Related papers: Relational Proofs for Quantum Programs
We introduce a quantitative relational Hoare logic for quantum programs. Assertions of the logic range over a new infinitary extension of positive semidefinite operators. We prove that our logic is sound, and complete for bounded…
Quantum correlations provide dramatic advantage over the corresponding classical resources in several communication tasks. However a broad class of probabilistic theories exists that attributes greater success than quantum theory in many of…
This study examines the simulation of quantum algorithms on a classical computer. The program code implemented on a classical computer will be a straight connection between the mathematical formulation of quantum mechanics and computational…
Various techniques have been used in recent years for verifying quantum computers, that is, for determining whether a quantum computer/system satisfies a given formal specification of correctness. Barrier certificates are a recent novel…
Quantitative aspects of computation are related to the use of both physical and mathematical quantities, including time, performance metrics, probability, and measures for reliability and security. They are essential in characterizing the…
This paper discusses the question of Stable Facts in Relational Quantum Mechanics. I examine how the approach to quantum logic in the consistent histories formalism can be used to clarify what information about a system can be shared…
Based on the connection between the categorical derivation of classical programs from specifications and the category-theoretic approach to quantum physics, this paper contributes to extending the laws of classical program algebra to…
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,…
Quantum computers are expected to offer substantial speedups over their classical counterparts and to solve problems that are intractable for classical computers. Beyond such practical significance, the concept of quantum computation opens…
We study effects of the physical realization of quantum computers on their logical operation. Through simulation of physical models of quantum computer hardware, we analyze the difficulties that are encountered in programming physical…
Quantum voting protocols aim to offer ballot secrecy and publicly verifiable tallies using physical guarantees from quantum mechanics, rather than relying solely on computational hardness. This article surveys whether such quantum voting…
Quantum computation teaches us that quantum mechanics exhibits exponential complexity. We argue that the standard scientific paradigm of "predict and verify" cannot be applied to testing quantum mechanics in this limit of high complexity.…
We propose a quantum programming paradigm where all data are familiar classical data, and the only non-classical element is a random number generator that can return results with negative probability. Currently, the vast majority of quantum…
Quantum program generation demands a level of precision that may not be compatible with the statistical reasoning carried out in the inference of large language models (LLMs). Hallucinations are mathematically inevitable and not addressable…
The nature and scope of various impossibility proofs as they relate to real-world situations are discussed. In particular, it is shown in words without technical symbols how secure quantum bit commitment protocols may be obtained with…
A wide range of interesting program properties are intrinsically relational, i.e., they relate two or more program traces. Two prominent relational properties are secure information flow and conditional program equivalence. By showing the…
An analysis using classical stochastic processes is used to construct a consistent system of quantum counterfactual reasoning. When applied to a counterfactual version of Hardy's paradox, it shows that the probabilistic character of quantum…
Temporal logics stands for a widely adopted family of formalisms for the verification of computational devices, enriching propositional logics by operators predicating on the step-wise behaviour of a system. Its quantified extensions allow…
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),…
Quantum walks can reconstruct quantum algorithms for quantum computation, where the precise controls of quantum state transfers between arbitrary distant sites are required. Here, we investigate quantum walks using a periodically…