arXiv subjects

Wang Fang

Publications and source records attributed to Wang Fang.

25 records · Page 2Linked to original sources

arXiv2022

Quantum Algorithm for Fidelity Estimation

For two unknown mixed quantum states $ρ$ and $σ$ in an $N$-dimensional Hilbert space, computing their fidelity $F(ρ,σ)$ is a basic problem with many important applications in quantum computing and quantum information, for example verification and characterization of the outputs of a quantum computer, and design and analysis of quantum algorithms. In this paper, we propose a quantum algorithm that solves this problem in $\operatorname{poly}(\log (N), r, 1/\varepsilon)$ time, where $r$ is the lower rank of $ρ$ and $σ$, and $\varepsilon$ is the desired precision, provided that the purifications of $ρ$ and $σ$ are prepared by quantum oracles. This algorithm exhibits an exponential speedup over the best known algorithm (based on quantum state tomography) which has time complexity polynomial in $N$.

quant-ph↗

arXiv2022

Verifying Fairness in Quantum Machine Learning

Due to the beyond-classical capability of quantum computing, quantum machine learning is applied independently or embedded in classical models for decision making, especially in the field of finance. Fairness and other ethical issues are often one of the main concerns in decision making. In this work, we define a formal framework for the fairness verification and analysis of quantum machine learning decision models, where we adopt one of the most popular notions of fairness in the literature based on the intuition -- any two similar individuals must be treated similarly and are thus unbiased. We show that quantum noise can improve fairness and develop an algorithm to check whether a (noisy) quantum machine learning model is fair. In particular, this algorithm can find bias kernels of quantum data (encoding individuals) during checking. These bias kernels generate infinitely many bias pairs for investigating the unfairness of the model. Our algorithm is designed based on a highly efficient data structure -- Tensor Networks -- and implemented on Google's TensorFlow Quantum. The utility and effectiveness of our algorithm are confirmed by the experimental results, including income prediction and credit scoring on real-world data, for a class of random (noisy) quantum decision models with 27 qubits ($2^{27}$-dimensional state space) tripling ($2^{18}$ times more than) that of the state-of-the-art algorithms for verifying quantum machine learning models.

quant-ph↗

arXiv2022

VeriQBench: A Benchmark for Multiple Types of Quantum Circuits

In this paper, we introduce VeriQBench -- an open source benchmark for quantum circuits. It offers high-level quantum circuit abstractions of various circuit types, including 1) combinational, 2) dynamic, 3) sequential, and 4) variational quantum circuits, which cover almost all existing types of quantum circuits in the literature. Meanwhile, VeriQBench is a versatile benchmark which can be used in verifying quantum software for different applications, as is evidenced by the existing works including quantum circuit verification (e.g., equivalence checking [Hon+21a; WLY21] and model checking [Yin21]), simulation (e.g., fault simulation), testing (e.g., test pattern generation [CY22]) and debugging (e.g., runtime assertions [Li+20b]). All the circuits are described in OpenQASM and are validated on Qiskit and QCOR simulators. With the hope that it can be used by other researchers, VeriQBench is released at: https://github.com/Veri-Q/Benchmark.

quant-ph↗

arXiv2021

Robustness Verification of Quantum Classifiers

Several important models of machine learning algorithms have been successfully generalized to the quantum world, with potential speedup to training classical classifiers and applications to data analytics in quantum physics that can be implemented on the near future quantum computers. However, quantum noise is a major obstacle to the practical implementation of quantum machine learning. In this work, we define a formal framework for the robustness verification and analysis of quantum machine learning algorithms against noises. A robust bound is derived and an algorithm is developed to check whether or not a quantum machine learning algorithm is robust with respect to quantum training data. In particular, this algorithm can find adversarial examples during checking. Our approach is implemented on Google's TensorFlow Quantum and can verify the robustness of quantum machine learning algorithms with respect to a small disturbance of noises, derived from the surrounding environment. The effectiveness of our robust bound and algorithm is confirmed by the experimental results, including quantum bits classification as the "Hello World" example, quantum phase recognition and cluster excitation detection from real world intractable physical problems, and the classification of MNIST from the classical world.

quant-ph↗

arXiv2020

An insight into acupoints and meridians in human body based on interstitial fluid circulation

The atlas of human acupoints and meridians has been utilized in clinical practice for almost a millennium although the anatomical structures and functions remain to be clarified. It has recently been reported that a long-distance interstitial fluid (ISF) circulatory pathway may originate from the acupoints in the extremities. As observed in living human subjects, cadavers and animals using magnetic resonance imaging and fluorescent tracers, the ISF flow pathways include at least 4 types of anatomical structures: the cutaneous-, perivenous-, periarterial-, and neural-pathways. Unlike the blood or lymphatic vessels, these ISF flow pathways are composed of highly ordered and topologically connected interstitial fibrous connective tissues that may work as guiderails for the ISF to flow actively over long distance under certain driving forces. Our experimental results demonstrated that most acupoints in the extremity endings connect with one or more ISF flow pathways and comprise a complex network of acupoint-ISF-pathways. We also found that this acupoint-ISF-pathway network can connect to visceral organs or tissues such as the pericardium and epicardium, even though the topographical geometry in human extremities does not totally match the meridian lines on the atlas that is currently used in traditional Chinese medicine. Based on our experimental data, the following working hypotheses are proposed. A comprehensive atlas will be constructed to systemically reveal the detailed anatomical structures of the acupoints-originated ISF circulation. Such an atlas may shed light on the mysteries shrouding the visceral correlations of acupoints and meridians, and inaugurate a new frontier for innovative medical applications.

q-bio.TO↗

arXiv2019

Active interfacial dynamic transport of fluid in fibrous connective tissues and a hypothesis of interstitial fluid circulatory system

Fluid in interstitial spaces accounts for ~20% of an adult body weight. Does it circulate around the body like vascular circulations besides a diffusive and short-ranged transport? This bold conjecture has been debated for decades. As a conventional physiological concept, interstitial space was the space between cells and a micron-sized space. Fluid in interstitial spaces is thought to be entrapped within interstitial matrix. However, our serial data have further defined an interfacial transport zone on a solid fiber of interstitial matrix. Within this fine space that is probably nanosized, fluid can transport along a fiber under a driving power. Since 2006, our imaging data from volunteers and cadavers have revealed a long-distance extravascular pathway for interstitial fluid flow, comprising four types of anatomic distributions at least. The framework of each extravascular pathway contains the longitudinally assembled and oriented fibers, working as a fibrous guiderail for fluid flow. Interestingly, our data showed that the movement of fluid in a fibrous pathway is in response to a dynamic driving source and named as dynamotaxis. By analysis of some representative studies and our experimental results, a hypothesis of interstitial fluid circulatory system is proposed.

q-bio.TO↗

arXiv2013

The one-loop on-shell renormalization of some vertexes in MSSM

The on-shell renormalization scheme for the electroweak theory is well studied in the standard model(SM), but a consistent on-shell renormalization scheme for the minimal supersymmetric standard model(MSSM) is still unknown. In MSSM, we study the on-shell scheme for three vertexes$Z\bar{l^I}l^I, W^+\bar{ν^I}l^I $ and $\tilde{L}^*_i\bar{χ^0_α}l^I$ with virtual SUSY particles (chargino, sneutrino, neutralino and slepton) at one-loop order. Instead of amplitude of a single triangle diagram, the sum of amplitude of triangle diagrams belonging to one suit can be renormalized in the on-shell scheme. One suit points out that the internal virtual particles are consistent. Zero-momentum scheme is also used for the renormalization. The two schemes can make the renormalized results decoupled. In MSSM, some special characters of the on-shell scheme are shown here. This work is propitious to complete the on-shell renormalization scheme in MSSM.

hep-ph↗