Density Functional theory (DFT) and its time-dependent extension (TDDFT) have become widely used methods in computational electronic structure theory. DFT and TDDFT are based on rigorous theorems, which reformulate many-electron quantum mechanics using the simple one-electron density as the basic variable of interest rather than the complicated many-electron wavefunction. In this talk I'll discuss how the theorems of TDDFT can be applied to a class of qubit Hamiltonians that are universal for quantum computation. In a similar spirit to DFT and TDDFT for electronic Hamiltonians, the theorems of TDDFT applied to universal Hamiltonians allow us to think of single-qubit expectation values as the basic variables in quantum computation and information theory, rather than the wavefunction. From a practical standpoint this also opens the possibility of approximating observables of interest in quantum computations directly in terms of single-qubit quantities (i.e. as density functionals). Additionally, we'll see that TDDFT provides an exact prescription for simulating universal Hamiltonians with other universal Hamiltonians that have different, and possibly easier-to-realize two-qubit interactions.

I'll also give a brief introduction to time-dependent density matrix functional theory (TD-DMFT) as an alternative to TDDFT and it's possible applications in quantum information theory.

Joel Yuen-Zhou

PhD candidate in Chemical Physics

Harvard University CCB,

12 Oxford St. Mailbox 107,

Cambridge, MA, USA.