Quantum algorithm for data fitting.

By Nathan Wiebe, Daniel Braun, Seth Lloyd. Physical Review Letters, 2012

486 citations recorded by the source corpus.

We provide a new quantum algorithm that efficiently determines the quality of a least-squares fit over an exponentially large data set by building upon an algorithm for solving systems of linear equations efficiently [Harrow et al., Phys. Rev. Lett. 103, 150502 (2009)]. In many cases, our algorithm can also efficiently find a concise function that approximates the data to be fitted and bound the approximation error. In cases where the input data are pure quantum states, the algorithm can be used to provide an efficient parametric estimation of the quantum state and therefore can be applied as an alternative to full quantum-state tomography given a fault tolerant quantum computer.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/d18bc5577746306c72276688b4ba6816eef7a219

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Citations in the corpus

Quantum algorithms: an overview (2015, unknown): “These include solving large systems of di(cid:11)erential equations [62, 13], data (cid:12)tting [97] and various tasks in machine learning [65].”
Quantum machine learning models are kernel methods (2021, background): “The reasons why quantum training could help to lower this scaling are hidden in results from the early days of quantum machine learning, when quantum-based training was actively studied in the hope of finding exponential speedups for classical machine learning [6, 32, 33].”
Quantum computing for finance: Overview and prospects (2018, methodology): “This can be done in a time which is exponentially faster than the fastest classical algorithm [27].”
Continuous-variable quantum neural networks (2018, background): “Sufficiently powerful quantum computers can in principle provide computational speedups for key machine learning algorithms and subroutines such as data fitting [4], principal component analysis [5], Bayesian inference [6, 7], Monte Carlo methods [8], support vector machines [9, 10], Boltzmann machi”
Circuit-centric quantum classifiers (2018, background): “[11] Nathan Wiebe, Daniel Braun, and Seth Lloyd.”
Quantum technology for military applications (2021, methodology): “Other methods are, for example, the quantum analogy of the least-squares fit [47] or semidefinite programming [48].”
Quantum machine learning (2016, unknown): “They further suggest that in many cases their algorithms can also eﬃciently ﬁnd a concise function that approximates the data to be ﬁt-ted and bound the approximation error [16], particularly when the data is sparse.”