Abstract. Relational safety specifications describe multiple runs of the same program or relate the behaviors of multiple programs. Approaches to automatic relational verification often compose the programs and analyze the result for safety, but a naively composed program can lead to difficult verification problems. We propose to exploit relational specifications for simplifying the generated verification subtasks. First, we maximize opportunities for synchronizing code fragments. Second, we compute symmetries in the specifications to reveal and avoid redundant subtasks. We have implemented these enhancements in a prototype for verifying k-safety properties on Java programs. Our evaluation confirms that our approach leads to a consistent performance speedup on a range of benchmarks.
Near-term quantum computers are expected to work in an environment where each operation is noisy, with no error correction. Therefore, quantum-circuit optimizers are applied to minimize the number of noisy operations. Today, physicists are constantly experimenting with novel devices and architectures. For every new physical substrate and for every modification of a quantum computer, we need to modify or rewrite major pieces of the optimizer to run successful experiments. In this paper, we present QUESO, an efficient approach for automatically synthesizing a quantum-circuit optimizer for a given quantum device. For instance, in 1.2 minutes, QUESO can synthesize an optimizer with high-probability correctness guarantees for IBM computers that significantly outperforms leading compilers, such as IBM's Qiskit and TKET, on the majority (85%) of the circuits in a diverse benchmark suite.
A number of theoretical and algorithmic insights underlie QUESO: (1) An algebraic approach for representing rewrite rules and their semantics. This facilitates reasoning about complex
symbolic
rewrite rules that are beyond the scope of existing techniques. (2) A fast approach for probabilistically verifying equivalence of quantum circuits by reducing the problem to a special form of
polynomial identity testing
. (3) A novel probabilistic data structure, called a
polynomial identity filter
(PIF), for efficiently synthesizing rewrite rules. (4) A beam-search-based algorithm that efficiently applies the synthesized symbolic rewrite rules to optimize quantum circuits.
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