Program Equivalence Checking for Automatic Recognition of Quantum-Compatible Code

The techniques used to program quantum computers are somewhat crude. As quantum computing progresses and becomes mainstream, a more efficient method of programming these devices would be beneficial. We propose a method that applies today’s programming techniques to quantum computing, with program equivalence checking used to discern between code suited for execution on a conventional computer and a quantum computer. This process involves determining a quantum algorithm’s implementation using a programming language. This so-called benchmark implementation can be checked against code written by a programmer, with semantic equivalence between the two implying the programmer’s code should be executed on a quantum computer instead of a conventional computer. Using a novel compiler optimization verification tool named CORK, we test for semantic equivalence between a portion of Shor’s algorithm (representing the benchmark implementation) and various modified versions of this code (representing the arbitrary code written by a programmer). Some of the modified versions are intended to be semantically equivalent to the benchmark while others semantically inequivalent. Our testing shows that CORK is able to correctly determine semantic equivalence or semantic inequivalence in a majority of cases

End-to-End Translation Validation for the Halide Language

International audienceThis paper considers the correctness of domain-specific compilers for tensor programming languages through the study of Halide, a popular representative. It describes a translation validation algorithm for affine Halide specifications, independently of the scheduling language. The algorithm relies on "propheticž annotations added by the compiler to the generated array assignments. The annotations provide a refinement mapping from assignments in the generated code to the tensor definitions from the specification. Our implementation leverages an affine solver and a general SMT solver, and scales to complete Halide benchmarks

On Program Equivalence with Reductions

International audienceProgram equivalence is a well-known problem with a wide range of applications, such as algorithm recognition, program verification and program optimization. This problem is also known to be undecidable if the class of programs is rich enough, in which case semi-algorithms are commonly used. We focus on programs represented as Systems of Affine Recurrence Equations (SARE), defined over parametric polyhedral domains, a well known formalism for the polyhedral model. SAREs include as a proper subset, the class of affine control loop programs. Several program equivalence semi-algorithms were already proposed for this class. Some take into account algebraic properties such as associativity and commutativity. To the best of our knowledge, none of them manage reductions, i.e., accumulations of a parametric number of sub-expressions using an associative and commutative operator. Our main contribution is a new semi-algorithm to manage reductions. In particular, we outline the ties between this problem and the perfect matching problem in a parametric bipartite graph

On Program Equivalence with Reductions

International audienceProgram equivalence is a well-known problem with a wide range of applications, such as algorithm recognition, program verification and program optimization. This problem is also known to be undecidable if the class of programs is rich enough, in which case semi-algorithms are commonly used. We focus on programs represented as Systems of Affine Recurrence Equations (SARE), defined over parametric polyhedral domains, a well known formalism for the polyhedral model. SAREs include as a proper subset, the class of affine control loop programs. Several program equivalence semi-algorithms were already proposed for this class. Some take into account algebraic properties such as associativity and commutativity. To the best of our knowledge, none of them manage reductions, i.e., accumulations of a parametric number of sub-expressions using an associative and commutative operator. Our main contribution is a new semi-algorithm to manage reductions. In particular, we outline the ties between this problem and the perfect matching problem in a parametric bipartite graph