Statistical Assertions for Validating Patterns and Finding Bugs in Quantum Programs

In support of the growing interest in quantum computing experimentation, programmers need new tools to write quantum algorithms as program code. Compared to debugging classical programs, debugging quantum programs is difficult because programmers have limited ability to probe the internal states of quantum programs; those states are difficult to interpret even when observations exist; and programmers do not yet have guidelines for what to check for when building quantum programs. In this work, we present quantum program assertions based on statistical tests on classical observations. These allow programmers to decide if a quantum program state matches its expected value in one of classical, superposition, or entangled types of states. We extend an existing quantum programming language with the ability to specify quantum assertions, which our tool then checks in a quantum program simulator. We use these assertions to debug three benchmark quantum programs in factoring, search, and chemistry. We share what types of bugs are possible, and lay out a strategy for using quantum programming patterns to place assertions and prevent bugs.Comment: In The 46th Annual International Symposium on Computer Architecture (ISCA '19). arXiv admin note: text overlap with arXiv:1811.0544

Quantum rejection sampling

Rejection sampling is a well-known method to sample from a target distribution, given the ability to sample from a given distribution. The method has been first formalized by von Neumann (1951) and has many applications in classical computing. We define a quantum analogue of rejection sampling: given a black box producing a coherent superposition of (possibly unknown) quantum states with some amplitudes, the problem is to prepare a coherent superposition of the same states, albeit with different target amplitudes. The main result of this paper is a tight characterization of the query complexity of this quantum state generation problem. We exhibit an algorithm, which we call quantum rejection sampling, and analyze its cost using semidefinite programming. Our proof of a matching lower bound is based on the automorphism principle which allows to symmetrize any algorithm over the automorphism group of the problem. Our main technical innovation is an extension of the automorphism principle to continuous groups that arise for quantum state generation problems where the oracle encodes unknown quantum states, instead of just classical data. Furthermore, we illustrate how quantum rejection sampling may be used as a primitive in designing quantum algorithms, by providing three different applications. We first show that it was implicitly used in the quantum algorithm for linear systems of equations by Harrow, Hassidim and Lloyd. Secondly, we show that it can be used to speed up the main step in the quantum Metropolis sampling algorithm by Temme et al.. Finally, we derive a new quantum algorithm for the hidden shift problem of an arbitrary Boolean function and relate its query complexity to "water-filling" of the Fourier spectrum.Comment: 19 pages, 5 figures, minor changes and a more compact style (to appear in proceedings of ITCS 2012