Entanglement complexity of quantum states, dynamics and quantum computation

Quantum entanglement has become the key notion bridging originally distinct fields of research over the last decade, namely, quantum information and computation, condensed matter physics, and quantum gravity. Previous studies on quantum entanglement have largely focused on the entanglement entropy, which quantifies the amount of entanglement. However, a natural question arises: is there additional information of a quantum state that is not captured by the entanglement entropy alone? For ground states of gapped Hamiltonians, this question has been answered in the affirmative. In this dissertation, I extend this idea to study highly entangled states typically having volume law entropy, and demonstrate that there is indeed much richer information on the complexity of a quantum state beyond the entanglement entropy. In the first part, I study the entanglement spectrum of highly entangled states corresponding to highly excited eigenstates of non-integrable Hamiltonians, time-evolved states after a quantum quench with Hamiltonians exhibiting different dynamical phases, and random unitary circuits consisting of random braids of non-Abelian anyons. I demonstrate that the entanglement spectrum is able to capture the degree of randomness of a quantum state, which we call the entanglement complexity. In the context of scrambling, this quantifies the degree of randomness produced by scrambling beyond entropic diagnostics. Our understanding of quantum entanglement in condensed matter systems and high energy physics have largely benefited from the field of quantum computation. In the second part of the dissertation, I present two examples of novel platforms for quantum computation using state-of-the-art experimental technologies. I demonstrate how one can use hybrid quantum-classical architecture to solve computational problems based on an optimal variational ansatz of the evolution protocol. I also present a hierarchical architecture of constructing logical Majorana zero modes which can be used for demonstrating non-Abelian braiding statistics experimentally

Early Warning System: Relay Sensor Deployment & Network Reliability Analysis

In this project, we continued Dr. Chipara\u27s study, which developed an early warning system (EWS) to detect the vital signs of patients in order to help doctors to intervene in time [1]. Since the number of wards increased, the environment our system faced with became more complicated and our network became more sensitive. This project focused on finding reasons on the relays that didn\u27t work and doing a reliability analysis on the network in one ward our study covered

Noncollinearity-modulated electronic properties of the monolayer CrI3_3

Introducing noncollinear magnetization into a monolayer CrI$_3$ is proposed to be an effective approach to modulate the local electronic properties of the two-dimensional (2D) magnetic material. Using first-principles calculation, we illustrate that both the conduction and valence bands in the monolayer CrI$_3$ are lowered down by spin spiral states. The distinct electronic structure of the monolayer noncollinear CrI$_3$ can be applied in nanoscale functional devices. As a proof of concept, we show that a magnetic domain wall can form a one-dimensional conducting channel in the 2D semiconductor via proper gating. Other possible applications such as electron-hole separation and identical quantum dots are also discussed

Unbiased Math Word Problems Benchmark for Mitigating Solving Bias

In this paper, we revisit the solving bias when evaluating models on current Math Word Problem (MWP) benchmarks. However, current solvers exist solving bias which consists of data bias and learning bias due to biased dataset and improper training strategy. Our experiments verify MWP solvers are easy to be biased by the biased training datasets which do not cover diverse questions for each problem narrative of all MWPs, thus a solver can only learn shallow heuristics rather than deep semantics for understanding problems. Besides, an MWP can be naturally solved by multiple equivalent equations while current datasets take only one of the equivalent equations as ground truth, forcing the model to match the labeled ground truth and ignoring other equivalent equations. Here, we first introduce a novel MWP dataset named UnbiasedMWP which is constructed by varying the grounded expressions in our collected data and annotating them with corresponding multiple new questions manually. Then, to further mitigate learning bias, we propose a Dynamic Target Selection (DTS) Strategy to dynamically select more suitable target expressions according to the longest prefix match between the current model output and candidate equivalent equations which are obtained by applying commutative law during training. The results show that our UnbiasedMWP has significantly fewer biases than its original data and other datasets, posing a promising benchmark for fairly evaluating the solvers' reasoning skills rather than matching nearest neighbors. And the solvers trained with our DTS achieve higher accuracies on multiple MWP benchmarks. The source code is available at https://github.com/yangzhch6/UnbiasedMWP