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We consider the issue of computability at the most fundamental level of physical reality: the Planck scale. To this aim, we consider the theoretical model of a quantum computer on a non commutative space background, which is a computational…
The problem of quantum test is formally addressed. The presented method attempts the quantum role of classical test generation and test set reduction methods known from standard binary and analog circuits. QuFault, the authors software…
While non-contextual hidden-variable theories are proved to be impossible, contextual ones are possible. In a contextual hidden-variable theory, an observable is called a beable if the hidden-variable assigns its value in a given…
As the variety of commercially available quantum computers continues to increase so does the need for tools that can characterize, verify and validate these computers. This work explores using quantum state tomography for characterizing the…
Generalizing earlier work characterizing the quantum query complexity of computing a function of an unknown classical ``black box'' function drawn from some set of such black box functions, we investigate a more general quantum query model…
Today, people are looking forward to get an awesome computational power. This kind of desire can be answered by quantum computing. By adopting quantum mechanics theory, it can generate a very fast computation result. As known, quantum…
A quantum computer is a machine that can perform certain calculations much faster than a classical computer by using the laws of quantum mechanics. Quantum computers do not exist yet, because it is extremely difficult to control quantum…
We review arXiv:1308.3444 and arXiv:1104.1891. The structure of the spectrum of a quantum integrable system is crucial to understand its properties. In his seminar 1971 paper, Baxter observed that the spectrum of the "ice model" has a very…
Recursive techniques have recently been introduced into quantum programming so that a variety of large quantum circuits and algorithms can be elegantly and economically programmed. In this paper, we present a proof system for formal…
A proof of quantumness is a method for provably demonstrating (to a classical verifier) that a quantum device can perform computational tasks that a classical device with comparable resources cannot. Providing a proof of quantumness is the…
We show how it is possible to realize quantum computations on a system in which most of the parameters are practically unknown. We illustrate our results with a novel implementation of a quantum computer by means of bosonic atoms in an…
The purpose of this paper is to explore the question "to what extent could we produce formal, machine-verifiable, proofs in real algebraic geometry?" The question has been asked before but as yet the leading algorithms for answering such…
In this paper we explore the structure and applicability of the Distributed Measurement Calculus (DMC), an assembly language for distributed measurement-based quantum computations. We describe the formal language's syntax and semantics,…
Recent works have explored the use of counting queries coupled with Description Logic ontologies. The answer to such a query in a model of a knowledge base is either an integer or $\infty$, and its spectrum is the set of its answers over…
CZF is a system of set theory which, over classical logic, is equivalent to ZF, while over intuitionistic logic, it has a well-known constructive type-theoretic interpretation. This article introduces a simpler, intuitive family of…
We show a similarity between two different classical simulation methods for measurement based quantum computation -- one relying on a low entanglement (tree tensor network) representation of the computer's state, and the other a tensor…
We study how the choices made when designing an oracle affect the complexity of quantum property testing problems defined relative to this oracle. We encode a regular graph of even degree as an invertible function $f$, and present $f$ in…
Quantum computers promise to revolutionise electronic simulations by overcoming the exponential scaling of many-electron problems. While electronic wave functions can be represented using a product of fermionic unitary operators, shallow…
In the study of quantum computation, data is represented in terms of linear operators which form a generalized model of probability, and computations are most commonly described as products of unitary transformations, which are the…
The aim of this paper is to analyze the reconstructability of quantum mechanics from classical conditional probabilities representing measurement outcomes conditioned on measurement choices. We will investigate how the quantum mechanical…