Research statement
Towards practical quantum technologies with constrained operations and limited resources.
My research area is quantum information science, which is a rapidly growing field that demands interdisciplinary knowledge in quantum physics, mathematics, and computer science. This field aims to harness quantum resources such as entanglement and coherence to enhance our capabilities for computation and communication. However, to turn the theoretically blueprinted quantum advantages into practice, a deep understanding of what can and cannot be done with these resources is required, along with a systematic strategy to translate these theories into engineering products. My research focuses on addressing the critical challenges in quantum information science by exploring the capabilities and limitations of various quantum resources. I also strive to translate these theories into engineering products that can benefit both industry and society. My experience as a quantum researcher
and software engineer
has equipped me with a comprehensive understanding of the grand journey towards quantum industrialization.
In the following, I will provide an overview of my research.
Resource benchmarks for quantum technology
Quantum technology is believed to be much more powerful than conventional technology in many cases. One of the main drivers of its superior performance is the effective utilization of quantum resources. These resources, analogous to fuel for a car, play a critical role in all kinds of quantum technologies, such as magic states for faulttolerant quantum computation, quantum channels for quantum communication, and quantum entanglement for quantum networking. However, these quantum resources are inherently fragile and vulnerable to noise effects induced by environmental factors, imperfect controls and unstable memories, severely compromising the accuracy, efficiency, and security of computation and communication tasks. To address this challenge, a standard approach known as quantum resource distillation has emerged. This process involves transforming a large amount of noisy resource into a smaller amount of pure resource, similar to the process of reducing a dilute solution to a more concentrated one. Alongside this approach, two fundamental questions have been extensively investigated over the past two decades in the quantum community:

How much noisy resource should we invest at least to obtain a fixed amount of pure resource?

How much pure resource can we obtain at most from a fixed amount of noisy resource?
A deeper understanding of these questions can provide invaluable insights into the resource cost of overcoming quantum noise, benchmark stateoftheart protocols, and ultimately remove the barriers to scaling quantum computers and quantum networks. Therefore, the main focus of my research has been on finding answers to these questions.
A universal law for quantum resource distillation (QIP talk^{1})
The celebrated nocloning theorem^{2} and nodeleting theorem^{3} similarly revealed nogo rules of information processing stemming from the basic laws of quantum mechanics and have had a profound impact on the development of quantum technologies. In the same spirit, my work [FL20PRL]^{4} proposed the first nogo theorem for quantum resource distillation
, which universally applies to any reasonable resource theory, demonstrating that the production of any pure resource state with an arbitrarily small error is generically prohibited. We also established a quantitative tradeoff between the accuracy and success probability of resource distillation, closely resembling the wellknown uncertainty relation of quantum mechanics and drawing practical boundaries for quantum error processing. This work has been highlighted as an Editors' Suggestion in Physical Review Letters
, placing it in the top 15% of all accepted papers, due to its particular importance, innovation, and broad appeal. Subsequently, my work [FL22PRX Quantum]^{5} expanded these results further to encompass dynamic quantum resources applicable to important areas such as quantum error correction and quantum communication.
Magic state distillation for faulttolerant quantum computing (QIP talk)
Quantum computing requires implementing a sequence of quantum gates, which serve as the building blocks for all quantum algorithms. However, a quantum computer that uses only Clifford gates would not be more powerful than a classical computer, as per the GottesmanKnill theorem. To construct a universal quantum computer, we need to supplement Clifford gates with a specific type of state known as magic state. These states are named as such because they can turn what is essentially classical into quantum, much like a magic wand. The quality of magic states is crucial to the performance of quantum computational tasks; if it is too noisy, the computational results may be inaccurate.
To address this issue, magic state distillation was introduced, and a longstanding open question in this area of research is whether we can distill a magic state using sublogarithmic resources. Applying the nogo theorem for quantum resource distillation, my work [FL20PRL]^{4} fully addressed this open problem
since its initial exploration in 2005 ^{6} ^{7} ^{8} ^{9} ^{10} ^{11} ^{12}. We proved that magic state distillation cannot be achieved with sublogarithmic resources. This provides useful benchmarks for the resource requirements of faulttolerant quantum computation, as the Heisenberg limit did for quantum metrology.
Quantum channel coding for reliable quantum communication (3 QIP talks)
Quantum communication is a fundamental technology in the next generation of information transmission, and also a cornerstone in building the future quantum internet. To prevent quantum data from being corrupted during transmission, senders encode their data before sending it through the channel, while receivers decode the incoming message to faithfully recover the sender’s intended information. This procedure is called quantum channel coding, a kind of resource distillation that corrects noisy quantum channels into noiseless ones. The core issue here is to understand the optimal coding strategy and determine how much information can be reliably transmitted under such a strategy. This ultimate capability is the socalled quantum channel capacity, which tells us what the best coding strategy can do. Such a problem was wellstudied in the classical case by Shannon in 1948, but quantum communication is much more challenging. There is a large body of literature working on the numerical evaluation of quantum channel capacity via different techniques. By exploiting the tools of quantum entropies and semidefinite programs, my works [WFD18IEEE TIT]^{13} [WFT19IEEE TIT]^{14} [FF21CMP]^{15} provided the stateoftheart algorithms
(from 2017 to 2020) for estimating the capacity of a quantum channel in general. Moreover, in [WFT19IEEE TIT]^{14}, we completely determined the secondorder asymptotics of the classical capacity of quantum erasure channels (an important noise model), which is of particular importance when the size of the quantum devices at the encoder and decoder is relatively small in the near term. This is also the first secondorder expansion
of classical capacity beyond entanglementbreaking channels and fills an important gap in the literature^{16}.
Quantum entanglement and coherence distillation for quantum networking
Quantum coherence and quantum entanglement are two landmark features of quantum physics. The former represents the quantumness of a single quantum system and is famously illustrated by Schrödinger’s Cat, a hypothetical cat simultaneously both alive and dead. The latter represents a remarkable correlation between different quantum systems and is referred to as the ``spooky action at a distance’’ by Einstein. These features serve as the key resources and building blocks for the future quantum internet, enabling exponential speedup in quantum computation, unhackable key distribution, ultrahigh precision clock synchronization, and privacypreserving cloud services. In all these scenarios, the quality of these resources is crucial as it directly impacts the efficiency and security of the corresponding tasks. Therefore, resource distillation is used to ensure the quality of these resources before their actual usage.
A major concern here is to understand the maximal amount of pure entanglement or coherence that can be extracted from a fixed amount of noisy resources. Using the techniques of semidefinite optimization, my work [FWTD19IEEE TIT]^{17} introduced efficiently computable frameworks for estimating the transformation rate of distilling quantum entanglement and initiated the first secondorder analysis
of this task under practical noise and operations. Similarly, in [HFW21IEEE TIT]^{18}, we have also made significant contributions by initiating the first secondorder analysis
on coherence distillation and establishing a precise connection between coherence distillation and randomness extraction in quantum cryptography.
Another set of works [FWLRA18PRL]^{19} [RFWA18PRL]^{20} [RFWG19NJP]^{21} [DFWRSCW18Quantum]^{22} provided quantitative analysis on the operational power of different classes of operations for distilling quantum entanglement and quantum coherence. These series of works have made groundbreaking contributions to understanding critical quantum resources in quantum networks and have attracted widespread attention
in the community (with over 350 citations to date) and have been successfully utilized as benchmarks in experiments
^{23}.
Mathematical tools for quantum information processing
The development of quantum information science often accompanies by a more thorough understanding of the mathematical framework underlying it. Of particular relevance are quantum entropies and optimization theories, which serve as valuable tools for analyzing quantum information processing.
Quantum relative entropy in quantum data discrimination (QIP talk)
Quantum relative entropies serve as quantum generalizations of the widely used KullbackLeibler divergence, providing a measure to quantify the distinguishability between different quantum data. My works [FF21CMP]^{15} [FFRS20PRL]^{24} proved the chain rule properties of two major variants of quantum relative entropies, namely the BelavkinStaszewski relative entropy and the Umegaki relative entropy. These results have established a crucial relationship between the entropy of a large quantum system and its individual subsystems, greatly generalizing the widely used quantum data processing inequalities. Remarkably, in [FF21CMP]^{15}, we addressed a critical open question
raised by Wilde et al. in ^{25} and provided the first sequence of quantum applications
of the BelavkinStaszewski relative entropy, sparking the community’s interest in this previously neglected quantity. As a result, numerous followup works have emerged in various domains, including quantum metrology^{26}, quantum machine learning^{27}, and even quantum field theory^{28}. Furthermore, in [FFRS20PRL]^{24}, we solved an open question
in the area of quantum channel discrimination^{29}: namely, adaptive and nonadaptive discrimination strategies have exactly the same power in the asymmetric discrimination of quantum channels, negating the widely held ``mistaken intuition’’ that adaptive strategies have more discrimination power.
Polynomial optimization and quantum entanglement verification
The sumofsquares (SOS) hierarchy is a series of increasingly tight relaxations of polynomial optimization problems and has profound impact in various fields, including control theory, statistics,
and quantum information. Despite extensive research, the rate of convergence of the SOS hierarchy has yet to be fully understood^{30}. Exploiting the polynomial kernel technique, my work [FF21MP]^{31} provided the first quadratic improvement
of the bestknown convergence rate of the SOS hierarchy on the sphere since 1995^{32}, solving an important open problem
in the optimization field^{33} and catalyzing subsequent breakthroughs on related topics ^{34} ^{35}. Furthermore, we established the first strict duality relationship
between the SOS hierarchy and the wellknown DohertyParriloSpedalieri (DPS) hierarchy in quantum theory for quantum entanglement verification, thereby solidifying the connection between optimization theory and quantum information.
Quantum software engineering for quantum internet
Quantum information science is a practical field that aims to solve realworld problems. This requires hardware engineering to actually build the quantum system and software engineering to control hardware devices so as to run useful quantum algorithms. My focus is on the software aspect that runs on top of hardware devices and supports higherlevel quantum applications. To fully tap into the unique features of quantum systems, quantum software must align with the principles of quantum physics and be optimized to a high degree, requiring expertise in both quantum information and software engineering. During my work at Baidu, I have successfully led multiple industrial projects that work coherently with the Baidu Quantum Platform, a fullstack quantum software and hardware platform developed by Baidu^{36}.
Efficient testbed for quantum internet
Quantum internet is essentially a distributed network of quantum computers and devices. Such a network has the potential to surpass its classical counterpart in various aspects, including the efficiency of data transmission, the security of network services, and the capability of information processing. To accelerate research and development on quantum networks, we have developed QNET ^{37}, an opensource software toolkit implemented in Python. It serves as a core component of the Baidu Quantum Platform and is the first quantum network toolkit
that interfaces with realworld quantum computers. QNET is built upon a solid foundation of over 40 patent applications
. The latest version, 1.4.0, comprises over 40 core modules, a vast repository of 25,000 lines of opensource code, 28 tutorials in both English and Chinese, a comprehensive API document, and a detailed white paper [FZLLD23SCIS]^{38}. The modular design of this toolkit provides flexibility for testing different quantum network architectures. In particular, we conducted a finegrained simulation of a quantum key distribution experiment on the renowned Micius quantum satellite^{39}, which demonstrated remarkable consistency with actual experimental data and underscored the effectiveness of QNET as a valuable testbed for future experiments. This toolkit has been presented at 2022 Baidu Create^{40} and reported by the mainstream news media in China
at PingWest^{41}, Toutiao^{42}, QbitAI^{43}, among others.
Privacypreserving quantum cloud service
Consider a scenario in which a client seeks to run a quantum algorithm to solve a problem but lacks access to a quantum computer. In such a situation, the client might opt to utilize a quantum cloud service provided by a company. However, there may be concerns regarding entrusting the service provider with the confidentiality of the client’s algorithm and data.
The blind quantum computation protocol offers a solution that empowers clients to leverage cloud services while safeguarding their privacy. Nonetheless, the protocol is intricate, necessitating interactive, realtime communication between the client and the server. It also involves the backandforth translation of the quantum circuit model to the measurementbased model.
In this project^{44}, we provided the first engineering implementation
of the universal blind quantum computation protocol since its proposal in 2009^{45}. Our implementation automatically translates a user’s quantum circuit algorithm into the brickwork pattern and processes the computation interactively and in realtime between the user’s local PC and the cloud server. This project brings the remarkable privacypreserving quantum computing scheme into practice and paves the way for its realization
with actual quantum computers.
New avenue for quantum machine learning
Quantum machine learning is a burgeoning field that seeks to harness the computational power of quantum computers for more efficient problemsolving. In this approach, we reconfigure our problem into a quantum algorithm, integrating learning parameters, and employ a quantum computer to assess the loss function. Subsequently, classical computers aid in iteratively adjusting the algorithm’s parameters until a solution is attained. The predominant model for quantum computing is the quantum circuit model, which entails a sequence of quantum gate operations followed by the measurement of the final state. However, an alternative model known as measurementbased quantum computation (MBQC) exists. It relies on measurements of a highly entangled quantum state to propel computation, proving particularly wellsuited for photonic quantum systems and exhibiting enhanced resilience to noise.
As a part of Paddle Quantum, a quantum machine learning toolkit, our project^{46} concentrates on the development of an efficient MBQC simulator and a transpiler that converts quantum circuits into their MBQC equivalents. This advancement marks the first implementation
of quantum machine learning within this unique computational framework, opening new avenues for exploring quantum machine learning and enabling delegated quantum machine learning with privacy.
This approach was later followed
by Xanadu^{47}, a pioneering quantum startup, as well as other university groups from Yale and Oxford^{48} ^{49}.
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