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Quantum programs are notoriously difficult to code and verify due to unintuitive quantum knowledge associated with quantum programming. Automated tools relieving the tedium and errors associated with low-level quantum details would hence be highly desirable. In this paper, we initiate the study of program synthesis for quantum unitary programs that recursively define a family of unitary circuits for different input sizes, which are widely used in existing quantum programming languages. Specifically, we present QSynth, the first quantum program synthesis framework, including a new inductive quantum programming language, its specification, a sound logic for reasoning, and an encoding of the reasoning procedure into SMT instances. By leveraging existing SMT solvers, QSynth successfully synthesizes ten quantum unitary programs including quantum adder circuits, quantum eigenvalue inversion circuits and Quantum Fourier Transformation, which can be readily transpiled to executable programs on major quantum platforms, e.g., Q#, IBM Qiskit, and AWS Braket. 

Distributed protocols have long been formulated in terms of their safety and liveness properties. Much recent work has focused on automatically verifying the safety properties of distributed protocols, but doing so for liveness properties has remained a challenging, unsolved problem. We present LVR, the first framework that can mostly automatically verify liveness properties for distributed protocols. Our key insight is that most liveness properties for distributed protocols can be reduced to a set of safety properties with the help of ranking functions. Such ranking functions for practical distributed protocols have certain properties that make them straightforward to synthesize, contrary to conventional wisdom. We prove that verifying a liveness property can then be reduced to a simpler problem of verifying a set of safety properties, namely that the ranking function is strictly decreasing and nonnegative for any protocol state transition, and there is no deadlock. LVR automatically synthesizes ranking functions by formulating a parameterized function of integer protocol variables, statically analyzing the lower and upper bounds of the variables as well as how much they can change on each state transition, then feeding the constraints to an SMT solver to determine the coefficients of the ranking function. It then uses an off-the-shelf verification tool to find inductive invariants to verify safety properties for both ranking functions and deadlock freedom. We show that LVR can mostly automatically verify the liveness properties of several distributed protocols, including various versions of Paxos, with limited user guidance. 

Quantum computing technology may soon deliver revolutionary improvements in algorithmic performance, but it is useful only if computed answers are correct. While hardware-level decoherence errors have garnered significant attention, a less recognized obstacle to correctness is that of human programming errors—“bugs.” Techniques familiar to most programmers from the classical domain for avoiding, discovering, and diagnosing bugs do not easily transfer, at scale, to the quantum domain because of its unique characteristics. To address this problem, we have been working to adapt formal methods to quantum programming. With such methods, a programmer writes a mathematical specification alongside the program and semiautomatically proves the program correct with respect to it. The proof’s validity is automatically confirmed—certified—by a “proof assistant.” Formal methods have successfully yielded high-assurance classical software artifacts, and the underlying technology has produced certified proofs of major mathematical theorems. As a demonstration of the feasibility of applying formal methods to quantum programming, we present a formally certified end-to-end implementation of Shor’s prime factorization algorithm, developed as part of a framework for applying the certified approach to general applications. By leveraging our framework, one can significantly reduce the effects of human errors and obtain a high-assurance implementation of large-scale quantum applications in a principled way. 

Concurrent systems software is widely-used, complex, and error-prone, posing a significant security risk. We introduce VRM, a new framework that makes it possible for the first time to verify concurrent systems software, such as operating systems and hypervisors, on Arm relaxed memory hardware. VRM defines a set of synchronization and memory access conditions such that a program that satisfies these conditions can be mostly verified on a sequentially consistent hardware model and the proofs will automatically hold on relaxed memory hardware. VRM can be used to verify concurrent kernel code that is not data race free, including code responsible for managing shared page tables in the presence of relaxed MMU hardware. Using VRM, we verify the security guarantees of a retrofitted implementation of the Linux KVM hypervisor on Arm. For multiple versions of KVM, we prove KVM's security properties on a sequentially consistent model, then prove that KVM satisfies VRM's required program conditions such that its security proofs hold on Arm relaxed memory hardware. Our experimental results show that the retrofit and VRM conditions do not adversely affect the scalability of verified KVM, as it performs similar to unmodified KVM when concurrently running many multiprocessor virtual machines with real application workloads on Arm multiprocessor server hardware. Our work is the first machine-checked proof for concurrent systems software on Arm relaxed memory hardware. 

Distributed systems are notoriously hard to implement correctly due to non-determinism. Finding the inductive invariant of the distributed protocol is a critical step in verifying the correctness of distributed systems, but takes a long time to do even for simple protocols. We present DistAI, a data-driven automated system for learning inductive invariants for distributed protocols. DistAI generates data by simulating the distributed protocol at different instance sizes and recording states as samples. Based on the observation that invariants are often concise in practice, DistAI starts with small invariant formulas and enumerates all strongest possible invariants that hold for all samples. It then feeds those invariants and the desired safety properties to an SMT solver to check if the conjunction of the invariants and the safety properties is inductive. Starting with small invariant formulas and strongest possible invariants avoids large SMT queries, improving SMT solver performance. Because DistAI starts with the strongest possible invariants, if the SMT solver fails, DistAI does not need to discard failed invariants, but knows to monotonically weaken them and try again with the solver, repeating the process until it eventually succeeds. We prove that DistAI is guaranteed to find the∃-free inductive invariant that proves the desired safety properties in finite time, if one exists. Our evaluation shows that DistAI successfully verifies 13 common distributed protocols automatically and outperforms alternative methods both in the number of protocols it verifies and the speed at which it does so, in some cases by more than two orders of magnitude.