Research Overview: Toward EndtoEnd Quantum ApplicationsThis is an exciting time for quantum computing where earlystage quantum computers become available at your fingertips through clouds. Conventional computer science study of quantum computing has focused on its algorithm and complexity perspective. While providing insights into its power and limits in the asymptotic regime, this kind of theoretical study fails to capture the opportunities and restrictions of realistic quantum machines or to address the challenges in building efficient and reliable systems that operate them. Research GoalsMy research aims to identify and fill these gaps, accompanying hardware development, for the actual deployment of practical endtoend quantum applications, i.e., provide the foundation of endtoend quantum applications. To that end, I am integrating ideas from the study of theoretical computer science, machine learning, formal methods, programming languages, and computer architecture with decades of research on quantum information. I deem this softwarehardwarealgorithmic codesign approach as a unique feature of my research, which has been published in prestigious venues of all relevant fields such as general venues (e.g., PNAS, Nature Communication), quantum information (e.g., QIP, Phys.Rev.Lett), programming languages (e.g., POPL, PLDI, OOPSLA, ECOOP), machine learning (e.g., ICML, NeurIPS, AAAI), cryptography and security (e.g., CCS, Crypto, EuroCrypt), and theoretical computer science (e.g., STOC, CCC, ICALP). An overview of my existing research and future plans is as follows. Hamiltonianoriented Quantum Algorithm Design and ProgrammingThe conventional design of quantum algorithms is centered around the abstraction of quantum circuits and relies on a digital mindset for application design and implementation. While serving as an elegant mathematical interface, circuitbased digital abstraction usually fails to capture the native programmability of quantum devices, and incurs large overheads, which significantly restricts its nearterm feasibility where the computing resource is the major limitation. Historically, circuitbased digital abstraction has been successful in scaling up the design and implementation of modern classical computing chips, however, under the condition of the abundance of computing resources where correctness becomes a major issue for scalability. The benefit of circuitbased digital abstraction for quantum computing is conceivably restrictive when the limitation of quantum computing resources is the major bottleneck in the near term. We hence propose to use quantum Hamiltonian evolution as the central object in endtoend quantum application design, the socalled Hamiltonianoriented paradigm, based on the observation that Hamiltonian evolution is a native abstraction for both lowlevel hardware control and highlevel quantum applications. We illustrate that the Hamiltonianoriented design not only allows more efficient implementation of known quantum algorithms but also inspires novel quantum algorithms, especially in optimization and scientific computing, which are hard to perceive in the circuit model. We also develop a programming infrastructure for easy implementation of Hamiltonianbased quantum applications for domain experts on heterogeneous quantum devices. Quantum Hamiltonian DescentGradientbased methods are important optimization techniques that are prevalent in both theoretical and empirical studies. A genuine quantum counterpart of gradientbased methods is however missing. Inspired by the correspondence between gradientbased methods and physicsinspired dynamical systems, we propose a quantization of such correspondence based on the path integral formulation of quantum mechanics, which in turn implies a quantum extension of gradient descent called the quantum Hamiltonian descent (QHD). We proved QHD’s convergence for any nonconvex function with a unique nondegenerate global minimum and observed its fasterconverging rate than any classical algorithms and the quantum adiabatic algorithm over a benchmark set of hard instances in nonconvex optimization. Excitingly, QHD could be realized on either circuitbased or analog (e.g., quantum simulators) quantum machines for a scalable empirical study. Our finding also opens the possibility of a unified framework for both quantum and classical gradientbased methods. Publications:
Hamiltonian EmbeddingThe realization of quantum computing is fundamentally based on the precise manipulation of Hilbert spaces of underlying quantum devices. The conventional wisdom relies on circuit synthesis techniques to decompose sophisticated operations on Hilbert space to a set of universal elementary gates. Although providing a universal solution in principle, this hardwareagnostic strategy typically leads to deep quantum circuits for interesting quantum algorithms, which makes them infeasible for implementation on nearterm quantum devices. We propose a technique named Hamiltonian embedding that simulates a desired Hamiltonian evolution by embedding it into the evolution of a large and structured quantum system, which, however, allows more efficient manipulation via hardwarenative operations. We conduct a systematic study of this embedding technique and demonstrate a significant computational resource save for implementing prominent quantum applications. As a result, we can experimentally realize quantum walks on complicated graphs (e.g., binary trees, gluedtree graphs), quantum spatial search, and the simulation of realspace Schrödinger equations on trappedion and neutralatom platforms today. Given the fundamental role of Hamiltonian evolution in quantum algorithm design, our technique significantly expands the horizon of implementable quantum advantage in the NISQ era. Publications:
Differentiable Analog Quantum ComputingWe formulate the first differentiable analog quantum computing framework with a specific parameterization design at the analog signal (pulse) level to better exploit nearterm quantum devices via variational methods. We further propose a scalable approach to estimate the gradients of quantum dynamics using a forward pass with Monte Carlo sampling, which leads to a quantum stochastic gradient descent algorithm for scalable gradientbased training in our framework. Applying our framework to quantum optimization and control, we observe a significant advantage of differentiable analog quantum computing against SOTAs based on parameterized digital quantum circuits by orders of magnitude. Publications:
Hamiltonianoriented Programming InfrastructureClassical analog computing, with a relaxed requirement on hardware, predates digital computers and has played an important role in many domain applications. Conceivably, applications based on analog quantum machines will become a major milestone for nearterm quantum computing. However, programming analog quantum simulators is much more challenging due to the lack of a unified interface between hardware and software. To remedy the situation, we have built a domainspecific modeling language for quantum simulation (called SIMUQ) inspired by the pioneering work of Simula, which allows the description of quantum evolution itself beyond any circuitbased model. The new abstraction provides structured information about the actual physics to simulate and allows more automation and optimization by compilers. More importantly, it also enables analog compilation to heterogeneous analog quantum simulators on various experimental platforms. Specifically, in SimuQ, frontend users specify the target quantum system with Hamiltonian Modeling Language, and the Hamiltonianlevel programmability of analog quantum simulators is specified through a new abstraction called the abstract analog instruction set (AAIS) and programmed in AAIS Specification Language by hardware providers. Building on top of SIMUQ, we plan to develop DSLs for domain applications, such as the simulation of highenergy physics & condensed physics, and analog computational tasks. Publications:
Software Foundation of Quantum ComputingFormally Verified Software Toolchain for Quantum ComputingThe complexity of quantum computing and the limitations of nearterm quantum devices suggest that the development of sophisticated quantum algorithms and clever optimizations is more likely to have mistakes. This calls for verifying every stage of quantum computation, from the software tools used to generate quantum circuits to the architecture and system design. We are inspired by formal methods applied in safetycritical domains to ensure the correctness of code by construction, especially in the example of CompCert (a C compiler written and proved correct in Coq) and the NSF project of deep specification (a project to develop specifications of software toolchains to prove endtoend correctness of whole systems). A verified quantum computing stack would ensure that each level of quantum computation is implemented satisfying certain specifications and the correctness of the final system, which would have a wide practical impact. This approach is especially appealing to quantum computing since alternative software assurance techniques are very limited due to the substantial expense involved in the quantum setting. As an important first step, we have built a provedcorrect optimizing compiler for quantum algorithms to optimize the gate count, the depth of circuits, etc., while adhering to any architectural constraints. To that end, we developed an infrastructure for reasoning about quantum programs/operations in Coq, which is so expressive and flexible that we recently accomplished an endtoend implementation of Shor's algorithm, with both classical and quantum parts as well as a formal correctness proof of everything, in Coq. Publications:
Quantum Program Analysis & VerificationQuantum programs are errorprone and their verification is challenging due to the limit of standard software assurance techniques in the quantum setting. My research investigates the verification of quantum programs via their static analysis with the help of quantum Hoare logic. A prominent approach for program verification is to generate invariants and inductive assertions, which is already a highly nontrivial task even classically. I made the first proposal of quantum invariants and demonstrated its use in quantum program verification, which can be generated by semidefinite programs (SDPs). We also investigate the algebraic reasoning of quantum programs inspired by the success of classical program analysis based on Kleene algebra. One prominent example of such is the famous Kleene Algebra with Tests (KAT), which has furnished both theoretical insights and practical tools. A few key features of KAT including the idempotent law and the nice properties of classical tests, however, fail to hold in the context of quantum programs due to their unique quantum features, especially in branching. We propose the Nonidempotent Kleena Algebra (NKA) as a natural alternative and identify complete and sound semantic models for NKA as well as their appropriate quantum interpretations, which hence enables algebraic proofs in NKA of quantum compiler optimization and the normal form of quantum whileprograms. Publications:
Quantum Applications in Optimization and Machine LearningProvable Quantum Advantages for Optimization and Machine LearningMy recent research aims to understand the landscape of provable quantum advantages in optimization and machine learning, a major targeted domain of quantum applications. To that end, I have developed quantum algorithms with polynomial speedups over classical ones for semidefinite programs (SDPs), general convex optimization, training linear and kernelized classifiers, and estimating volumes of highdimensional convex bodies. My algorithms also hint at possible exponential quantum speedups when using quantum data as inputs/outputs of SDPs and the principal component analysis problem. Publications:
Variational Quantum MethodsQuantum Neuralnetworks (i.e., parameterized quantum circuits) are important and promising candidates for applications of quantum machine learning. My research aims to conduct a theoryguided comprehensive investigation in this regard, including functionality (e.g., representation learning, generative models), training methods (e.g., landscape characterization, under/overparameterization), and separation between quantum and classical neural networks. Publications:
Differentiable Quantum Programming Languages & Quantum NeuroSymbolic ApplicationsInspired by the emerging paradigm shift from deep learning toward differentiable programming promoted by prominent classical machine learning researchers, I have initiated the formalization of differentiable quantum programming. This project not only provides the autodifferentiation technique for quantum programs, in particular the possibility of using quantum programs to compute the gradients of another quantum program, for the scalability of gradientbased training in quantum machine learning. It also opens the possibility of designing novel quantum “neurosymbolic” applications that combine program features/synthesis with simple neural networks. The study of their classical counterpart, although still in its infancy, has already shown great potential and promise over conventional neural networks. We demonstrated, for the first time, one such example for quantum machine learning. Publications:
Quantum Algorithms for Property TestingAnother wellmotivated topic is the property test of quantum and classical distributions. I have closed a longstanding gap between the upper and the lower bound of the sample complexity of testing the whole information of quantum states, socalled quantum tomography, which is a fundamental step to verify the preparation of the experimental setup. I also demonstrated the quantum speedup in estimating the Shannon and Renyi entropies of classical distributions. Publications:
Quantum Architecture Engineering for NISQ eraNearterm quantum computers are likely to have very restricted hardware resources, where precisely controllable qubits are expensive, errorprone, and scarce. Therefore, application designers for such nearterm intermediatesize quantum (NISQ) computers are forced to investigate the best balance of tradeoffs among a large number of (potentially heterogeneous) factors specific to the targeted application and quantum hardware. NoiseAnalysis of Quantum ApplicationsWe believe that one way to attack these problems is to set aside a onesizefitsall approach to fault tolerance and instead consider elevating the question of errors and related architecturespecific resource optimization to the level of the programming language and algorithm design. In particular, inspired by techniques in approximate computing that optimize computation on unreliable classical hardware, we've built formal semantics and a logic for reasoning about reliability in the presence of noise in quantum computation. Publications:
MetaProgramming Framework for Automating NISQ Application DesignWe propose Meta Quantum Circuits with Constraints (MQCC), a metaprogramming framework for quantum programs, to assist the balance of tradeoffs in NISQ application design. Designers express their application as a succinct collection of normal quantum circuits stitched together by a set of metalevel choice variables, whose values are constrained according to a programmable set of quantitative optimization criteria. MQCC's compiler automatically generates the appropriate constraints, hands them to a solver (e.g., a Satisfiability Modulo Theories (SMT) solver), and from the solution produces an optimized, runnable program. We demonstrate MQCC's expressiveness through an extensive case study, demonstrating that ideas from previous examples of NISQ application design – such as multiprogramming, costeffective uncomputation, and crosstalk mitigation, as well as their combination – can be readily implemented in MQCC, and produce comparable results. Publications:
Leveraging Small Quantum Machines for NISQ ApplicationsTo accelerate NISQ quantum applications on small quantum machines, we designed a systematic framework of decomposing quantum computation into small pieces and then combining simulation results from each piece for the final output. A particular application is, e.g., a practical scheme to implement a 60qubit quantum computation with only 45qubit quantum machines.
Cryptography & Security in the Quantum RegimeTamperresilient Cryptography under Physical AssumptionsDevices, classical or quantum, are subject to tampering in cryptographic settings, especially due to the proliferation of sidechannel attacks. These attacks exploit the fact that de vices leak information to the outside world not just through inputoutput interaction, but through physical characteristics of computation such as power consumption, timing, and electromagnetic radiation. Research on this topic explores two possible solutions to protect cryptographic systems from (quantum) sidechannel attacks.
Both deviceindependent and leakageresilient cryptography can be deemed as tamperresilient cryptography under physical assumptions. My future plan is to bring these cryptographic designs closer to practice, with better efficiency and broader functionality. Publications:
(Practical) Delegation and Verification of Quantum ComputationIn a recent breakthrough, Mahadev constructed a classical verification of quantum computation (CVQC) protocol for a classical client to delegate decision problems in BQP to an untrusted quantum prover under computational assumptions. We explore further the feasibility of CVQC with the more general sampling problems in BQP and with the desirable blindness property, and contribute affirmative solutions to both. We also investigate the lightweight verification of quantum supremacy, where all existing protocols, either based on classical simulation or publickey quantum cryptography, are too expensive to serve the purpose of practical verification. We propose a circuitobfuscationbased verification scheme for quantum supremacy that is scalable and has some complexitytheoretic support based on the quantum minimum equivalent circuit problem (QMECP). We also implement a prototype of our circuit obfuscator which has the desired empirical performance against the attack from all the offtheshelf tools. Publications:
Mechanized and Automated Security Analysis of Cryptographic Systems under Quantum AttacksThe emergence of quantum computing technology has promised unprecedented improvement in our computational ability, which, however, also leads to quantum attacks that would put many security techniques for modern communication in peril in the nottoodistant future. The defense against quantum attacks should ideally be deployed in the near future to protect today's secret information from future quantum attacks, especially in securitycritical domains like hardware signatures or blockchains, both with very long life cycles. Inspired by the success of the development of formal methods in the security analysis for large, realworld cryptographic systems, we are excited to develop and apply formal method techniques in quantum cryptography for automated security analysis of cryptographic systems under quantum attacks. Formally generated security analysis will provide not only efficient and high assurance proofs that can replace the tedious and errorprone analysis for experts, but also independently verifiable proofs that can be used by security practitioners without much quantum knowledge. One of our ultimate goals is to formally verify candidates of cryptographic systems from the NIST quantumsecure cryptography standardization. Publications:
Computeraided Design of Quantum DevicesExisting quantum devices are relatively small, and their design is mostly done manually, which requires domain experts, and is usually timeconsuming, and errorprone. Scaling up this approach for slightly larger or more complicated quantum devices seems very challenging. A natural alternative is to enable the computeraided design of quantum devices or even let the design bootstrap on existing quantum devices. We are motivated to develop quantum hardware description languages (QHDL) inspired by classical hardware description languages. To that end, we will develop formal abstractions of various quantum experimental platforms, building on top of which we will develop design automation, automatic control generation, and formal verification. Some of our ongoing efforts include (1) the extension of SPICE to support circuit QED for superconducting qubits, the simulation of which will be delegated to SimuQ, and in turn, enables a quantumaided design of quantum devices; (2) the automatic generation of machine specifications in AAIS for the analog compilation in SimuQ. By exposing quantum hardware specifications to highlevel quantum programming languages, we will build a hardwaresoftware codesign framework for quantum applications. Quantum Sensing NetworksThe demand for highly accurate position and time information, provided by localization and synchronization methods, respectively, is growing rapidly. However, classical localization and synchronization methods are approaching their limits. Utilizing quantum properties promises to push these boundaries beyond classical limitations and provide unprecedented accuracy. We aim to develop theoretical and practical methodologies for the design and analysis of quantum localization and synchronization networks. These methodologies consist of statistical models and distributed algorithms to harness quantum phenomena for beyondclassical localization and synchronization. Publications:
Earlier Theoretical Studies in Quantum Information and ComputationEntanglement, Quantum Correlations, and SumofSquaresResearch on this topic studies many aspects of one of the key quantum features, entanglement and nonlocality. I attack this topic by exploring a surprising connection between quantum information and the sumofsquares (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 include the characterization of separable (unentangled) states, the complexity of quantum MerlinArthur games with unentangled provers (QMA(2)), the possibility of a quantuminspired approach to attack the UGC. Publications:
Quantum Computational ComplexityInteractive proof systems have been a central model in complexity theory with applications ranging from the PCP theorem in the hardness of approximation to cryptography. It studies problems with efficiently verifiable proofs via interactions between a polynomialtime verifier and allpowerful 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 spaceefficient 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 kplayer games. Publications:
