Mingsheng Ying

Ji Guan, Wang Fang, Mingsheng Ying

Due to the beyond-classical capability of quantum computing, quantum machine learning is applied independently or embedded in classical models for decision making, especially in the field of finance. Fairness and other ethical issues are often one of the main concerns in decision making. In this work, we define a formal framework for the fairness verification and analysis of quantum machine learning decision models, where we adopt one of the most popular notions of fairness in the literature based on the intuition -- any two similar individuals must be treated similarly and are thus unbiased. We show that quantum noise can improve fairness and develop an algorithm to check whether a (noisy) quantum machine learning model is fair. In particular, this algorithm can find bias kernels of quantum data (encoding individuals) during checking. These bias kernels generate infinitely many bias pairs for investigating the unfairness of the model. Our algorithm is designed based on a highly efficient data structure -- Tensor Networks -- and implemented on Google's TensorFlow Quantum. The utility and effectiveness of our algorithm are confirmed by the experimental results, including income prediction and credit scoring on real-world data, for a class of random (noisy) quantum decision models with 27 qubits ($2^{27}$-dimensional state space) tripling ($2^{18}$ times more than) that of the state-of-the-art algorithms for verifying quantum machine learning models.

Wang Fang, Mingsheng Ying, Xiaodi Wu

The emergence of variational quantum applications has led to the development of automatic differentiation techniques in quantum computing. Recently, Zhu et al. (PLDI 2020) have formulated differentiable quantum programming with bounded loops, providing a framework for scalable gradient calculation by quantum means for training quantum variational applications. However, promising parameterized quantum applications, e.g., quantum walk and unitary implementation, cannot be trained in the existing framework due to the natural involvement of unbounded loops. To fill in the gap, we provide the first differentiable quantum programming framework with unbounded loops, including a newly designed differentiation rule, code transformation, and their correctness proof. Technically, we introduce a randomized estimator for derivatives to deal with the infinite sum in the differentiation of unbounded loops, whose applicability in classical and probabilistic programming is also discussed. We implement our framework with Python and Q#, and demonstrate a reasonable sample efficiency. Through extensive case studies, we showcase an exciting application of our framework in automatically identifying close-to-optimal parameters for several parameterized quantum applications.

Zihao Li, Ji Guan, Mingsheng Ying

We present a tool QSeqSim, a Qiskit-integrated symbolic backend that fills the current gap of having no Qiskit-native support for simulating while-loop quantum programs and their induced sequential quantum circuits. QSeqSim takes Qiskit QuantumCircuit objects, translates them into OpenQASM 3 code, and organises the resulting program into a combination of combinational, dynamic, and sequential circuits, thereby assigning while-loops a precise sequential circuit semantics with explicit internal and external qubits. Building on this semantics, QSeqSim adopts a Binary Decision Diagram (BDD)-based symbolic representation and integrates weighted model counting to compute measurement probabilities efficiently by exploiting sharing in structured and sparse BDDs. On top of this Boolean backbone, it introduces dedicated symbolic operators for state composition and state retention, thereby enabling efficient symbolic execution of sequential quantum circuits. Our experiments demonstrate that QSeqSim scales to substantial while-induced sequential circuits; in particular, in the quantum random walk benchmark we successfully simulate circuits with over 1000 qubits for more than 10 loop iterations. QSeqSim is available at https://github.com/Veri-Q/QSeqSim.

Qifan Huang, Minbo Gao, Li Zhou et al.

Most quantum compilers assume programs are reversible unitary circuits. This fits closed-system algorithms, but not open-system simulation, where the natural program objects are quantum channels describing non-unitary dynamics. We present a channel-first compilation framework that treats channels as first-class compilation objects. Our core IR, ChannelIR, represents channels explicitly in Kraus form, a standard channel representation, with Pauli-sum structure, enabling algebraic rewrites before circuit synthesis. We instantiate the framework with LindFront, a frontend that lowers continuous-time Lindbladian generators to short-time channels, and a backend that compiles these channels to executable circuits with structure-aware optimizations. On Lindbladian and channel-simulation benchmarks, the optimized pipeline reduces gate count by up to 99% over an unoptimized channel-first baseline and scales better than circuit-first Stinespring compilation.

Ji Guan, Wang Fang, Mingyu Huang et al.

Quantum algorithms for solving a wide range of practical problems have been proposed in the last ten years, such as data search and analysis, product recommendation, and credit scoring. The concern about privacy and other ethical issues in quantum computing naturally rises up. In this paper, we define a formal framework for detecting violations of differential privacy for quantum algorithms. A detection algorithm is developed to verify whether a (noisy) quantum algorithm is differentially private and automatically generate bugging information when the violation of differential privacy is reported. The information consists of a pair of quantum states that violate the privacy, to illustrate the cause of the violation. Our algorithm is equipped with Tensor Networks, a highly efficient data structure, and executed both on TensorFlow Quantum and TorchQuantum which are the quantum extensions of famous machine learning platforms -- TensorFlow and PyTorch, respectively. The effectiveness and efficiency of our algorithm are confirmed by the experimental results of almost all types of quantum algorithms already implemented on realistic quantum computers, including quantum supremacy algorithms (beyond the capability of classical algorithms), quantum machine learning models, quantum approximate optimization algorithms, and variational quantum eigensolvers with up to 21 quantum bits.

Mingsheng Ying

In this paper, we present a Hoare-style logic for reasoning about quantum programs with classical variables. Our approach offers several improvements over previous work: (1) Enhanced expressivity of the programming language: Our logic applies to quantum programs with classical variables that incorporate quantum arrays and parameterised quantum gates, which have not been addressed in previous research on quantum Hoare logic, either with or without classical variables. (2) Intuitive correctness specifications: In our logic, preconditions and postconditions for quantum programs with classical variables are specified as a pair consisting of a classical first-order logical formula and a quantum predicate formula (possibly parameterised by classical variables). These specifications offer greater clarity and align more closely with the programmer's intuitive understanding of quantum and classical interactions. (3) Simplified proof system: By introducing a novel idea in formulating a proof rule for reasoning about quantum measurements, along with (2), we develop a proof system for quantum programs that requires only minimal modifications to classical Hoare logic. Furthermore, this proof system can be effectively and conveniently combined with classical first-order logic to verify quantum programs with classical variables. As a result, the learning curve for quantum program verification techniques is significantly reduced for those already familiar with classical program verification techniques, and existing tools for verifying classical programs can be more easily adapted for quantum program verification.

Chenjian Li, Mingsheng Ying

We analyze the DP (differential privacy) properties of the quantum recommendation algorithm and the quantum-inspired-classical recommendation algorithm. We discover that the quantum recommendation algorithm is a privacy curating mechanism on its own, requiring no external noise, which is different from traditional differential privacy mechanisms. In our analysis, a novel perturbation method tailored for SVD (singular value decomposition) and low-rank matrix approximation problems is introduced. Using the perturbation method and random matrix theory, we are able to derive that both the quantum and quantum-inspired-classical algorithms are $\big(\tilde{\mathcal{O}}\big(\frac 1n\big),\,\, \tilde{\mathcal{O}}\big(\frac{1}{\min\{m,n\}}\big)\big)$-DP under some reasonable restrictions, where $m$ and $n$ are numbers of users and products in the input preference database respectively. Nevertheless, a comparison shows that the quantum algorithm has better privacy preserving potential than the classical one.

Ji Guan, Wang Fang, Mingsheng Ying

Several important models of machine learning algorithms have been successfully generalized to the quantum world, with potential speedup to training classical classifiers and applications to data analytics in quantum physics that can be implemented on the near future quantum computers. However, quantum noise is a major obstacle to the practical implementation of quantum machine learning. In this work, we define a formal framework for the robustness verification and analysis of quantum machine learning algorithms against noises. A robust bound is derived and an algorithm is developed to check whether or not a quantum machine learning algorithm is robust with respect to quantum training data. In particular, this algorithm can find adversarial examples during checking. Our approach is implemented on Google's TensorFlow Quantum and can verify the robustness of quantum machine learning algorithms with respect to a small disturbance of noises, derived from the surrounding environment. The effectiveness of our robust bound and algorithm is confirmed by the experimental results, including quantum bits classification as the "Hello World" example, quantum phase recognition and cluster excitation detection from real world intractable physical problems, and the classification of MNIST from the classical world.

Gushu Li, Li Zhou, Nengkun Yu et al.

In this paper, we propose Proq, a runtime assertion scheme for testing and debugging quantum programs on a quantum computer. The predicates in Proq are represented by projections (or equivalently, closed subspaces of the state space), following Birkhoff-von Neumann quantum logic. The satisfaction of a projection by a quantum state can be directly checked upon a small number of projective measurements rather than a large number of repeated executions. On the theory side, we rigorously prove that checking projection-based assertions can help locate bugs or statistically assure that the semantic function of the tested program is close to what we expect, for both exact and approximate quantum programs. On the practice side, we consider hardware constraints and introduce several techniques to transform the assertions, making them directly executable on the measurement-restricted quantum computers. We also propose to achieve simplified assertion implementation using local projection technique with soundness guaranteed. We compare Proq with existing quantum program assertions and demonstrate the effectiveness and efficiency of Proq by its applications to assert two ingenious quantum algorithms, the Harrow-Hassidim-Lloyd algorithm and Shor's algorithm.

Shenggang Ying, Mingsheng Ying, Yuan Feng

With the extensive applications of machine learning, the issue of private or sensitive data in the training examples becomes more and more serious: during the training process, personal information or habits may be disclosed to unexpected persons or organisations, which can cause serious privacy problems or even financial loss. In this paper, we present a quantum privacy-preserving algorithm for machine learning with perceptron. There are mainly two steps to protect original training examples. Firstly when checking the current classifier, quantum tests are employed to detect data user's possible dishonesty. Secondly when updating the current classifier, private random noise is used to protect the original data. The advantages of our algorithm are: (1) it protects training examples better than the known classical methods; (2) it requires no quantum database and thus is easy to implement.

Shenggang Ying, Mingsheng Ying, Yuan Feng

Data analytics (such as association rule mining and decision tree mining) can discover useful statistical knowledge from a big data set. But protecting the privacy of the data provider and the data user in the process of analytics is a serious issue. Usually, the privacy of both parties cannot be fully protected simultaneously by a classical algorithm. In this paper, we present a quantum protocol for data mining that can much better protect privacy than the known classical algorithms: (1) if both the data provider and the data user are honest, the data user can know nothing about the database except the statistical results, and the data provider can get nearly no information about the results mined by the data user; (2) if the data user is dishonest and tries to disclose private information of the other, she/he will be detected with a high probability; (3) if the data provider tries to disclose the privacy of the data user, she/he cannot get any useful information since the data user hides his privacy among noises.

Shenggang Ying, Mingsheng Ying, Yuan Feng

Data mining is a key technology in big data analytics and it can discover understandable knowledge (patterns) hidden in large data sets. Association rule is one of the most useful knowledge patterns, and a large number of algorithms have been developed in the data mining literature to generate association rules corresponding to different problems and situations. Privacy becomes a vital issue when data mining is used to sensitive data sets like medical records, commercial data sets and national security. In this Letter, we present a quantum protocol for mining association rules on vertically partitioned databases. The quantum protocol can improve the privacy level preserved by known classical protocols and at the same time it can exponentially reduce the computational complexity and communication cost.

Yuan Feng, Mingsheng Ying

Several quantum process algebras have been proposed and successfully applied in verification of quantum cryptographic protocols. All of the bisimulations proposed so far for quantum processes in these process algebras are state-based, implying that they only compare individual quantum states, but not a combination of them. This paper remedies this problem by introducing a novel notion of distribution-based bisimulation for quantum processes. We further propose an approximate version of this bisimulation that enables us to prove more sophisticated security properties of quantum protocols which cannot be verified using the previous bisimulations. In particular, we prove that the quantum key distribution protocol BB84 is sound and (asymptotically) secure against the intercept-resend attacks by showing that the BB84 protocol, when executed with such an attacker concurrently, is approximately bisimilar to an ideal protocol, whose soundness and security are obviously guaranteed, with at most an exponentially decreasing gap.

Yangjia Li, Mingsheng Ying

Since observation on a quantum system may cause the system state collapse, it is usually hard to find a way to monitor a quantum process, which is a quantum system that continuously evolves. We propose a protocol that can debug a quantum process by monitoring, but not disturb the evolution of the system. This protocol consists of an error detector and a debugging strategy. The detector is a projection operator that is orthogonal to the anticipated system state at a sequence of time points, and the strategy is used to specify these time points. As an example, we show how to debug the computational process of quantum search using this protocol. By applying the Skolem--Mahler--Lech theorem in algebraic number theory, we find an algorithm to construct all of the debugging protocols for quantum processes of time independent Hamiltonians.

Mingsheng Ying, Yuang Feng, Nengkun Yu

Quantum cryptography has been extensively studied in the last twenty years, but information-flow security of quantum computing and communication systems has been almost untouched in the previous research. Duo to the essential difference between classical and quantum systems, formal methods developed for classical systems, including probabilistic systems, cannot be directly applied to quantum systems. This paper defines an automata model in which we can rigorously reason about information-flow security of quantum systems. The model is a quantum generalisation of Goguen and Meseguer's noninterference. The unwinding proof technique for quantum noninterference is developed, and a certain compositionality of security for quantum systems is established. The proposed formalism is then used to prove security of access control in quantum systems.

Guoxin Su, Mingsheng Ying, Chengqi Zhang

The scenario-based specification of a large distributed system is usually naturally decomposed into various modules. The integration of specification modules contrasts to the parallel composition of program components, and includes various ways such as scenario concatenation, choice, and nesting. The recent development of multiparty session types for process calculi provides useful techniques to accommodate the protocol modularisation, by encoding fragments of communication protocols in the usage of private channels for a class of agents. In this paper, we extend forgoing session type theories by enhancing the session integration mechanism. More specifically, we propose a novel synchronous multiparty session type theory, in which sessions are separated into the communicating and integrating levels. Communicating sessions record the message-based communications between multiple agents, whilst integrating sessions describe the integration of communicating ones. A two-level session type system is developed for pi-calculus with syntactic primitives for session establishment, and several key properties of the type system are studied. Applying the theory to system description, we show that a channel safety property and a session conformance property can be analysed. Also, to improve the utility of the theory, a process slicing method is used to help identify the violated sessions in the type checking.