East Lake Quantum Seminar

Organizers: Li Gao and Yinan Li and Lijun Wang and Xin Zhang ( Wuhan University )

Conference booklet

Time and Location: November 9-10, at Wuhan University. The conference will be one and half day, starting from Saturday 9th morning and ending at Sunday 10th noon.  The participants can arrive at Wuhan in the afternoon/evening of Friday Nov 8 and leave in the afternoon of Sunday 10th.

Registration is closed. We expect to arrange the local lodging for most of the partipants. If you have any questions and inquiries, please send to gao.li@whu.edu.cn

Invited Speakers: 

• Yangjing Dong* (Nanjing University)

• Kun Fang (Chinese University of Hong Kong-Shenzhen)

• Masahito Hayashi (Chinese University of Hong Kong-Shenzhen)

• Zhengfeng Ji (Tsinghua University)

• Ke Li (Harbin Institute of Technology)

• Zimu Li* (Tsinghua University)

• Jinpeng Liu (Tsinghua University)

• Ziwen Liu (Tsinghua University)

• Shunlong Luo (Chinese Academy of Sciences)

• Xin Wang (Hong Kong University of Science and Technology-Guangzhou)

• Chengkai Zhu* (Hong Kong University of Science and Technology-Guangzhou)

* are graduate student speakers.

Titles and abstracts

Generalized Quantum Stein’s Lemma and Second Law of Quantum Resource Theories

Masahito Hayashi 

The Chinese University of Hongkong (ShenZhen)

Abstract: The second law of thermodynamics is the corner stone of physics, characterizing the convertibility between ther modynamic states through a single function, entropy. Given the universal applicability of thermodynamics, a fundamental ques tion in quantum information theory is whether an analogous sec ond law can be formulated to characterize the convertibility of resources for quantum information processing by a single func tion. In 2008, a promising formulation was proposed, linking resource convertibility to the optimal performance of a variant of the quantum version of hypothesis testing. Central to this formulation was the generalized quantum Stein’s lemma, which aimed to characterize this optimal performance by a measure of quantum resources, the regularized relative entropy of resource. If proven valid, the generalized quantum Stein’s lemma would lead to the second law for quantum resources, with the regu larized relative entropy of resource taking the role of entropy in thermodynamics. However, in 2023, a logical gap was found in the original proof of this lemma, casting doubt on the possibility of such a formulation of the second law. In this work, we resolve this problem by developing alternative techniques and success fully proving the generalized quantum Stein’s lemma. Based on our proof, we reestablish and extend the formulation of quan tum resource theories with the second law, applicable to both static resources of quantum states and a fundamental class of dy namical resources represented by classical-quantum (CQ) chan nels. These results resolve the fundamental problem of bridging the analogy between thermodynamics and quantum information theory. This is a joint work with Hayata Yamasaki and the con tents is available from https://arxiv.org/abs/2408.02722. 

Convergence efficiency of quantum gates and circuits

Ziwen Liu

Tsinghua University

Abstract: TBD 

Quantum R´ enyi divergence and its use in quantum information

Ke Li

Harbin Institute of Technology

Abstract: I will talk about the quantum generalization of R´enyi’s information divergence and its use in quantum information the ory. Due to the noncommutativity of quantum theory, the quan tum version of R´ enyi divergence is not unique, and we still lack a full understanding of it. A proper formula of the quantum R´ enyi divergence should admit precise operational interpreta tion. Based on a series of recent works with coauthors, I will report: (1) how quantum R´enyi divergence characterizes exactly the error exponents in quantum information, and (2) conversely, how the former operational characterization sheds light on the quantum generalization of R´enyi’s information divergence. 

Parameterized Hamiltonian Complexity

Zhengfeng Ji

Tsinghua University

Abstract: Parameterized complexity theory offers a powerful framework for analyzing the computational hardness of problems, where complexity is measured not just by input size but by additional parameters. In this talk, we introduce a parame terized version of the local Hamiltonian problem, which we refer to as the weighted local Hamiltonian problem. In this variation, the relevant quantum states are superpositions of computational basis states with a fixed Hamming weight. 

We demonstrate that this problem belongs to QW[1], the first level of the quantum weft hierarchy, and we further show that it is hard for QM[1], the quantum analog of the classical param eterized class M[1]. These findings indicate that the weighted lo cal Hamiltonian problem is not fixed-parameter quantum tractable (FPQT) unless a natural quantum analog of the Exponential Time Hypothesis (QETH) is false.

Moreover, we apply this perspective to the complexity analy sis of quantum chemistry problems, highlighting that the N representability problem—a central challenge in quantum chem istry—is also hard for QM[1]. These results provide new insights into the computational limitations of quantum algorithms for quantum many-body physics and quantum chemistry. 

Efficient quantum pseudorandomness under conservation laws

Zimu Li

Tsinghua University

Abstract: Efficient generation of quantum pseudorandomness unitary k-designs–under conservation laws has conceived a wide array of interests and intensive studies in the study of quantum information as well as physics. Despite this, no circuit archi tectures are known that are capable of forming designs with guaranteed convergence time upper-bounds. We address this long-standing open question by explicitly constructing quan tum circuits that approximate unitary 2-design under U(1) and SU(d) symmetries in polynomial time with respect to the system size n. We also discuss why it is difficult to evaluate the con vergence time mathematically through several classical meth ods that worked well for the case without symmetries. We would provide some applications, including information scram bling with conserved quantities and covariant error-correcting random codes, if time permits.

Quantum Unitary Reversal Algorithm

Yin Mo

The Hong Kong University of Science and Technology (Guangzhou)

Abstract: Reversing an unknown unitary evolution remains a formidable challenge, as conventional methods necessitate an infinite number of queries to fully characterize the quantum pro cess. Here we introduce the Quantum Unitary Reversal Algo rithm (QURA), a deterministic and exact approach to univer sally reverse arbitrary unknown unitary transformations using O(d2) calls of the unitary, where d is the system dimension. Our construction resolves a fundamental problem of time-reversal simulations for closed quantum systems by affirming the feasi bility of reversing any unitary evolution without knowing the exact process. The algorithm also provides the construction of a key oracle for unitary inversion in quantum algorithm frame works such as quantum singular value transformation. Notably, our work reveals a sharp boundary between the quantum and classical realms and unveils a quadratic quantum advantage in computational complexity for this foundational task. 

Amortized Stabilizer Renyi Entropy of Quantum Dynamics

Chengkai Zhu

The Hong Kong University of Science and Technology (Guangzhou)

Abstract: Unraveling the secrets of how much nonstabilizer ness a quantum dynamic can generate is crucial for harnessing the power of magic states, the essential resources for achieving quantum advantage and realizing fault-tolerant quantum com putation. In this work, we introduce the amortized α-stabilizer R´ enyi entropy, a magic monotone for unitary operations that quantifies the nonstabilizerness generation capability of quan tum dynamics. Amortization is key in quantifying the magic of quantum dynamics, as we reveal that nonstabilizerness genera tion can be enhanced by prior nonstabilizerness in input states when considering the α-stabilizer R´enyi entropy, while this is not the case for robustness of magic or stabilizer extent. We demon strate the versatility of the amortized α-stabilizer R´enyi entropy in investigating the nonstabilizerness resources of quantum dy namics of computational and fundamental interest. In partic ular, we establish improved lower bounds on the T-count of quantum Fourier transforms and the quantum evolutions of one dimensional Heisenberg Hamiltonians, showcasing the power of this tool in studying quantum advantages and the correspond ing cost in fault-tolerant quantum computation. 

From Magic States to Zauner’s Conjectures

Shunlong Luo

Chinese Academy of Sciences

Abstract: In the paradigm of quantum measurement, com plete mutually unbiased bases (MUBs) and symmetric infor mationally complete positive operator valued measures (SIC POVMs) are two prominent objects due to their structural sym metry and remarkable features. However, their existences in ar bitrary dimensions (Zauner’s conjectures) remain elusive. We discuss some aspects in the pursuing and constructing of MUBs and SIC-POVMs via group frames and magic states. We high light the key roles played by the orbit of Heisenberg-Weyl group and certain mystical fiducial states (vectors in finite dimensional Hilbert spaces), which are most magic. Some related open prob lems are also presented.

Provably Efficient Adiabatic Learning for Quantum-Classical Dynamics

Jinpeng Liu

Tsinghua University

Abstract: Quantum-classical hybrid dynamics is crucial for ac curately simulating complex systems where both quantum and classical behaviors need to be considered. However, coupling be tween classical and quantum degrees of freedom and the expo nential growth of the Hilbert space present significant challenges. Current machine learning approaches for predicting such dy namics, while promising, remain unknown in their error bounds, sample complexity, and generalizability. In this work, we es tablish a generic theoretical framework for analyzing quantum classical adiabatic dynamics with learning algorithms. Based on quantum information theory, we develop a provably efficient adiabatic learning (PEAL) algorithm with logarithmic system size sampling complexity and favorable time scaling properties. We benchmark PEAL on the Holstein model, and demonstrate its accuracy in predicting single-path dynamics and ensemble dynamics observables as well as transfer learning over a family of Hamiltonians. Our framework and algorithm open up new avenues for reliable and efficient learning of quantum-classical dynamics. 

On the Computational Power of QAC0 with Barely Superlinear Ancillae

Yangjing Dong

Nanjing University

Abstract: QAC0 is the family of constant-depth polynomial size quantum circuits consisting of arbitrary single qubit uni taries and multi-qubit Toffoli gates. It was introduced by Moore [arXiv: 9903046] as a quantum counterpart of AC0, along with the conjecture that QAC0 circuits can not compute PARITY. In this work we make progress on this longstanding conjecture: we show that any depth-d QAC0 circuit requires n1+3−d ancil lae to compute a function with approximate degree Θ(n), which includes PARITY, MAJORITY and MODk. This is the first superlinear lower bound on the size of the ancillae required for computing parity. We further establish superlinear lower bounds on quantum state synthesis and quantum channel syn thesis. These lower bounds are derived by giving low-degree ap proximations to QAC0 circuits. We show that a depth-d QAC0 circuit with a ancillae, when applied to low-degree operators, has a degree (n+a)1−3−d polynomial approximation in the spec tral norm. This implies that the class QLC0, corresponding to linear size QAC0 circuits, has approximate degree o(n). This is a quantum generalization of the result that LC0 circuits have approximate degree o(n) by Bun, Kothari, and Thaler [SODA 2019]. Our result also implies that QLC0= NC1. 

Dynamic quantum circuit compilation

Kun Fang

The Chinese University of Hongkong (ShenZhen)

Abstract: Quantum computing has shown tremendous promise in addressing complex computational problems, yet its practical realization is hindered by the limited availability of qubits for computation. Recent advancements in quantum hardware have introduced mid-circuit measurements and resets, enabling the reuse of measured qubits and significantly reducing the qubit requirements for executing quantum algorithms. In this work, we present a systematic study of dynamic quantum circuit com pilation, a process that transforms static quantum circuits into their dynamic equivalents with a reduced qubit count through qubit-reuse. We establish the first general framework for opti mizing the dynamic circuit compilation via graph manipulation. In particular, we completely characterize the optimal quantum circuit compilation using binary integer programming, provide efficient algorithms for determining whether a given quantum circuit can be reduced to a smaller circuit and present heuristic algorithms for devising dynamic compilation schemes in gen eral. Furthermore, we conduct a thorough analysis of quan tum circuits with practical relevance, offering optimal compila tions for well-known quantum algorithms in quantum computa tion, ansatz circuits utilized in quantum machine learning, and measurement-based quantum computation crucial for quantum networking. We also perform a comparative analysis against state-of-the-art approaches, demonstrating the superior perfor mance of our methods in both structured and random quantum circuits. Our framework lays a rigorous foundation for compre hending dynamic quantum circuit compilation via qubit-reuse, bridging the gap between theoretical quantum algorithms and their physical implementation on quantum computers with lim ited resources. 

Talk Slides

 Masahito Hayashi, Generalized Quantum Stein’s Lemma and Second Law of Quantum Resource Theories. [Slides]

Ziwen Liu, Convergence efficiency of quantum gates and circuits. [Slides]

Ke Li, Quantum R´ enyi divergence and its use in quantum information. [Slides]

Zhengfeng Ji, Parameterized Hamiltonian Complexity. [Slides]

Zimu Li, Efficient quantum pseudorandomness under conservation laws. [Slides]

Yin Mo, Quantum Unitary Reversal Algorithm. [Slides]

Chengkai Zhu, Amortized Stabilizer Renyi Entropy of Quantum Dynamics. [Slides]

Shunlong Luo, From Magic States to Zauner’s Conjectures. [Slides]

Jinpeng Liu, Provably Efficient Adiabatic Learning for Quantum-Classical Dynamics. [Slides]

Yangjing Dong, On the Computational Power of QAC0 with Barely Superlinear Ancillae. [Slides]

Kun Fang , Dynamic quantum circuit compilation. [Slides]

Gallary

Conference Venue: 

Lodging information:  All conference lodging will be reserved at Junyi Dynasty Hotel (君宜王朝大酒店)

Address: No.87, Luoyu Road, Hongshan, Wuhan (武汉市洪山区珞喻路87号)

Phone: +86 027 8768 7777 

Transportation to Hotel

From Tianhe Airport: 

By Taxi or E-hailing：100-150 yuan, ~1 hour (if no traffic). 

By Metro Line 2: 1.5 hour.

From Wuhan Railway Station: 

By Taxi or E-hailing：30-50 yuan, ~30 mins (if no traffic). 

By Metro Line 4+Line 2: 50 mins.

When buying tickets, note that there are also two different rail stations: Wuchang Station and Haikou Station.

Supports from

• School of Mathematics and Statistics, Wuhan University  (武汉大学数学与统计学院）

• Tianyuan Mathematical Center at Central China  (天元数学中部中心）

• National Natural Science Foundation of China  (国家自然科学基金委)