Research OverviewHere I will briefly describe some of my existing and on-going projects.
Research GoalsMy research aims to contribute to the development of quantum information and computation through the study in theoretical computer science (complexity & algorithms), cryptography, and formal methods & programming languages. On one side, my research aims to study the impact of quantum mechanics on the theoretical foundation of computer science. On the other side, I am also aiming to provide solutions to challenges in the near-term quantum hardware and software research. My research is interdisciplinary in nature: many of my quantum projects are not only related to classical theoretical computer science topics, but also naturally connect to central topics in physics and mathematics. Entanglement, Non-locality, and Sum-of-SquaresResearch on this topic studies many aspects of one of the key quantum features, entanglement and non-locality. I attack this topic by exploring a surprising connection between quantum information and the sum-of-squares (SOS) proof in approximation algorithms and the famous Unique Games Conjecture (UGC). This connection allows one to leverage technical advances in one field to apply to the other. Specific problems that I am working on includes the characterization of separable (unentangled) states, the complexity of quantum Merlin-Arthur games with unentangled provers (QMA(2)), the possibility of a quantum-inspired approach to attack the UGC. Publications:
Tamper-resilient Cryptography under Physical AssumptionsDevices, classical or quantum, are subject to tampering in cryptographic settings, especially due to the proliferation of side-channel attacks. These attacks exploit the fact that de- vices leak information to the outside world not just through input-output interaction, but through physical characteristics of computation such as power consumption, timing, and electro-magnetic radiation. Research on this topic explores two possible solutions to protect cryptographic systems from (quantum) side-channel attacks.
Both device-independent and leakage-resilient cryptography can be deemed as tamper-resilient cryptography under physical assumptions. My future plan is to bring these cryptographic designs closer to practice, with better efficiency and broader functionality. Publications:
Quantum Computational ComplexityInteractive proof systems have been a central model in complexity theory with applications ranging from the PCP theorem in hardness of approximation to cryptography. It studies problems with efficiently verifiable proofs via interactions between a polynomial-time verifier and all-powerful provers, where the verifier determines the validity of the proofs. My main contribution on this topic is the development of the Equilibrium Value Method to obtain space-efficient simulations of quantum interactive proof systems, including QIP=PSPACE, QRG(2)=PSPACE. Recently, I have been working on the quantum variant of the PCP theorem in the interactive proof setting. As a concrete first step, I have obtained a parallel repetition result for entangled k-player games. Publications:
Provable Quantum Advantage in Property Testing, Monte Carlo Methods, Optimization, and Machine LearningIt is a fundamental question and a long-term pursuit to establish quantum advantage in algorithms that goes beyond the techniques in Grover's and Shor's algorithms. I adopt a humble approach to tackle this ultimate goal. In particular, I am fascinated by a few emerging topics which, on one side, are well-motivated and timely for various reasons, and on the other side introduce new technical challenges that potentially request revolutionary techniques. Specifically, my on-going research on this topic investigates the potential quantum advantage in property testing, Monte Carlo methods (over general domains), optimization (e.g., convex optimization, semi-definite programming, sub-modular optimization), and high-dimensional geometrical problems in machine learning. Publications:
Theoretical Solutions to Quantum Engineering ProblemsMedium-size quantum devices are expected in the next five or ten years. My research aims to facilitate applications of medium-size quantum devices via theoretical techniques. In an on-going project, I study the possibility of simulating large-scale quantum computation with limited resources that are expected to be available in the near future. A specific goal is, e.g., to perform 60-qubit quantum computation with 40-qubit quantum devices, which is already a significant advance for major applications of medium-size quantum machines, such as quantum simulation or quantum supremacy. My ultimate goal is to build a theoretical foundation for this purpose, which could be valuable to both theorists as well as experimentalists and engineers. In a recent project, I have also closed a long-standing gap between the upper and lower bounds for quantum tomography. Publications:
Formal Methods and Programming Languages for Quantum Software, Hardware, and CryptographyFormal methods and programming languages have been the cornerstone in software and hardware engineering. In particular, they provide appropriate mathematically based techniques for the specification, development, and verification of software and hardware systems. It won't be surprised at all that these methods will play important roles in quantum systems. This is a timely and exciting direction. In particular, my research on this topic aims to contribute to the formal method for quantum software, hardware, and cryptography. In a recent result, I made the first attempt to define the notion of invariant and to develop a method of invariant generation for quantum programs. My on-going projects include (1) theory of quantum programming languages, (2) verifiable compliers of quantum programs with optimization of hardware factors (e.g., architectural constraints, error, and relevant resources), and (3) automatic verification of the security of classical protocols against quantum attacks. Publications:
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