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several universities and research institutions offer Ph.D. programs or research opportunities in the field of quantum machine learning. However, it's important to note that the availability of specific programs may vary over time. Here are a few renowned institutions that have been active in quantum machine learning research:

  1. Massachusetts Institute of Technology (MIT) - Center for Quantum Engineering: MIT's Center for Quantum Engineering focuses on research at the intersection of quantum science, engineering, and technology. They offer a Ph.D. program in Quantum Science and Engineering, which encompasses various areas, including quantum machine learning.

  2. Stanford University - Institute for Quantum Computing (SQuInT): Stanford's Institute for Quantum Computing offers a Ph.D. program in Applied Physics with a specialization in Quantum Information Science and Technology. This program covers research areas like quantum computing, quantum machine learning, and quantum algorithms.

  3. University of California, Berkeley - Quantum Information and Computation Center: UC Berkeley's Quantum Information and Computation Center conducts research in various aspects of quantum information science. They offer a Ph.D. program in Physics with opportunities for research in quantum machine learning.

  4. University of Waterloo - Institute for Quantum Computing: The Institute for Quantum Computing (IQC) at the University of Waterloo is a leading center for quantum research. They offer a Ph.D. program in Quantum Information with interdisciplinary research options, including quantum machine learning.

  5. University of Oxford - Quantum Machine Learning Group: The Quantum Machine Learning Group at the University of Oxford focuses on the intersection of quantum computing and machine learning. While Oxford does not have a specific Ph.D. program in quantum machine learning, they offer research opportunities in this field through their Quantum Information and Foundations doctoral program.

These are just a few examples, and there are likely other institutions that offer research opportunities in quantum machine learning. It is recommended to explore the websites of specific universities, research centers, or departments related to quantum computing, machine learning, or physics to find up-to-date information on available Ph.D. programs and potential advisors in the field of quantum machine learning.

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