Fast Quantum Algorithms for Trace Distance Estimation

In quantum information, trace distance is a basic metric of distinguishability between quantum states. However, there is no known efficient approach to estimate the value of trace distance in general. In this paper, we propose efficient quantum algorithms for estimating the trace distance within additive error $\varepsilon$ between mixed quantum states of rank $r$. Specifically, we first provide a quantum algorithm using $r \cdot \widetilde O(1/\varepsilon^2)$ queries to the quantum circuits that prepare the purifications of quantum states. Then, we modify this quantum algorithm to obtain another algorithm using $\widetilde O(r^2/\varepsilon^5)$ samples of quantum states, which can be applied to quantum state certification. These algorithms have query/sample complexities that are independent of the dimension $N$ of quantum states, and their time complexities only incur an extra $O(\log (N))$ factor. In addition, we show that the decision version of low-rank trace distance estimation is $\mathsf{BQP}$-complete.Comment: Final version. Improve proof details, add BQP-completeness. 31 pages, 2 algorithms, 2 tables, 2 figure

Parallel Quantum Algorithm for Hamiltonian Simulation

We study how parallelism can speed up quantum simulation. A parallel quantum algorithm is proposed for simulating the dynamics of a large class of Hamiltonians with good sparse structures, called uniform-structured Hamiltonians, including various Hamiltonians of practical interest like local Hamiltonians and Pauli sums. Given the oracle access to the target sparse Hamiltonian, in both query and gate complexity, the running time of our parallel quantum simulation algorithm measured by the quantum circuit depth has a doubly (poly-)logarithmic dependence $\operatorname{polylog}\log(1/\epsilon)$ on the simulation precision $\epsilon$. This presents an exponential improvement over the dependence $\operatorname{polylog}(1/\epsilon)$ of previous optimal sparse Hamiltonian simulation algorithm without parallelism. To obtain this result, we introduce a novel notion of parallel quantum walk, based on Childs' quantum walk. The target evolution unitary is approximated by a truncated Taylor series, which is obtained by combining these quantum walks in a parallel way. A lower bound $\Omega(\log \log (1/\epsilon))$ is established, showing that the $\epsilon$-dependence of the gate depth achieved in this work cannot be significantly improved. Our algorithm is applied to simulating three physical models: the Heisenberg model, the Sachdev-Ye-Kitaev model and a quantum chemistry model in second quantization. By explicitly calculating the gate complexity for implementing the oracles, we show that on all these models, the total gate depth of our algorithm has a $\operatorname{polylog}\log(1/\epsilon)$ dependence in the parallel setting.Comment: Minor revision. 55 pages, 6 figures, 1 tabl

The Skipped Beat: A Study of Sociopragmatic Understanding in LLMs for 64 Languages

Instruction tuned large language models (LLMs), such as ChatGPT, demonstrate remarkable performance in a wide range of tasks. Despite numerous recent studies that examine the performance of instruction-tuned LLMs on various NLP benchmarks, there remains a lack of comprehensive investigation into their ability to understand cross-lingual sociopragmatic meaning (SM), i.e., meaning embedded within social and interactive contexts. This deficiency arises partly from SM not being adequately represented in any of the existing benchmarks. To address this gap, we present SPARROW, an extensive multilingual benchmark specifically designed for SM understanding. SPARROW comprises 169 datasets covering 13 task types across six primary categories (e.g., anti-social language detection, emotion recognition). SPARROW datasets encompass 64 different languages originating from 12 language families representing 16 writing scripts. We evaluate the performance of various multilingual pretrained language models (e.g., mT5) and instruction-tuned LLMs (e.g., BLOOMZ, ChatGPT) on SPARROW through fine-tuning, zero-shot, and/or few-shot learning. Our comprehensive analysis reveals that existing open-source instruction tuned LLMs still struggle to understand SM across various languages, performing close to a random baseline in some cases. We also find that although ChatGPT outperforms many LLMs, it still falls behind task-specific finetuned models with a gap of 12.19 SPARROW score. Our benchmark is available at: https://github.com/UBC-NLP/SPARROWComment: Accepted by EMNLP 2023 Main conferenc

A Method to Generate and Analyze Modified Myristoylated Proteins

Covalent lipid modification of proteins is essential to their cellular localizations and functions. Engineered lipid motifs, coupled with bio-orthogonal chemistry, have been utilized to identify myristoylated or palmitoylated proteins in cells. However, whether modified proteins have similar properties as endogenous ones has not been well investigated mainly due to lack of methods to generate and analyze purified proteins. We have developed a method that utilizes metabolic interference and mass spectrometry to produce and analyze modified, myristoylated small GTPase ADP-ribosylation factor 1 (Arf1). The capacities of these recombinant proteins to bind liposomes and load and hydrolyze GTP were measured and compared with the unmodified myristoylated Arf1. The ketone-modified myristoylated Arf1 could be further labeled by fluorophore-coupled hydrazine and subsequently visualized through fluorescence imaging. This methodology provides an effective model system to characterize lipid-modified proteins with additional functions before applying them to cellular systems

Dual-Polarized On-Chip Antenna for 300 GHz Full-Duplex Communication System

This paper presents a novel design of compact orthogonally polarized on-chip antenna to realize 300 GHz full-duplex communication system with high isolation. It consists of a dipole antenna for horizontal polarization and a disk-loaded monopole antenna for vertical polarization. They are in good cross-polarization state with more than 90 dB of self-interference suppression and then can be used to achieve good isolation between transmitting and receiving antennas. In addition, two dual-polarized antennas have been adopted in two separated transceivers to study their isolation performance. Furthermore, this compact antenna only occupies an active area of 390 μm × 300 μm × 78 μm and can be used for multiple-input multiple-output application as well