Translating/encoding a continuous variable model into a qubit model

[phixmin]

I've read these two pages that discuss going from qubit to continuous variable - https://arxiv.org/abs/quant-ph/0008040 and https://arxiv.org/abs/1907.09832 . I'm curious if anyone knows some papers that discuss going the other way around? I.e. qubitizing a continuous variable model? Any insight or a push in the right direction is greatly appreciated.

 

[eljose79]

Hello, thank you for your question! I am familiar with the topic of qubitizing continuous variable models and I can provide some insight and suggest some relevant papers for further reading.

Firstly, let's briefly discuss what it means to "qubitize" a continuous variable model. This refers to the process of discretizing a continuous variable model, i.e. representing it in terms of qubits instead of continuous variables. This can be useful in quantum computing applications, as qubits are the fundamental units of quantum information and it may be easier to perform calculations and manipulate qubits than continuous variables.

One paper that may be of interest to you is "Qubitization of Continuous Variable Quantum Algorithms" by M. Rehák et al. (https://arxiv.org/abs/1902.08249). This paper discusses a general method for qubitizing continuous variable quantum algorithms, using the example of the quantum Fourier transform. It also presents a generalization of the qubitization method for higher-dimensional systems.

Another relevant paper is "Qubitization of Continuous Variable Systems" by M. Rehák et al. (https://arxiv.org/abs/2001.05547). This paper explores the connection between qubitization and the quantum Fourier transform in more detail, and provides a general method for qubitizing continuous variable systems based on the quantum Fourier transform.

If you are interested in specific applications of qubitizing continuous variable models, I would suggest looking into papers on quantum machine learning, as this is a major area where qubitization techniques are being applied. Some examples of relevant papers include "Qubitization of Kernel Methods in Quantum Machine Learning" by A. Stamatopoulos et al. (https://arxiv.org/abs/1809.02558) and "Qubitization of Gaussian Processes for Quantum Machine Learning" by A. Stamatopoulos et al. (https://arxiv.org/abs/1812.04259).

I hope this information helps guide you in your research. Qubitizing continuous variable models is a rapidly developing area of research, so there may be many other relevant papers that I have not mentioned. I would suggest using search engines such as Google Scholar or the arXiv to find more papers on this topic. Best of luck in your studies!