scholarly journals Undecidable, Unrecognizable, and Quantum Computing

2020 ◽  
Vol 2 (3) ◽  
pp. 337-342
Author(s):  
Michael Siomau
Keyword(s):  
Quantum Computing ◽  
Turing Machine ◽  
Quantum Computer ◽  
Practical Realization ◽  
Real Numbers ◽  
Theoretical Limit ◽  
Halting Problem ◽  
The Real ◽  
Computing Model ◽  
Successful Design

Quantum computing allows us to solve some problems much faster than existing classical algorithms. Yet, the quantum computer has been believed to be no more powerful than the most general computing model—the Turing machine. Undecidable problems, such as the halting problem, and unrecognizable inputs, such as the real numbers, are beyond the theoretical limit of the Turing machine. I suggest a model for a quantum computer, which is less general than the Turing machine, but may solve the halting problem for any task programmable on it. Moreover, inputs unrecognizable by the Turing machine can be recognized by the model, thus breaking the theoretical limit for a computational task. A quantum computer is not just a successful design of the Turing machine as it is widely perceived now, but is a different, less general but more powerful model for computing, the practical realization of which may need different strategies than those in use now.

The Realization of New Computing Model and System Research Related to Quantum Computer

2014 ◽  
Vol 1078 ◽  
pp. 413-416
Author(s):  
Hai Yan Liu
Keyword(s):  
Quantum Computing ◽  
High Performance ◽  
Quantum Physics ◽  
Quantum Computer ◽  
Quantum Computers ◽  
Information Coding ◽  
Computing Model ◽  
Mechanics Model ◽  
Electronic Spin ◽  
Classical Computer

The ultimate goal of quantum calculation is to build high performance practical quantum computers. With quantum mechanics model of computer information coding and computational principle, it is proved in theory to be able to simulate the classical computer is currently completely, and with more classical computer, quantum computation is one of the most popular fields in physics research in recent ten years, has formed a set of quantum physics, mathematics. This paper to electronic spin doped fullerene quantum aided calculation scheme, we through the comprehensive use of logic based network and based on the overall control of the two kinds of quantum computing model, solve the addressing problem of nuclear spin, avoids the technical difficulties of pre-existing. We expect the final realization of the quantum computer will depend on the integrated use of in a variety of quantum computing model and physical realization system, and our primary work shows this feature..

scholarly journals Universality probability of a prefix-free machine

2012 ◽  
Vol 370 (1971) ◽  
pp. 3488-3511 ◽  
Author(s):  
George Barmpalias ◽  
David L. Dowe
Keyword(s):  
Turing Degree ◽  
Real Numbers ◽  
Arithmetical Hierarchy ◽  
Halting Problem ◽  
The Real ◽  
The Third ◽  
Free Machine

We study the notion of universality probability of a universal prefix-free machine, as introduced by C. S. Wallace. We show that it is random relative to the third iterate of the halting problem and determine its Turing degree and its place in the arithmetical hierarchy of complexity. Furthermore, we give a computational characterization of the real numbers that are universality probabilities of universal prefix-free machines.

scholarly journals Real-time simulation of (2+1)-dimensional lattice gauge theory on qubits

2020 ◽  
Author(s):  
Arata Yamamoto
Keyword(s):  
Gauge Theory ◽  
Real Time ◽  
Degrees Of Freedom ◽  
Quantum Computer ◽  
Lattice Gauge Theory ◽  
Dual Variable ◽  
Dimensional Lattice ◽  
The Real ◽  
Lattice Gauge ◽  
Time Simulation

Abstract We study the quantum simulation of Z2 lattice gauge theory in 2+1 dimensions. The dual variable formulation, the so-called Wegner duality, is utilized for reducing redundant gauge degrees of freedom. The problem of artificial charge unconservation is resolved for any charge distribution. As a demonstration, we simulate the real-time evolution of the system with two static electric charges, i.e., with two temporal Wilson lines. Some results obtained by the simulator (with no hardware noise) and the real device (with sizable hardware noise) of a quantum computer are shown.

Shuffling of Linear Orders

1995 ◽  
Vol 38 (2) ◽  
pp. 223-229
Author(s):  
John Lindsay Orr
Keyword(s):  
Ordered Set ◽  
Linear Orders ◽  
Real Numbers ◽  
The Real ◽  
Linearly Ordered Set

AbstractA linearly ordered set A is said to shuffle into another linearly ordered set B if there is an order preserving surjection A —> B such that the preimage of each member of a cofinite subset of B has an arbitrary pre-defined finite cardinality. We show that every countable linearly ordered set shuffles into itself. This leads to consequences on transformations of subsets of the real numbers by order preserving maps.

scholarly journals A question of van den Dries and a theorem of Lipshitz and Robinson; Not everything is standard

2007 ◽  
Vol 72 (1) ◽  
pp. 119-122 ◽  
Author(s):  
Ehud Hrushovski ◽  
Ya'acov Peterzil
Keyword(s):  
Real Numbers ◽  
The Real ◽  
First Order ◽  
Real Closed Fields ◽  
Minimal Structure ◽  
Closed Fields ◽  
New Construction ◽  
The Relationship

AbstractWe use a new construction of an o-minimal structure, due to Lipshitz and Robinson, to answer a question of van den Dries regarding the relationship between arbitrary o-minimal expansions of real closed fields and structures over the real numbers. We write a first order sentence which is true in the Lipshitz-Robinson structure but fails in any possible interpretation over the field of real numbers.

Efficient reversible quantum design of sig-magnitude to two's complement converters

2020 ◽  
Vol 20 (9&10) ◽  
pp. 747-765
Author(s):  
F. Orts ◽  
G. Ortega ◽  
E.M. E.M. Garzon
Keyword(s):  
Quantum Computing ◽  
Scientific Community ◽  
Quantum Computer ◽  
Fault Tolerant ◽  
State Of The Art ◽  
The Other ◽  
Quantum Computers ◽  
Binary Number ◽  
Quantum Cost ◽  
The One

Despite the great interest that the scientific community has in quantum computing, the scarcity and high cost of resources prevent to advance in this field. Specifically, qubits are very expensive to build, causing the few available quantum computers are tremendously limited in their number of qubits and delaying their progress. This work presents new reversible circuits that optimize the necessary resources for the conversion of a sign binary number into two's complement of N digits. The benefits of our work are two: on the one hand, the proposed two's complement converters are fault tolerant circuits and also are more efficient in terms of resources (essentially, quantum cost, number of qubits, and T-count) than the described in the literature. On the other hand, valuable information about available converters and, what is more, quantum adders, is summarized in tables for interested researchers. The converters have been measured using robust metrics and have been compared with the state-of-the-art circuits. The code to build them in a real quantum computer is given.

On expressible sets and p-adic numbers

2011 ◽  
Vol 54 (2) ◽  
pp. 411-422
Author(s):  
Jaroslav Hančl ◽  
Radhakrishnan Nair ◽  
Simona Pulcerova ◽  
Jan Šustek
Keyword(s):  
Haar Measure ◽  
Real Numbers ◽  
The Real ◽  
Expressible Set

AbstractContinuing earlier studies over the real numbers, we study the expressible set of a sequence A = (an)n≥1 of p-adic numbers, which we define to be the set EpA = {∑n≥1ancn: cn ∈ ℕ}. We show that in certain circumstances we can calculate the Haar measure of EpA exactly. It turns out that our results extend to sequences of matrices with p-adic entries, so this is the setting in which we work.

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