low-rank matrices [Wossnig et al., Physical Review Letters'18], when the input matrix $A$ is stored in a data structure applicable for QRAM-based state preparation. Namely, given an $A \in \mathbb{C}^{m\times n}$ with minimum singular value $\sigma$ and which supports certain efficient $\ell_2$-norm importance sampling queries… Expand
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An improved classical algorithm for solving linear systems in a model analogous to the QRAM that is used by quantum linear solvers based on the randomized Kaczmarz method, which is a particular case of stochastic gradient descent. Expand
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We consider performing phase estimation under the following conditions: we are given only one copy of the input state, the input state does not have to be an eigenstate of the unitary, and the stateExpand
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Quantum Algorithms for Linear Algebra and Machine Learning.
This dissertation makes progress on all three aspects of the quantum machine learning problem and obtain quantum algorithms for low rank approximation and regularized least squares and quadratic speedups for a large class of linear algebra algorithms that rely on importance sampling from the leverage score distribution. Expand
Exploiting Numerical Sparsity for Efficient Learning : Faster Eigenvector Computation and Regression
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A quantum-inspired classical algorithm for recommendation systems
  • Ewin Tang
  • Computer Science, Physics
  • Electron. Colloquium Comput. Complex.
  • 2018
A classical analogue to Kerenidis and Prakash’s quantum recommendation system is given, previously believed to be one of the strongest candidates for provably exponential speedups in quantum machine learning, which produces recommendations exponentially faster than previous classical systems, which run in time linear in m and n. Expand
Sampling-based sublinear low-rank matrix arithmetic framework for dequantizing Quantum machine learning
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Quantum Linear System Algorithm for Dense Matrices.
A quantum algorithm is described that achieves a sparsity-independent runtime scaling of O(κ^{2}sqrt[n]polylog(n)/ε) for an n×n dimensional A with bounded spectral norm, which amounts to a polynomial improvement over known quantum linear system algorithms when applied to dense matrices. Expand
Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics
A new “Quantum singular value transformation” algorithm is developed that can directly harness the advantages of exponential dimensionality by applying polynomial transformations to the singular values of a block of a unitary operator. Expand
Quantum linear systems algorithms: a primer
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On the Robustness of Bucket Brigade Quantum RAM
It is argued that quantum error correction for the circuit causes the quantum bucket brigade architecture to lose its primary advantage of a small number of "active" gates, since all components have to be actively error corrected. Expand
Quantum Recommendation Systems
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Fast Monte Carlo Algorithms for Matrices II: Computing a Low-Rank Approximation to a Matrix
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