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Register a new userSome Open Problems in Quantum Information Theory
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This article is a snap-shot of a web site, which has been collecting open problems in quantum information for several years, and documenting the progress made on these problems. By posting it we make the complete collection available in one printout. We also hope to draw more attention to this project, inviting every researcher in the field to raise to the challenges, but also to suggest new problems.
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Is there a connection between the branch point singularity at the particle emission threshold and the appearance of cluster states which reveal the structure of a corresponding reaction channel? Which nuclear states are most impacted by the coupling to the scattering continuum? What should be the most important steps in developing the theory that will truly unify nuclear structure and nuclear reactions? The common denominator of these questions is the continuum shell-model approach to bound and unbound nuclear states, nuclear decays, and reactions.
Almost all of the most successful quantum algorithms discovered to date exploit the ability of the Fourier transform to recover subgroup structure of functions, especially periodicity. The fact that Fourier transforms can also be used to capture shift structure has received far less attention in the context of quantum computation. In this paper, we present three examples of ``unknown shift problems that can be solved efficiently on a quantum computer using the quantum Fourier transform. We also define the hidden coset problem, which generalizes the hidden shift problem and the hidden subgroup problem. This framework provides a unified way of viewing the ability of the Fourier transform to capture subgroup and shift structure.
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I consider some promising future directions for quantum information theory that could influence the development of 21st century physics. Advances in the theory of the distinguishability of superoperators may lead to new strategies for improving the precision of quantum-limited measurements. A better grasp of the properties of multi-partite quantum entanglement may lead to deeper understanding of strongly-coupled dynamics in quantum many-body systems, quantum field theory, and quantum gravity.
I offer a case that quantum query complexity still has loads of enticing and fundamental open problems -- from relativized QMA versus QCMA and BQP versus IP, to time/space tradeoffs for collision and element distinctness, to polynomial degree versus quantum query complexity for partial functions, to the Unitary Synthesis Problem and more.
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