LOCALITY, SYMMETRY, AND DIGITAL SIMULATION OF QUANTUM SYSTEMS

Besides potentially delivering a huge leap in computational power, quantum computers also offer an essential platform for simulating properties of quantum systems. Consequently, various algorithms have been developed for approximating the dynamics of a target system on quantum computers. But generic quantum simulation algorithms—developed to simulate all Hamiltonians—are unlikely to result in optimal simulations of most physically relevant systems; optimal quantum algorithms need to exploit unique properties of target systems. The aim of this dissertation is to study two prominent properties of physical systems, namely locality and symmetry, and subsequently leverage these properties to design efficient quantum simulation algorithms. In the first part of the dissertation, we explore the locality of quantum systems and the fundamental limits on the propagation of information in power-law interacting systems. In particular, we prove upper limits on the speed at which information can propagate in power-law systems. We also demonstrate how such speed limits can be achieved by protocols for transferring quantum information and generating quantum entanglement. We then use these speed limits to constrain the propagation of error and improve the performance of digital quantum simulation. Additionally, we consider the implications of the speed limits on entanglement generation, the dynamics of correlation, the heating time, and the scrambling time in power-law interacting systems. In the second part of the dissertation, we propose a scheme to leverage the symmetry of target systems to suppress error in digital quantum simulation. We first study a phenomenon called destructive error interference, where the errors from different steps of a simulation cancel out each other. We then show that one can induce the destructive error interference by interweaving the simulation with unitary transformations generated by the symmetry of the target system, effectively providing a faster quantum simulation by symmetry protection. We also derive rigorous bounds on the error of a symmetry-protected simulation algorithm and identify conditions for optimal symmetry protection

ASSESSING THE ADAPTIVE CAPACITY OF HOUSEHOLDS TO CLIMATE CHANGE: A CASE STUDY IN QUANG DIEN DISTRICT, THUA THIEN HUE PROVINCE

Abstract: This study aims to identify the adaptation capacity undertaken by households in response to natural disasters and climate changes (CC). A total of 100 households in two communes including Quang Phuoc and Quang Cong, Quang Dien district were interviewed. The findings indicate that in the last few years, these communes have been badly affected by various types of natural hazards, including typhoons, floods, droughts and, and extremely cold weather. The study demonstrates that the adaptive capacity index in Quang Cong is significantly lower than that in Quang Phuoc (0.50 and 0.52). Also, the current adaptation actions of local households in response to natural disasters and CC have focused on short-term actions only. On the basis of the findings, the study proposes key recommendations to local households in Quang Dien district to effectively mitigate and adapt to natural disasters and CC. The recommendations encompass three groups, namely (i) raising awareness and understanding about CC; (ii) improving the infrastructure system; and (iii) diversifying livelihood strategies to increase income.Keywords: climate change, natural disasters, adaptive capacity, inde

Depth of powers of edge ideals of cycles and trees

Let $I$ be the edge ideal of a cycle of length $n \ge 5$ over a polynomial ring $S = \mathrm{k}[x_1,\ldots,x_n]$. We prove that for $2 \le t < \lceil (n+1)/2 \rceil$, $$\operatorname{depth} (S/I^t) = \lceil \frac{n -t + 1}{3} \rceil.$$ When $G = T_{\mathbf{a}}$ is a starlike tree which is the join of $k$ paths of length $a_1, \ldots, a_k$ at a common root $1$, we give a formula for the depth of powers of $I(T_{\mathbf{a}})$