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Yuan Su

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4 papers

2 author rows

FOCS Conference 2024 Conference Paper

Quantum Eigenvalue Processing

Guang Hao Low
Yuan Su

Many problems in linear algebra-such as those arising from non-Hermitian physics, transcorrelated quantum chemistry and differential equations-can be solved on a quan-tum computer by processing eigenvalues of the non-normal input matrices. However, the existing Quantum Singular Value Transformation (QSVT) framework is ill-suited to this task, as eigenvalues and singular values are different in general. We present a Quantum EigenValue Transformation (QEVT) framework for applying arbitrary polynomial transformations on eigenvalues of block-encoded non-normal operators, and a related Quantum EigenValue Estimation (QEVE) algorithm for operators with real spectra. QEVT has query complexity to the block encoding nearly recovering that of the QSVT for a Hermitian input, and QEVE achieves the Heisenberg-limited scaling for diagonalizable input matrices. As applications, we develop a linear differential equation solver with strictly linear time query complexity for average-case diagonalizable operators, as well as a ground state preparation algorithm that upgrades previous nearly optimal results for Hermitian Hamiltonians to diagonalizable matrices with real spectra. Underpinning our algorithms is an efficient method to prepare a quantum super-position of Faber polynomials, which generalize the nearly-best uniform approximation properties of Chebyshev polynomials to the complex plane. Of independent interest, we also develop techniques to generate $n$ Fourier coefficients with 0 (poly log ( $n$ )) gates compared to prior approaches with linear cost.

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ICRA Conference 2024 Conference Paper

The Joint-Space Reconstruction of Human Fingers by using a Highly Under-Actuated Exoskeleton

Yuan Su
Gaofeng Li
Yongsheng Deng
Ioannis Sarakoglou
Nikos G. Tsagarakis
Jiming Chen

Hand motion tracking is essential in many fields, e. g. , immersive virtual reality, teleoperation of robotic hand, and hand rehabilitation of stroke patient, as human hand plays a crucial role in our daily life. The highly under-actuated hand exoskeleton, which can track the 6-DoF motions of each fingertip via a highly under-actuated kinematic chain, exhibits many benefits in wearability and portability over other solutions. However, due to the non-anthropomorphic linkage, this hand exoskeleton also encounters difficulties in measuring human-finger’s joint angles. While the joint-space is important in many scenarios, such as teleoperating a robotic hand with anthropomorphic kinematics but with different size to human. Here we proposed a new method to reconstruct the human finger joints by using a highly under-actuated hand exoskeleton. Our key contribution is the arc-fitting algorithm, which is able to calibrate the misalignment between the exoskeleton’s and the human-finger’s base frames and estimate the length of human’s phalanxes, by using the fingertip’s circular motions. With knowing the aforementioned informations, the joint angles can be reconstructed in high precision based on the inverse kinematics models of human fingers. Furthermore, our proposed method is compared with a baseline method, in which the joint angles obtained by a motion capture system are served as ground-truth. The results demonstrate that our proposed method exhibits excellent performance in reconstructing finger’s joint configurations.

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STOC Conference 2019 Conference Paper

Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics

András Gilyén
Yuan Su
Guang Hao Low
Nathan Wiebe

An n -qubit quantum circuit performs a unitary operation on an exponentially large, 2 n -dimensional, Hilbert space, which is a major source of quantum speed-ups. We develop a new “Quantum singular value transformation” algorithm that can directly harness the advantages of exponential dimensionality by applying polynomial transformations to the singular values of a block of a unitary operator. The transformations are realized by quantum circuits with a very simple structure - typically using only a constant number of ancilla qubits - leading to optimal algorithms with appealing constant factors. We show that our framework allows describing many quantum algorithms on a high level, and enables remarkably concise proofs for many prominent quantum algorithms, ranging from optimal Hamiltonian simulation to various quantum machine learning applications. We also devise a new singular vector transformation algorithm, describe how to exponentially improve the complexity of implementing fractional queries to unitaries with a gapped spectrum, and show how to efficiently implement principal component regression. Finally, we also prove a quantum lower bound on spectral transformations.

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IJCAI Conference 2016 Conference Paper

Understanding Information Diffusion under Interactions

Yuan Su
Xi Zhang
Philip S. Yu
Wen Hua
Xiaofang Zhou
Binxing Fang

Information diffusion in online social networks has attracted substantial research effort. Although recent models begin to incorporate interactions among contagions, they still don't consider the comprehensive interactions involving users and contagions as a whole. Moreover, the interactions obtained in previous work are modeled as latent factors and thus are difficult to understand and interpret. In this paper, we investigate the contagion adoption behavior by incorporating various types of interactions into a coherent model, and propose a novel interaction-aware diffusion framework called IAD. IAD exploits the social network structures to distinguish user roles, and uses both structures and texts to categorize contagions. Experiments with large-scale Weibo dataset demonstrate that IAD outperforms the state-of-art baselines in terms of F1-score and accuracy, as well as the runtime for learning. In addition, the interactions obtained through learning reveal interesting findings, e. g. , food-related contagions have the strongest capability to suppress other contagions' propagation, while advertisement-related contagions have the weakest capability.

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