Related papers: Computability and Complexity of Unconventional Com…
The class $\mathcal{UP}$ of `ultimate polynomial time' problems over $\mathbb C$ is introduced; it contains the class $\mathcal P$ of polynomial time problems over $\mathbb C$. The $\tau$-Conjecture for polynomials implies that…
What is the computational power of a quantum computer? We show that determining the output of a quantum computation is equivalent to counting the number of solutions to an easily computed set of polynomials defined over the finite field…
We propose a decision-theoretic framework for computational complexity, complementary to classical theory: moving from syntactic exactness (Turing / Shannon) to semantic simulability (Le Cam). While classical theory classifies problems by…
This preliminary report addresses the expressive power of unit resolution regarding input data encoded with partial truth assignments of propositional variables. A characterization of the functions that are computable in this way, which we…
We examine various categorical structures that can and cannot be constructed. We show that total computable functions can be mimicked by constructible functors. More generally, whatever can be done by a Turing machine can be constructed by…
We explore the possible connections between the dynamic behaviour of a system and Turing universality in terms of the system's ability to (effectively) transmit and manipulate information. Some arguments will be provided using a defined…
Recently, among experiments for realization of quantum computers, NMR quantum computers have achieved the most impressive succession. There is a model of the NMR quantum computation,namely Atsumi and Nishino's bulk quantum Turing Machine.…
Quantum computers use quantum mechanical phenomena to perform conventionally intractable calculations for specific problems. Despite being universal machines, quantum computers are not expected to replace classical computers, but rather, to…
This paper furthers existing evidence that quantum computers are capable of computations beyond classical computers. Specifically, we strengthen the collapse of the polynomial hierarchy to the second level if: (i) Quantum computers with…
Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and…
Quantum information processing is the use of inherently quantum mechanical phenomena to perform information processing tasks that cannot be achieved using conventional classical information technologies. One famous example is quantum…
This article addresses the question of when physical laws and their consequences can be computed. If a physical system is capable of universal computation, then its energy gap can't be computed. At an even more fundamental level, the most…
This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…
With a growing interest in quantum technology globally, there is an increasing need for accessing relevant physical systems for education and research. In this paper we introduce a commercially available on-site quantum computer utilizing…
Systems are growing into more complex ones for developing and maintaining. Existing systems which do not have much in common on the first look are connected, due to the technical progress, even if it was never intended that way. It is an…
Experiments with superconducting quantum processors have successfully demonstrated the basic functions needed for quantum computation and evidence of utility, albeit without a sizable array of error-corrected qubits. The realization of the…
We use the powerful tools of counting complexity and generic oracles to help understand the limitations of the complexity of quantum computation. We show several results for the probabilistic quantum class BQP. 1. BQP is low for PP, i.e.,…
The Church-Turing thesis states that any sufficiently powerful computational model which captures the notion of algorithm is computationally equivalent to the Turing machine. This equivalence usually holds both at a computability level and…
This paper constructively proves the existence of an effective procedure generating a computable (total) function that is not contained in any given effectively enumerable set of such functions. The proof implies the existence of machines…
A physical system is determined by a finite set of initial conditions and "laws" represented by equations. The system is computable if we can solve the equations in all instances using a "finite body of mathematical knowledge". In this…