Quantum assisted Gaussian process regression

@article{Zhao2015QuantumAG,
  title={Quantum assisted Gaussian process regression},
  author={Zhikuan Zhao and Jack K. Fitzsimons and Joseph Fitzsimons},
  journal={ArXiv},
  year={2015},
  volume={abs/1512.03929},
  url={https://api.semanticscholar.org/CorpusID:18303333}
}
It is shown that even in some cases not ideally suited to the quantum linear systems algorithm, a polynomial increase in efficiency still occurs, leading to an exponential reduction in computation time in some instances.
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105 Citations
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105 Citations

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48 References

An introduction to quantum machine learning

This contribution gives a systematic overview of the emerging field of quantum machine learning and presents the approaches as well as technical details in an accessible way, and discusses the potential of a future theory of quantum learning.

Preconditioned quantum linear system algorithm.

A quantum algorithm that generalizes the quantum linear system algorithm to arbitrary problem specifications is described and it is shown how it can be used to compute the electromagnetic scattering cross section of an arbitrary target exponentially faster than the best classical algorithm.

Quantum Algorithm for Systems of Linear Equations with Exponentially Improved Dependence on Precision

The algorithm is based on a general technique for implementing any operator with a suitable Fourier or Chebyshev series representation, and allows the quantum phase estimation algorithm, whose dependence on $\epsilon$ is prohibitive, to be bypassed.

Quantum adiabatic machine learning

An approach to machine learning and anomaly detection via quantum adiabatic evolution, which is strictly limited to two-qubit interactions so as to ensure physical feasibility, is developed and applied to the problem of software verification and validation.

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.

Efficient Quantum Algorithms for Simulating Sparse Hamiltonians

We present an efficient quantum algorithm for simulating the evolution of a quantum state for a sparse Hamiltonian H over a given time t in terms of a procedure for computing the matrix entries of H.…

Quantum support vector machine for big feature and big data classification

This work shows that the support vector machine, an optimized binary classifier, can be implemented on a quantum computer, with complexity logarithmic in the size of the vectors and the number of training examples, and an exponential speedup is obtained.

Fast graph operations in quantum computation

This work shows that this correspondence between certain entangled states and graphs can be harnessed in the reverse direction to yield a graph data structure, which allows for more efficient manipulation and comparison of graphs than any possible classical structure.

Quantum Computation and Quantum Information

This paper introduces the basic concepts of quantum computation and quantum simulation and presents quantum algorithms that are known to be much faster than the available classic algorithms and provides a statistical framework for the analysis of quantum algorithms and quantum Simulation.

Quantum random access memory.

An architecture that exponentially reduces the requirements for a memory call: O(logN) switches need be thrown instead of the N used in conventional RAM designs, which yields a more robust QRAM algorithm, as it in general requires entanglement among exponentially less gates, and leads to an exponential decrease in the power needed for addressing.