Alternate perspectives on quantum query complexity
Quantum query complexity is a widely studied model for understanding the capabilities and limitations of quantum computers. In this dissertation, we aim to better understand this complexity measure with respect to many natural models that are not well-studied. In particular, we are interested in the following concrete questions.
1) How powerful are quantum computers that could make multiple queries in parallel relative to analogous classical computers?
2) Can there be a simple quantum algorithmic primitive that inherently combines quantum walks and quantum search?
Quantum Algorithms for Simulation and Spectroscopy of Nuclear Physics
In this talk I will discuss ongoing progress in two projects. The first project is related to implementing the time-evolution operator corresponding to the Kogut-Susskind formulation of Lattice Gauge Theories (U(1), SU(2), and SU(3)), and an improvement thereof called the Loop-String-Hadron formulation. We give a simple, generic method of decomposing a Hamiltonian into a minimal sum of easily-diagonalizable summands, suitable to plug into Trotter- or Block-Encoding-based Hamiltonian simulation methods.