Many open problems in physics from the Haldane conjecture regarding Heisenberg models with integer spins to the existence of the topological spin liquid phase to the Yang-Mills mass gap problem, one of the famed millennium problems, and an explanation of quark confinement are concerned with spectral gaps. The spectral gap is the energy difference between the ground and first excited states of a system and governs many of its behaviors, especially at lower energy. We show that the spectral gap can be calculated as a simple ratio of the two expectation values calculated over the wave function propagated in imaginary time. This method constitutes a significant simplification over the existing methods for spectral gap calculation. We demonstrate the effectiveness of this method on the Fermi-Hubbard and transverse field Ising models. Additionally, we discuss the implementation of the method on a quantum computer. Sandia National Labs is managed and operated by NTESS under DOE NNSA contract DENA0003525. SAND2022-14593 A.

I am a fifth year PhD student at Tulane University under Dr. Denys Bondar. The primary focus of our group is the research of quantum technologies and systems. Recently, my research has been directed towards the development of novel methods for obtaining the energies of quantum systems, with a particular focus on the ground and low-lying excited states. These methods often take some inspiration from the techniques of quantum control theory. Previously, I have also done work in researching the analogies between classical optics and quantum mechanics. The principles of quantum control theory could be useful in further exploring these types of analogies.