CQCC & GQSF 2026概况

安冬，北京大学北京国际数学研究中心助理教授。2016年获得北京大学计算数学学士学位，2021年获得加州大学伯克利分校应用数学博士学位，自2021年9月起在马里兰大学量子信息和计算机科学联合中心(QuICS)担任哈特里博士后研究员，2024年9月入职北京大学。主要研究兴趣包括量子算法、计算量子力学，以及量子计算和应用数学的跨学科研究，包括隔热量子计算、量子模拟、线性系统和微分方程的量子算法等。

赖志坚，北京大学北京国际数学研究中心博雅博士后。2024年博士毕业于日本筑波大学，毕业至今在北京大学文再文课题组从事博士后研究工作。研究方向为流形优化，量子计算和优化。国家自然科学青年基金项目负责人。

2018年在澳大利亚悉尼科技大学获得博士学位。2018年至2022年在荷兰国家数学与计算机中心（CWI）和日本名古屋大学从事博士后研究。2022年9月入职武汉大学。主要研究兴趣包括量子计算理论及其在数学、物理和计算机科学中的交叉应用。

Tongyang Li is currently an assistant professor at Center on Frontiers of Computing Studies, Peking University. Previously he was a postdoctoral associate at the Center for Theoretical Physics, Massachusetts Institute of Technology. He received Master and Ph.D. degrees in computer science from University of Maryland, and Bachelor of Engineering from IIIS, Tsinghua University with a second degree in mathematics. Tongyang’s research focuses on designing quantum algorithms for optimization and machine learning. He has published more than 40 papers in Nature Physics, Nature Communications, Journal of the ACM, Physical ReviewLetters, IEEE Transactions on Information Theory, STOC, ICML, NeurlPS, ICLR, and other top venues.

报告主题：Optimization by Comparison: Classical and Quantum Algorithms

摘要： In this talk, I will introduce optimization algorithms using comparisons. Specifically, given a smooth function f: R^n - R, we only assume a comparison oracle that inputs two points x1 and x2 and outputs 1 if f(x1)<=f(x2) and -1 otherwise. We cover the following problems: (1) gradient testing, (2) gradient estimation, (3) convex optimization, and (4) finding stationary points in nonconvex optimization. We introduce both classical as well as quantum algorithms for solving these problems, and also introduced both classical and quantum lower bounds.

刘锦鹏，清华大学丘成桐数学科学中心助理教授，博士生导师，入选国家海外高层次人才引进计划，2022-2024年在麻省理工和伯克利任博士后，2022年博士毕业于马里兰大学，2017年本科毕业于北航-中国科学院华罗庚班。研究方向为量子科学计算与量子科学智能，在PNAS、Nat.Commun. 、PRL、CMP、JCP、Quantum等期刊和NeurIPS、QIP、TQC等会议发表多篇论文，受到Quanta、SIAM News、MATH+等科技媒体报道，获得世界华人数学家大会ICCM毕业论文金奖，受邀在菲尔兹研究院作专题报告，担任量子信息权威期刊Quantum（JCR Q1，IF 6.4）的编委。

报告主题：Sign Embedding Quantum Algorithms for Matrix Equations and Matrix Functions

摘要：We develop a systematic framework of quantum algorithms for matrix equations (ordinary and generalized Sylvester equations, generalized Lyapunov equations, algebraic Riccati equations) and matrix functions (principal square roots, inverse square roots, geometric means).  Our algorithms relax non-normal and non-diagonalizable settings, given a field-of-values (FoV) gap or strip-resolvent hypotheses. Differing from the contour-integral treatment, our framework contains the three ingredients: matrix-sign embedding (real-line contour simplification), log-sinc rational approximation, and nodewise rebalancing of the shifted-inverse implementation.  The matrix-sign embedding route support a broad class of quantum algorithms and is resuable for structured operator-output quantum linear algebra.

2024年博士毕业于日本筑波大学，毕业至今在北京大学文再文课题组从事博士后研究工作。研究方向为流形优化，量子计算和优化。国家自然科学青年基金项目负责人。

报告主题：基于黎曼优化框架的量子线路设计

摘要：面向基态制备的量子线路设计是量子信息科学领域的基础研究问题。然而，标准变分量子算法普遍存在量子线路拟设表达能力有限、优化过程易陷入困境等瓶颈。为突破上述局限，本文从几何视角出发，将量子线路设计问题转化为酉群上的能量函数最小化问题，构建了基于回缩的黎曼优化框架，确保算法各步骤可直接在量子硬件上执行。依托该框架，本文提出黎曼随机子空间梯度投影法（Riemannian Random Subspace Gradient Projection, RRSGP），实现了对现有随机梯度类算法的统一表述。另外，相关几何优化方法多聚焦于一阶梯度下降算法，针对高效二阶算法的系统性研究仍较为匮乏。为此，本文还推导了黎曼 Hessian 的显式表达式，证明其可通过参数平移规则在量子硬件上直接估算。基于此，进一步提出黎曼随机子空间牛顿法（Riemannian Random Subspace Newton, RRSN），该算法为可扩展的二阶优化方法，能够依托测量数据构建牛顿方程。数值实验结果表明，相较于现有一阶算法及标准变分量子算法，RRSN 算法具备二次收敛特性，仅需更少迭代次数即可制备出高精度基态。综上，本工作为将各类高效黎曼优化算法系统性应用于量子线路设计奠定了理论与方法基础。

2023年入职中国科学院数学与系统科学研究院，担任副研究员。这之前，在英国布里斯托大学读博士后，主要从事量子算法与复杂度方面的研究，相关学术工作发表在权威期刊Communications in Mathematical Physics，SIAM Journal on Matrix Analysis and Applications和会议STOC上发表过论文，在量子计算权威会议QIP上做过4次报告。

报告主题：DQC1-completeness of normalized trace estimation for functions of log-local Hamiltonians

摘要：We study the computational complexity of estimating the normalized trace $2^{-n}\tr[f(A)]$ for a log-local Hamiltonian $A$ acting on $n$ qubits. This problem arises naturally in the DQC1 model, yet its complexity is only understood for a limited class of functions $f(x)$. We show that if $f(x)$ is a continuous function with approximate degree $\Omega(\mathrm{poly}(n))$, then estimating $2^{-n}\tr[f(A)]$ up to constant additive error is DQC1-complete, under a technical condition on the polynomial approximation error of $f(x)$. This condition holds for a broad class of functions, including exponentials, trigonometric functions, logarithms, and inverse-type functions. We further prove that when $A$ is sparse, the classical query complexity of this problem is exponential in the approximate degree. Together, these results identify the approximate degree as the key parameter governing the complexity of normalized trace estimation: it characterizes both the quantum complexity (via efficient DQC1 algorithms) and, conditionally, the classical hardness, yielding an exponential quantum–classical separation. Our proof develops a unified framework that cleanly combines circuit-to-Hamiltonian constructions, periodic Jacobi operators, and tools from polynomial approximation theory, including the Chebyshev equioscillation theorem. The talk is based on joint work with Zhengfeng Ji, Tongyang Li, Xinzhao Wang and Yuxin Zhang, see arXiv:2604.01519.

Zhong-Xia Shang is currently a postdoc of QMATH at the University of Copenhagen. Previously, he was an HKIQST postdoctoral fellow affiliated with the University of Hong Kong (HKU). He obtained his Ph.D. degree in Physics at University of Science and Technology of China (USTC) (2024). His advisor is Prof. Chao-Yang Lu. He also obtained his B.S. degree in Physics at the School of Gifted Young, USTC (2019). His current insterests are designing quantum algorithms and exploring quantum advantages

报告主题：Hamiltonian dynamics from pure dissipation

摘要：The fundamental difference between closed and open quantum dynamics lies in their environmental interaction: closed systems are perfectly isolated and evolve reversibly under unitary Hamiltonian dynamics, whereas open systems continuously couple to an external bath, resulting in irreversible dissipation and information loss. In this talk, I will show internal Hamiltonian dynamics can be "faked`` via external pure dissipation, i.e., Lindbladians without a coherent Hamiltonian part. More concretely, we show that, in a GKSL representation with zero explicit Hamiltonian, bounded-norm dissipative generators can approximate Hamiltonian dynamics within $\epsilon$ error in diamond norm using $\mathcal{O}(t^2/\epsilon)$ evolution time. We further prove that for time-independent dynamics this $\mathcal{O}(t^2/\epsilon)$ scaling is in the worst case, necessary and optimal from a geometric perspective, which captures the fundamental decoherence cost for catching up with the speed of Hamiltonian dynamics. For practical considerations, we establish an autonomous QDRIFT protocol and show how to exponentially improve the dependence on $\epsilon$ for expectation value estimation via extrapolations. Our construction leads to various implications, including the BQP-completeness of purely dissipative dynamics even before reaching approximate equilibrium, a Zeno-adjacent state-independent freezing effect, the no super-quadratic fast-forwarding theorem of a class of purely dissipative dynamics, and reducing Lindbladian simulation cost via gauge changing.