Friday Quantum Seminar

Abstract: Antiferromagnetic materials with microscopic behavior resembling that of the Fermi-Hubbard model are expected to host excitons, or bound electron-hole pairs. In order to investigate such behavior, we have optimized states of the t-J model in the single-particle-single-hole sector using the density matrix renormalization group (DMRG).

Abstract: The intersection of quantum electrodynamics (QED) and density-functional theory (DFT) has opened up exciting opportunities in controlling quantum matter through light-matter coupling. This frontier, however, is beset with computational challenges, especially in the weak and strong coupling regimes. Building upon previous research, we present the results of nonperturbative QED functional in the long-wavelength limit, centered solely on the matter Hilbert space.

Abstract:  Topological band structures are well known to produce symmetry-protected chiral edge states which transport particles unidirectionally. These same effects can be harnessed in the frequency domain using a spin-1/2 system subject to periodic drives.

Abstract: A variety of quantum algorithms employ Pauli operators as a convenient basis for studying the spectrum or evolution of Hamiltonians or measuring multibody observables. One strategy to reduce circuit depth in such algorithms involves simultaneous diagonalization of Pauli operators generating unitary evolution operators or observables of interest. We propose an algorithm yielding quantum circuits with depths O(nlogr) diagonalizing n-qubit operators generated by r Pauli operators.

Abstract: Circuit quantum electrodynamics (circuit QED) has become one of the main platforms for quantum simulation and computation. One of its notable advantages is its ability to facilitate the study of new regimes of light-matter interactions. This is achieved due to the native strong coupling between superconducting qubits and microwave resonators, and the ability to lithographically define a large variety of resonant microwave structures, for example, photonic crystals.

Abstract: Nagaoka ferromagnetism (NF) is a long-predicted example of itinerant ferromagnetism in the Hubbard model and has been studied theoretically for many years. NF occurs when there is one hole in a half-filled band and a large onsite Coulomb repulsion, which does not arise naturally in materials. Quantum dots systems like dopant arrays in Si, can be fabricated with atomically precise complex geometries to create highly controllable systems. This makes them good candidates to study itinerant ferromagnetism in different array geometries.

Abstract: Theories whose fluctuating degrees of freedom live on extended loops as opposed to points, are abundant in nature. One example is the action obtained upon eliminating the redundant gauge fields in a gauge theory. Formulating a Renormalization Group (RG) procedure for such a theory is an open problem. In this work, we outline a procedure that in principle computes the outcome of coarse-graining and rescaling of such a theory. We make estimates that lead to qualitative agreement with known results of phase transitions in gauge theories and the XY-model.

Abstract: In gradient descent dynamics of neural networks, the top eigenvalue of the Hessian of the loss (sharpness) displays a variety of robust phenomena throughout training. This includes early time regimes where the sharpness may decrease during early periods of training (sharpness reduction), and later time behavior such as progressive sharpening and edge of stability. We demonstrate that a simple $2$-layer linear network (UV model) trained on a single training example exhibits all of the essential sharpness phenomenology observed in real-world scenarios.

Abstract: In order to simulate interacting fermionic systems on quantum computers, the first step is to encode the physical Hamiltonian into qubit operators. Existing encoding procedures such as the Jordan-Wigner transformation and Bravyi-Kitaev transformation are not resource efficient because they encode each second-quantized fermionic operator into a Pauli string without incorporating the structure of the Hamiltonian in question.