Related papers: Refinement calculus of quantum programs with proje…
Many tools used to process programs, like compilers, analyzers, or verifiers, perform transformations on their intermediate program representation, like abstract syntax trees. Implementing such program transformations is a non-trivial task,…
Quantum reservoir computing (QRC) is a hardware-implementation-friendly quantum neural network scheme with minimal physical system requirements and a proven advantage over classical counterparts. We use an extension of the positive-P phase…
Program refinement involves correctness-preserving transformations from formal high-level specification statements into executable programs. Traditional verification tool support for program refinement is highly interactive and lacks…
The refinement calculus for logic programs is a framework for deriving logic programs from specifications. It is based on a wide-spectrum language that can express both specifications and code, and a refinement relation that models the…
Quantum computing exploits quantum phenomena such as superposition and entanglement to realize a form of parallelism that is not available to traditional computing. It offers the potential of significant computational speed-ups in quantum…
Stepwise refinement of algebraic specifications is a well known formal methodology for program development. However, traditional notions of refinement based on signature morphisms are often too rigid to capture a number of relevant…
We present a framework for differentiable quantum transforms. Such transforms are metaprograms capable of manipulating quantum programs in a way that preserves their differentiability. We highlight their potential with a set of relevant…
The refinement calculus provides a methodology for transforming an abstract specification into a concrete implementation, by following a succession of refinement rules. These rules have been mechanized in theorem-provers, thus providing a…
Quantum computing is an emerging computational paradigm that leverages the laws of quantum mechanics to perform elementary logic operations. Existing programming models for quantum computing were designed with fault-tolerant hardware in…
The Quantum Query Model is a framework that allows us to express most known quantum algorithms. Algorithms represented by this model consist on a set of unitary operators acting over a finite Hilbert space, and a final measurement step…
A fundamental model of quantum computation is the programmable quantum gate array. This is a quantum processor that is fed by a program state that induces a corresponding quantum operation on input states. While being programmable, any…
To derive a program for a given specification R means to find an artifact P that satisfies two conditions: P is executable in some programming language; and P is correct with respect to R. Refinement-based program derivation achieves this…
Essentially, in a reversible programming language, for each forward computation from state $S$ to state $S'$, there exists a constructive method to go backwards from state $S'$ to state $S$. Besides its theoretical interest, reversible…
We present a theory of "quantum references", similar to lenses in classical functional programming, that allow to point to a subsystem of a larger quantum system, and to mutate/measure that part. Mutable classical variables, quantum…
Quantum computation is the suitable orthogonal encoding of possibly holistic functional properties into state vectors, followed by a projective measurement.
Quantum computation is a topic of significant recent interest, with practical advances coming from both research and industry. A major challenge in quantum programming is dealing with errors (quantum noise) during execution. Because quantum…
Programming for today's quantum computers is making significant strides toward modern workflows compatible with high performance computing (HPC), but fundamental challenges still remain in the integration of these vastly different…
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),…
The paper extends the expectation transformer based analysis of higher-order probabilistic programs to the quantum higher-order setting. The quantum language we are considering can be seen as an extension of PCF, featuring unbounded…
We propose a novel optimization scheme designed to find optimally correctable subspace codes for a known quantum noise channel. To each candidate subspace code we first associate a universal recovery map, as if the code was perfectly…