Seminar

I’ll tell you how quantum spin chains, some of the simplest quantum mechanical systems, encode a number of solutions to problems in representation theory, combinatorics, and algebraic geometry. This is revealed by the quantum integrability of the spin chains and the theory of (quantized) symmetric functions. This suggests a program to uncover the computational complexity of these computational problems, informed by the physics of 1d quantum integrable systems. 

ATL 3100A and Virtual Via Zoom

In this talk we give polynomial time algorithms for the following two problems:  (1) Given access to an unknown constant depth quantum circuit U on a finite-dimensional lattice, learn a constant depth circuit that approximates U to small diamond distance.  (2) Given copies of an unknown quantum state |ψ>=U|0^n> that is prepared by an unknown constant depth circuit U on a finite-dimensional lattice, learn a constant depth circuit that prepares |ψ>.  These algorithms extend to the case when the depth of U is polylog(n) with a quasi

Ab initio simulations of the Standard Model will require thousands of qubits and millions of gates. Developing efficient quantum simulation algorithms for such settings, which will only be feasible in the era of fault-tolerant quantum computing, necessitates principles entirely different from those used in the near term.

Quantum ergodicity refers to the remarkable ability of quantum systems to explore their entire state space allowed by symmetry. Mechanisms for violating ergodicity are of fundamental interest in statistical and molecular physics and can offer novel insights into decoherence phenomena in complex molecular qubits.  I will discuss the recent experimental observation of ergodicity breaking in rapidly rotating C60 fullerene molecules as a function of rotational angular momentum [1].

Our recent work investigated the use of divide-and-conquer strategies in the design of quantum query algorithms. Following a brief review of these findings, this talk will focus on ongoing work aimed at strengthening one of our earlier results. In particular, we will propose a randomized quantum query algorithm for checking membership in a specific regular language. The analysis of this algorithm will be discussed, with an emphasis on some of the technical details. We conclude with some of the potential implications of our research.

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).

Existing schemes for demonstrating quantum computational advantage are subject to various practical restrictions, including the hardness of verification and challenges in experimental implementation. Meanwhile, analog quantum simulators have been realized in many experiments to study novel physics.

Quantum simulation stands as an important application of quantum computing, offering insights into quantum many-body systems that are beyond the reach of classical computational methods. For many quantum simulation applications, accurate initial state preparation is typically the first step for subsequent computational processes. This dissertation specifically focuses on state preparation procedures for quantum states with chiral topological order, states that are notable for their robust edge modes and topological properties.

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.

Since the discovery of Shor’s factoring algorithm, there has been a sustained interest in finding more such examples of quantum advantage, that is, tasks where a quantum device can outperform its classical counterpart. While the universal, programmable quantum computers that can run Shor’s algorithm represent one direction in which to search for quantum advantage, they are certainly not the only one. In this dissertation, we study the theory of quantum advantage along two alternative avenues: sensing and simulation.