Chetan Nayak (Microsoft Research, Station Q and UC Santa Barbara)
Alan Aspuru-Guzik (Harvard University)
Density functional theory (DFT) and it's time-dependent counterpart (TDDFT) have been cornerstones in the field of numerical simulations, e.g. in computational materials science, ad computational physics and chemistry. The DFT theorems demonstrate that the exact energy of the ground state of a quantum system is a functional of the density of the system. The time-dependent counterpart (TDDFT) demonstrates that a time-evolving density is enough, in theory, to obtain all observables of a quantum system. In this talk, I will discuss our group's work on the connections of time-dependent density functional theory (TDDFT) and quantum information. In particular, we have proved the TDDFT theorems for the case of open quantum systems. I will discuss the implications of this to problems such as decoherence and the emergence of density functionals for dissipation and relaxation. We also recently showed that TDDFT theorems also exist for the case of distinguishable spin 1/2 systems (e.g. qubits) that are able to perform universal quantum computation. I will discuss the theorems and some potential applications to quantum simulation and also to the possibility of approximating the results of quantum information processing tasks. Recently, we have worked on the complexity of TDDFT as a procedure and show that, within certain physical and computational considerations, it belongs to the bounded quantum polynomial complexity class. This is joint work with Joel Yuen-Zhou, currently a Silbey postdoctoral fellow at MIT, David Tempel, currently a postdoctoral researcher in my group, as well as James Whitfield, former PhD. student currently in Vienna, Sergio Boixo, now at Google and Man-Hong Yung now Assistant Professor at Tsinghua University.
Lorenza Viola (Dartmouth College)
Hamiltonian engineering via unitary open-loop quantum control provides a versatile and experimentally validated framework for precisely manipulating a broad class of non-Markovian dynamical evolutions of interest, with applications ranging from dynamical decoupling and dynamically corrected quantum gates to noise spectroscopy and quantum simulation. In this context, transfer-function techniques directly motivated by control engineering have proved invaluable for obtaining a transparent picture of the controlled dynamics in the frequency domain and for quantitatively analyzing control performance. In this talk, I will show how to construct a general filter-function approach, which overcomes the limitations of the existing formalism. The key insight is to identify a set of "fundamental filter functions", whose knowledge suffices to construct arbitrary filter functions in principle and to determine the minimum "filtering order" that a given control protocol can guarantee. Implications for dynamical control in multi-qubit systems and/or in the presence of non-Gaussian noise will be discussed.
John Preskill (California Institute of Technology)
Jess Riedel (Perimeter Institute)