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Zihan Hu

Publications and source records attributed to Zihan Hu.

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A Meta-Complexity Characterization of Minimal Quantum Cryptography

We give a meta-complexity characterization of EFI pairs, which are considered the "minimal" primitive in quantum cryptography (and are equivalent to quantum commitments). More precisely, we show that the existence of EFI pairs is equivalent to the following: there exists a non-uniformly samplable distribution over pure states such that the problem of estimating a certain Kolmogorov-like complexity measure is hard given a single copy. A key technical step in our proof, which may be of independent interest, is to show that the existence of EFI pairs is equivalent to the existence of non-uniform single-copy secure pseudorandom state generators (nu 1-PRS). As a corollary, we get an alternative, arguably simpler, construction of a universal EFI pair.

quant-ph

CANDLE: A Cross-Modal Agentic Knowledge Distillation Framework for Interpretable Sarcopenia Diagnosis

Background and Aims: Large language models (LLMs) have shown remarkable generalization and transfer capabilities by learning from vast corpora of text and web data. Their semantic representations allow cross-task knowledge transfer and reasoning, offering promising opportunities for data-scarce and heterogeneous domains such as clinical medicine. Yet, in diagnostic tasks like sarcopenia, major challenges remain: interpretability, transparency, and deployment efficiency. Traditional machine learning (TML) models provide stable performance and feature-level attribution, ensuring traceable and auditable decision logic, but lack semantic breadth. Conversely, LLMs enable flexible inference but often function as opaque predictors. Existing integration strategies remain shallow, rarely embedding the structured reasoning of TML into LLM inference. Methods: Using sarcopenia diagnosis as a case study, SHapley Additive exPlanations (SHAP) were extracted from a baseline XGBoost model and transformed into structured, LLM-compatible representations. An actor-critic reinforcement learning (RL) strategy guided the LLM to reason over these SHAP-based inputs, producing calibrated rationales and refined decision rules. The distilled reasoning was consolidated into a structured knowledge repository and deployed via retrieval-augmented generation (RAG) for case-based inference. Results: (Omitted here.) Conclusion: By coupling SHAP-derived statistical evidence with reinforcement-trained LLM reasoning, CANDLE mitigates the interpretability-performance trade-off, enhances predictive accuracy, and preserves high decision consistency. The framework offers a scalable approach to knowledge assetization of TML models, enabling interpretable, reproducible, and clinically aligned decision support in sarcopenia and potentially broader medical domains.

cs.LG

LWE with Quantum Amplitudes: Algorithm, Hardness, and Oblivious Sampling

In this paper, we show new algorithms, hardness results and applications for $\sf{S|LWE\rangle}$ and $\sf{C|LWE\rangle}$ with real Gaussian, Gaussian with linear or quadratic phase terms, and other related amplitudes. Let $n$ be the dimension of LWE samples. Our main results are 1. There is a $2^{\tilde{O}(\sqrt{n})}$-time algorithm for $\sf{S|LWE\rangle}$ with Gaussian amplitude with \emph{known} phase, given $2^{\tilde{O}(\sqrt{n})}$ many quantum samples. The algorithm is modified from Kuperberg's sieve, and in fact works for more general amplitudes as long as the amplitudes and phases are completely \emph{known}. 2. There is a polynomial time quantum algorithm for solving $\sf{S|LWE\rangle}$ and $\sf{C|LWE\rangle}$ for Gaussian with quadratic phase amplitudes, where the sample complexity is as small as $\tilde{O}(n)$. As an application, we give a quantum oblivious LWE sampler where the core quantum sampler requires only quasi-linear sample complexity. This improves upon the previous oblivious LWE sampler given by Debris-Alazard, Fallahpour, Stehl\'{e} [STOC 2024], whose core quantum sampler requires $\tilde{O}(nr)$ sample complexity, where $r$ is the standard deviation of the error. 3. There exist polynomial time quantum reductions from standard LWE or worst-case GapSVP to $\sf{S|LWE\rangle}$ with Gaussian amplitude with small \emph{unknown} phase, and arbitrarily many samples. Compared to the first two items, the appearance of the unknown phase term places a barrier in designing efficient quantum algorithm for solving standard LWE via $\sf{S|LWE\rangle}$.

quant-ph

On the (Im)plausibility of Public-Key Quantum Money from Collision-Resistant Hash Functions

Public-key quantum money is a cryptographic proposal for using highly entangled quantum states as currency that is publicly verifiable yet resistant to counterfeiting due to the laws of physics. Despite significant interest, constructing provably-secure public-key quantum money schemes based on standard cryptographic assumptions has remained an elusive goal. Even proposing plausibly-secure candidate schemes has been a challenge. These difficulties call for a deeper and systematic study of the structure of public-key quantum money schemes and the assumptions they can be based on. Motivated by this, we present the first black-box separation of quantum money and cryptographic primitives. Specifically, we show that collision-resistant hash functions cannot be used as a black-box to construct public-key quantum money schemes where the banknote verification makes classical queries to the hash function. Our result involves a novel combination of state synthesis techniques from quantum complexity theory and simulation techniques, including Zhandry's compressed oracle technique.

quant-ph