Related papers: Quantum Weakest Preconditions
This paper presents a novel semantics for a quantum programming language by operator algebras, which are known to give a formulation for quantum theory that is alternative to the one by Hilbert spaces. We show that the opposite category of…
In this short paper we present the main features of a new quantum programming language proposed recently by Peter Selinger which gives a good idea about the difficulties of constructing a scalable quantum computer. We show how some of these…
We propose a new approach to the theory of conditioning for numerical analysis problems for which both classical and stochastic perturbation theory fail to predict the observed accuracy of computed solutions. To motivate our ideas, we…
The outcome of a weak quantum measurement conditioned to a subsequent postselection (a weak value protocol) can assume peculiar values. These results cannot be explained in terms of conditional probabilistic outcomes of projective…
For a given set of input-output pairs of quantum states or observables, we ask the question whether there exists a physically implementable transformation that maps each of the inputs to the corresponding output. The physical maps on…
The subject of this work is quantum predicative programming -- the study of developing of programs intended for execution on a quantum computer. We look at programming in the context of formal methods of program development, or programming…
Weak values inferred from weak measurements have been proposed as a tool to investigate trajectories of pre- and post-selected quantum systems. Are the inferences drawn from the weak values about the past of a quantum particle fully true?…
Quantum advantage is notoriously hard to find and even harder to prove. For example the class of functions computable with classical physics actually exactly coincides with the class computable quantum-mechanically. It is strongly believed,…
Demonstrating quantum advantage has been a pressing challenge in the field. Most claimed quantum speedups rely on a subroutine in which classical information can be accessed in a coherent quantum manner, which imposes a crucial constraint…
Qubits are a great way to build a quantum computer, but a limited way to program one. We replace the usual "states and gates" formalism with a "props and ops" (propositions and operators) model in which (a) the C*-algebra of observables…
Data refinement is the standard extension of a refinement relation from programs to datatypes (i.e. a behavioural subtyping relation). Forward/backward simulations provide a tractable method for establishing data refinement, and have been…
We propose a usage of a weak value for a quantum processing between preselection and postselection. While the weak value of a projector of 1 provides a process with certainty like the probability of 1, the weak value of -1 negates the…
A new paradigm of quantum computing, namely, soft quantum computing, is proposed for nonclassical computation using real world quantum systems with naturally occurring environment-induced decoherence and dissipation. As a specific example…
The notion of weak measurement provides a formalism for extracting information from a quantum system in the limit of vanishing disturbance to its state. Here we extend this formalism to the measurement of sequences of observables. When…
State-of-the-art classical optimization solvers set a high bar for quantum computers to deliver utility in this domain. Here, we introduce a quantum preconditioning approach based on the quantum approximate optimization algorithm. It…
A field dependent $su(2)$ gauge transformation connects between the adiabatic and diabatic pictures in the (Landau-Zener-Stueckelberg) potential curve crossing problem. It is pointed out that weak and strong potential curve crossing…
This paper introduces a novel type theory and logic for probabilistic reasoning. Its logic is quantitative, with fuzzy predicates. It includes normalisation and conditioning of states. This conditioning uses a key aspect that distinguishes…
Quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a quregister, a system of qubits, representing a…
We present a relatively simple description of binary, definable subsets of models of weakly quasi-o-minimal theories. In particular, we closely describe definable linear orders and prove a weak version of the monotonicity theorem. We also…
We use a natural generalization of the discrete Fourier transform to define transition maps between Hilbert subspaces and the global transport operator $Z$. By using these transition maps as Kraus (or noise) operators, an extension of the…