In this talk, I discuss recent results on theoretically and experimentally quantifying Entanglement. In particular, newfound quantum laws dictate that classical information (the outcome of a measurement) can freely spread into the Universe, while broadcasting quantum information (the wavefunction of a system) is subject to limitations, as local Entanglement in systems of many particles is inevitably suppressed.

Refs:

Npj Quantum Information 10 (1), 60 (2024);

Physical review letters 129 (1), 010401 (2022);

Physical review letters 128 (1), 010401 (2022)

Group action based cryptography was formally proposed in the seminal paper of Brassard and Yung (Crypto ’90) and recently further developed by Ji et al. (TCC ’19) and Alamati et al. (AsiaCrypt ’19). Based on a one-way group action, Three submissions to the NIST’s call for additional post-quantum digital signatures, such as ALTEQ and MEDS. These schemes can be shown to be secure in the quantum random oracle model (QROM) modulo certain assumptions on the group actions, thanks to the progress on the QROM security of the Fiat–Shamir transformation (Liu–Zhandry and Don et al., Crypto ’19). One approach to proving the QROM security for such group action based schemes uses the perfect unique response property introduced by Unruh (Eurocrypt ’12; AsiaCrypt ’17). In the contexts of ALTEQ and MEDS, this means that a random element does not have a non-trivial automorphism. Before this work, only computational evidence for small dimensions (Bläser et al., PQCrypto ’24; Reijnders–Samardjiska–Trimoska, Des. Codes Cryptogr. ’24) or subexponential bounds (Li–Qiao, FOCS ’17) are known.

In this work, we formally prove that the average order of stabilizer groups is asymptotically trivial. As a result, when the dimension is large enough, all but an exponentially small fraction of alternating trilinear forms or matrix codes have the trivial stabilizer, confirming the assumptions for alternating trilinear forms (ALTEQ) and matrix codes (MEDS). Our approach is to examine the fixed points of the induced action of an invertible matrix over a finite field on trilinear forms.

Measurement-assisted quantum circuits offer a powerful approach to quantum computing by “trading measurement and space for circuit depth,” a key advantage for mitigating noise in shallow architectures. Yet, their resource requirements and fundamental limits has remained elusive, hindering systematic optimization. This talk introduces a unified embedded complexity framework to characterize such circuits. We prove that for states generated by general measurement-assisted circuits, embedded complexity is lower-bounded by circuit volume, extending the linear growth theorem and showing that intermediate measurements and ancillas cannot drastically reduce the cost of generic state preparation. This delineates the intrinsic limits of measurement-assisted protocols and informs applications such as random circuit sampling and quantum shadow tomography. For specific targets, we present a variational optimization scheme using parameterized measurements and efficient gradient estimation to avoid “barren plateaus,” enabling high-fidelity preparation of long-range entangled states at shallow depths and outperforming conventional circuits. These results map the capability boundaries and implementation pathways of measurement-assisted circuits, providing new foundations for fault-tolerant quantum computing and resource optimization. This work is published in [PRL 134, 170601 (2025); arXiv:2408.16602].

Bio: Xiongfeng Ma is a professor at the Institute for Interdisciplinary Information Sciences, Tsinghua University. He is a Fellow of the American Physical Society (APS), and a Fellow of Optica. He received his Bachelor of Science degree from Peking University in 2003 and his Ph.D. from the University of Toronto in 2008. His main research direction is quantum information science, including quantum cryptography, quantum computing, and quantum foundational theories.

We develop new algorithms for Quantum Singular Value Transformation (QSVT), a unifying framework that encapsulates most known quantum algorithms and serves as the foundation for new ones. Existing implementations of QSVT rely on block encoding, incurring an intrinsic \(O(\log L)\) ancilla overhead and circuit depth \(\widetilde{O}(L d\lambda )\) for polynomial transformations of a Hamiltonian \(H=\sum_{k=1}^L H_k\), where \(d\) is the polynomial degree and \(\lambda=\sum_{k}\|H_k\|\).

We introduce a simple yet powerful approach that utilizes only basic Hamiltonian simulation techniques, namely, Trotter methods, to: (i) eliminate the need for block encoding, (ii) reduce the ancilla overhead to only a single qubit, and (iii) still maintain near-optimal complexity. Our method achieves a circuit depth of \(\widetilde{O}(L(d\lambda_{\mathrm{comm}})^{1+o(1)})\), without requiring any complicated multi-qubit controlled gates. Moreover, \(\lambda_{\mathrm{comm}}\) depends on the nested commutators of the terms of \(H\) and can be substantially smaller than \(\lambda\) for many physically relevant Hamiltonians, a feature absent in standard QSVT. To achieve these results, we make use of Richardson extrapolation in a novel way, systematically eliminating errors in any interleaved sequence of arbitrary unitaries and Hamiltonian evolution operators, thereby establishing a general framework that encompasses QSVT but is more broadly applicable.

As applications, we develop end-to-end quantum algorithms for solving linear systems and estimating ground state properties of Hamiltonians, both achieving near-optimal complexity without relying on oracular access. Overall, our results establish a new framework for quantum algorithms, significantly reducing hardware overhead while maintaining near-optimal performance, with implications for both near-term and fault-tolerant quantum computing.

Self-tests are a fundamental class of nonlocal games, which allow one to uniquely determine the underlying quantum state and measurement operators used by the players, based solely on their observed input-output correlations. Motivated by the limitations of current quantum devices, we study self-testing in the high-noise regime, where the two players are restricted to sharing many copies of a noisy entangled state with an arbitrary constant noise rate. In this setting, many existing self-tests fail to certify any nontrivial structure. We first characterize the maximal winning probabilities of the CHSH game, the Magic Square game, and the 2-out-of-\(n\) CHSH game as functions of the noise rate, under the assumption that players use traceless binary observables. These results enable the construction of device-independent protocols for estimating the noise rate. Building on this analysis, we show that these three games—together with an additional test enforcing the tracelessness of binary observables—can self-test one, two, and \(n\) pairs of anticommuting Pauli operators, respectively. These are the first known self-tests that are robust in the high-noise regime and remain sound even when the players’ measurements are noisy. Our proofs rely on Sum-of-Squares (SoS) decompositions and Pauli analysis techniques developed in the contexts of quantum proof systems and quantum learning theory.

This is a joint work with Honghao Fu, Minglong Qin and Haochen Xu.

Quantum entanglement is an essential feature of many-body systems that impacts both quantum information processing and fundamental physics. The growth of entanglement is a major challenge for classical simulation methods. In our recent work [Nature Physics 25, QIP 2025], we investigate the relationship between quantum entanglement and quantum simulation, showing that product-formula approximations can perform better for entangled systems, tending to the average-performance [PRL 129 (27), 270502, QIP22 talk]. We establish a tighter upper bound for algorithmic error in terms of entanglement entropy and develop an adaptive simulation algorithm incorporating measurement gadgets to estimate the algorithmic error. This shows that entanglement is not only an obstacle to classical simulation, but also a feature that can accelerate quantum simulation algorithms.

Bio: Prof. Qi Zhao is an Assistant Professor in the Department of Computer Science, the University of Hongkong (HKU). In 2024, he was recognized as one of the MIT Technology Review “Innovators Under 35” for the Asia Pacific Region. His research interests include quantum simulation, quantum computing, quantum information, and entanglement detection. He obtained a Bachelor’s and Doctoral degree from Tsinghua University in 2014 and 2018 respectively. He was a postdoctoral researcher at the University of Science and Technology of China in 2019. He was a Hartree Postdoctoral Fellow at the University of Maryland in the United States before joining HKU as Assistant Professor in 2022. He has published 46 journal articles, including Nature, Nature Physics, PRL, PRX, npj Quantum Information, PNAS, and IEEE TIT. His works have also been presented as contributed talks at important conferences in quantum information theory, such as QIP, AQIS, TQC, and QCrypt.