Robust online Hamiltonian learning

@article{Granade2013RobustOH,
  title={Robust online Hamiltonian learning},
  author={Christopher E. Granade and Christopher Ferrie and Nathan Wiebe and David G. Cory},
  journal={New Journal of Physics},
  year={2013},
  volume={14}
}
In this work we combine two distinct machine learning methodologies, sequential Monte Carlo and Bayesian experimental design, and apply them to the problem of inferring the dynamical parameters of a quantum system. We design the algorithm with practicality in mind by including parameters that control trade-offs between the requirements on computational and experimental resources. The algorithm can be implemented online (during experimental data collection), avoiding the need for storage and… 

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References

SHOWING 1-10 OF 96 REFERENCES

ADAPTIVE HAMILTONIAN ESTIMATION USING BAYESIAN EXPERIMENTAL DESIGN

TLDR
An adaptive protocol which finds the optimal experiments based on previous observations is derived, and it is shown that the risk associated with this algorithm is close to the global optimum, given a uniform prior.

How to best sample a periodic probability distribution, or on the accuracy of Hamiltonian finding strategies

TLDR
Heuristic strategies for experiment design are derived that enjoy the same exponential scaling as fully optimized strategies and generalizations to the case of finite relaxation times, T2 < ∞ are discussed.

Simplified quantum process tomography

We propose and evaluate experimentally an approach to quantum process tomography that completely removes the scaling problem plaguing the standard approach. The key to this simplification is the

Adaptive Bayesian quantum tomography

In this letter we revisit the problem of optimal design of quantum tomographic experiments. In contrast to previous approaches where an optimal set of measurements is decided in advance of the

Characterization of a qubit Hamiltonian using adaptive measurements in a fixed basis

We investigate schemes for Hamiltonian parameter estimation of a two-level system using repeated measurements in a fixed basis. The simplest (Fourier based) schemes yield an estimate with a

Quantum adiabatic machine learning

TLDR
This work applies and illustrates this approach to machine learning and anomaly detection via quantum adiabatic evolution in detail to the problem of software verification and validation, with a specific example of the learning phase applied to a problem of interest in flight control systems.

The learnability of quantum states

  • S. Aaronson
  • Physics
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2007
TLDR
This theorem has the conceptual implication that quantum states, despite being exponentially long vectors, are nevertheless ‘reasonable’ in a learning theory sense and has two applications to quantum computing: first, a new simulation of quantum one-way communication protocols and second, the use of trusted classical advice to verify untrusted quantum advice.

Robust method for estimating the Lindblad operators of a dissipative quantum process from measurements of the density operator at multiple time points

We present a robust method for quantum process tomography, which yields a set of Lindblad operators that optimally fit the density operators measured at a sequence of time points. The benefits of

Bayesian Adaptive Exploration

We describe a framework for adaptive astronomical exploration based on iterating an Observation-Inference-Design cycle that allows adjustment of hypotheses and observing protocols in response to the
...