Fall 2023

Abstract: Calculating the equilibrium properties of condensed matter systems is one of the promising applications of near-term quantum computing. Recently, hybrid quantum-classical time-series algorithms have been proposed to efficiently extract these properties (time evolution up to short times t). In this work, we study the operation of this algorithm on a present-day quantum computer. Specifically, we measure the Loschmidt amplitude for the Fermi-Hubbard model on a 16-site ladder geometry (32 orbitals) on the Quantinuum H2-1 trapped-ion device.

One of the most striking many-body phenomena in nature is the sudden change of macroscopic properties as the temperature or energy reaches a critical value. Such equilibrium transitions have been predicted and observed in two and three spatial dimensions, but have long been thought not to exist in one-dimensional (1D) systems.

Abstract: In this talk, I will introduce a family of dynamically generated quantum error correcting codes that we call “hyperbolic Floquet codes.” These codes are defined by a specific sequence of non-commuting two-body measurements arranged periodically in time that stabilize a topological code on a hyperbolic manifold with negative curvature. We focus on a family of lattices for n qubits that, according to our prescription that defines the code, provably achieve a finite encoding rate (1/8+2/n) and have a depth-3 syndrome extraction circuit.

Abstract: Neutral atoms in highly-excited Rydberg states are actively utilized in a variety of research directions such as ultracold chemistry and many-body physics, precision measurements and emerging quantum technologies. This talk is focused on using Rydberg atoms for creating long-range molecular states and for sensing AC/DC electric fields. First, I will present a novel type of Rydberg dimer formed through long-range electric-multipole interactions between a Rydberg atom and an ion. Its vibrational spectra and stability against nonadiabatic effects will be discussed.

Abstract: Finding the ground energy of a quantum system is a fundamental problem in condensed matter physics and quantum chemistry. Existing classical algorithms for tackling this problem often assume that the ground state has a succinct classical description, i.e. a poly-size classical circuit for computing the amplitude. Notable examples of succinct states encompass matrix product states, contractible projected entangled pair states, and states that can be represented by classical neural networks. We study the complexity of the local Hamiltonian problem with succinct ground state.

Abstract: Decoding algorithms based on approximate tensor network contraction have proven tremendously successful in decoding 2D local quantum codes such as surface/toric codes and color codes, effectively achieving optimal decoding accuracy. We introduce several techniques to generalize tensor network decoding to higher dimensions so that it can be applied to 3D codes as well as 2D codes with noisy syndrome measurements (phenomenological noise or circuit-level noise).

Abstract: We analyze a model of qubits which we argue has an emergent quantum gravitational description similar to the fermionic Sachdev-Ye-Kitaev (SYK) model. The model we consider is known as the quantum q-spin model because it features q-local interactions between qubits.

Abstract: Thermodynamics plays an important role both in the foundations of physics and in technological applications. An operational perspective adopted in recent years is to formulate it as a quantum resource theory. I will begin with a quick introduction to the general framework of quantum resource theories, in particular motivating it and explaining why the convertibility of resourceful states is at its core.

Abstract: Composite fermion wavefunctions describe a one to one correspondence between the low energy properties of the FQH and the IQH phases which has been tested extensively in experiments and through numerical studies [1]. Here we consider the FQH state in the presence of a weak disorder potential. The full many-body problem is numerically difficult [2,3] but the effective Hamiltonian of a single quasiparticle can numerically be calculated in a weak disorder regime; and here we find a one to one correspondence between the FQH and the IQH systems [4].