arXiv subjects

Chia-Ying Lin

Publications and source records attributed to Chia-Ying Lin.

4 recordsLinked to original sources

arXiv2025

Shadow Tomography Against Adversaries

We study single-copy shadow tomography in the adversarial robust setting, where the goal is to learn the expectation values of $M$ observables $O_1, \ldots, O_M$ with $\varepsilon$ accuracy, but $\gamma$-fraction of the outcomes can be arbitrarily corrupted by an adversary. We show that all non-adaptive shadow tomography algorithms must incur an error of $\varepsilon=\tilde{\Omega}(\gamma\min\{\sqrt{M}, \sqrt{d}\})$ for some choice of observables, even with unlimited copies. Unfortunately, the classical shadows algorithm by [HKP20] and naive algorithms that directly measure each observable suffer even more. We design an algorithm that achieves an error of $\varepsilon=\tilde{O}(\gamma\max_{i\in[M]}\|O_i\|_{HS})$, which nearly matches our worst-case error lower bound for $M\ge d$ and guarantees better accuracy when the observables have stronger structure. Remarkably, the algorithm only needs $n=\frac{1}{\gamma^2}\log(M/\delta)$ copies to achieve that error with probability at least $1-\delta$, matching the sample complexity of the classical shadows algorithm that achieves the same error without corrupted measurement outcomes. Our algorithm is conceptually simple and easy to implement. Classical simulation for fidelity estimation shows that our algorithm enjoys much stronger robustness than [HKP20] under adversarial noise. Finally, based on a reduction from full-state tomography to shadow tomography, we prove that for rank $r$ states, both the near-optimal asymptotic error of $\varepsilon=\tilde{O}(\gamma\sqrt{r})$ and copy complexity $\tilde{O}(dr^2/\varepsilon^2)=\tilde{O}(dr/\gamma^2)$ can be achieved for adversarially robust state tomography, closing the large gap in [ABCL25] where optimal error can only be achieved using pseudo-polynomial number of copies in $d$.

quant-ph↗

arXiv2025

Efficient Matrix Product State Learning in Logarithmic Depth

Learning the closest matrix product state (MPS) representation of a quantum state enables useful tools for quantum machine learning and analysis of complex quantum systems. In this work, we study the problem of learning MPS in the following setting: given many copies of an input MPS, the task is to recover a classical description of the state. The best known polynomial-time algorithm, introduced by [LCLP10, CPF+10], requires linear circuit depth and $\widetilde O(n^5)$ samples, and has seen no improvement in over a decade. These costs, neither known to be optimal, renders existing algorithms impractical for near-term quantum devices with limited resources. We introduce parallel disentangling algorithms for MPS learning. For exact MPS learning, our algorithm runs in polynomial time and uses circuit depth $O(\log n)$ and sample complexity $\widetilde O(n^3)$, improving both the depth and the dependence on the system size $n$. The key idea is to exploit the bounded-rank structure of reduced states on middle blocks of an MPS and organize the disentangling operations in a tree structure. We further extend the algorithm to closest MPS learning, improving the sample complexity dependence on $n$ from $n^9$ to $n^7$ and complement the algorithms with an $\Omega(n)$ product-state lower bound. We also investigate MPS learning under hardware constraints, including restricted measurements and geometric connectivity. Under the Learning Parity with Noise (LPN) assumption, we show computational hardness for learning an MPS(2) family with non-adaptive single-qubit measurements. Finally, we show that our algorithm can be implemented with depth $O(q n^{1/q})$ on a $q$-dimensional hypercubic lattice, giving an asymptotic reduction in depth. Together, our work provides a complete characterization of the quantum resources needed for efficient MPS learning.

quant-ph↗

arXiv2022

Sparse Edge Encoder (SEE): I. Visual recognition in neuronal networks

In the past few decades, there have been intense debates whether the brain operates at a critical state. To verify the criticality hypothesis in the neuronal networks is challenging and the accumulating experimental and theoretical results remain controversial at this point. Here we simulate how visual information of a nature image is processed by the finite Kinouchi-Copelli neuronal network, extracting the trends of the mutual information (how sensible the neuronal network is), the dynamical range (how sensitive the network responds to external stimuli) and the statistical fluctuations (how criticality is defined in conventional statistical physics). It is rather remarkable that the optimized state for visual recognition, although close to, does not coincide with the critical state where the statistical fluctuations reach the maximum. Different images and/or network sizes of course lead to differences in details but the trend of the information optimization remains the same. Our findings pave the first step to investigate how the information processing is optimized in different neuronal networks and suggest that the criticality hypothesis may not be necessary to explain why a neuronal network can process information smartly.

q-bio.NC↗

arXiv2021

U(1) dynamics in neuronal activities

Neurons convert the external stimuli into action potentials, or spikes, and encode the contained information into the biological nerve system. Despite the complexity of neurons and the synaptic interactions in between, the rate models are often adapted to describe neural encoding with modest success. However, it is not clear whether the firing rate, the reciprocal of the time interval between spikes, is sufficient to capture the essential feature for the neuronal dynamics. Going beyond the usual relaxation dynamics in Ginzburg-Landau theory for statistical systems, we propose the neural activities can be captured by the U(1) dynamics, integrating the action potential and the ``phase" of the neuron together. The gain function of the Hodgkin-Huxley neuron and the corresponding dynamical phase transitions can be described within the U(1) neuron framework. In addition, the phase dependence of the synaptic interactions is illustrated and the mapping to the Kinouchi-Copelli neuron is established. It suggests that the U(1) neuron is the minimal model for single-neuron activities and serves as the building block of the neuronal network for information processing.

q-bio.NC↗