Undecidable, Unrecognizable, and Quantum Computing
نویسندگان
چکیده
منابع مشابه
Quantum measurement occurrence is undecidable.
In this work, we show that very natural, apparently simple problems in quantum measurement theory can be undecidable even if their classical analogues are decidable. Undecidability hence appears as a genuine quantum property here. Formally, an undecidable problem is a decision problem for which one cannot construct a single algorithm that will always provide a correct answer in finite time. The...
متن کاملDecidable and Undecidable Problems about Quantum Automata
We study the following decision problem: is the language recognized by a quantum finite automaton empty or nonempty? We prove that this problem is decidable or undecidable depending on whether recognition is defined by strict or nonstrict thresholds. This result is in contrast with the corresponding situation for probabilistic finite automata, for which it is known that strict and nonstrict thr...
متن کاملMeasurement - based quantum computation and undecidable logic
We establish a connection between measurement-based quantum computation and the field of mathematical logic. We show that the computational power of an important class of quantum states called graph states, representing resources for measurement-based quantum computation, is reflected in the expressive power of (classical) formal logic languages defined on the underlying mathematical graphs. In...
متن کاملQuantum Topology and Quantum Computing
I. Introduction This paper is a quick introduction to key relationships between the theories of knots,links, three-manifold invariants and the structure of quantum mechanics. In section 2 we review the basic ideas and principles of quantum mechanics. Section 3 shows how the idea of a quantum amplitude is applied to the construction of invariants of knots and links. Section 4 explains how the ge...
متن کاملQuantum Computing and Quantum Cryptography
Entrust is a registered trademark of Entrust, Inc. in the United States and certain other countries. Entrust is a registered trademark of Entrust Limited in Canada. All other Entrust product names and service names are trademarks or registered trademarks of Entrust, Inc or Entrust Limited. All other company and product names are trademarks or registered trademarks of their respective owners.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Quantum Reports
سال: 2020
ISSN: 2624-960X
DOI: 10.3390/quantum2030023