Sequentially constrained Monte Carlo sampler for quantum states
- URL: http://arxiv.org/abs/2109.14215v1
- Date: Wed, 29 Sep 2021 06:45:42 GMT
- Title: Sequentially constrained Monte Carlo sampler for quantum states
- Authors: Weijun Li, Rui Han, Jiangwei Shang, Hui Khoon Ng, Berthold-Georg
Englert
- Abstract summary: We present the Sequentially Constrained Monte Carlo (SCMC) algorithm as a powerful and versatile method for sampling quantum states.
We obtain nearly ten thousand bound entangled two-qutrit states in a few minutes -- a colossal speed-up over independence sampling.
In yet another application, the SCMC algorithm produces uniformly distributed quantum states in regions bounded by values of the problem-specific target distribution.
- Score: 4.289102530380288
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- Abstract: Random samples of quantum states with specific properties are useful for
various applications, such as Monte Carlo integration over the state space. In
the high-dimensional situations that one encounters already for a few qubits,
the quantum state space has a very complicated boundary, and it is challenging
to incorporate the specific properties into the sampling algorithm. In this
paper, we present the Sequentially Constrained Monte Carlo (SCMC) algorithm as
a powerful and versatile method for sampling quantum states in accordance with
any desired properties that can be stated as inequalities. We apply the SCMC
algorithm to the generation of samples of bound entangled states; for example,
we obtain nearly ten thousand bound entangled two-qutrit states in a few
minutes -- a colossal speed-up over independence sampling, which yields less
than ten such states per day. In the second application, we draw samples of
high-dimensional quantum states from a narrowly peaked target distribution and
observe that SCMC sampling remains efficient as the dimension grows. In yet
another application, the SCMC algorithm produces uniformly distributed quantum
states in regions bounded by values of the problem-specific target
distribution; such samples are needed when estimating parameters from the
probabilistic data acquired in quantum experiments.
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