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We show that there exists a universal quantum Turing machine (UQTM) that can simulate every other QTM until the other QTM has halted and then halt itself with probability one. This extends work by Bernstein and Vazirani who have shown that…

In this work, we reveal a new type of impossibility discovered in our recent research which forbids comparing the closeness of multiple unknown quantum states with any non-trivial threshold in a perfect or an unambiguous way. This…

We give a proof of impossibility of probabilistic exact $1\to 2$ cloning of any three different states of a qubit. The simplicity of the proof is due to the use of a surprising result of remote state preparation [M.-Yong Ye, Y.-Sheng Zhang…

According to Deutsch, a universal quantum Turing machine (UQTM) is able to perform, in repeating a fixed unitary transformation on the total system, an arbitrary unitary transformation on an arbitrary data state, by including a program as…

Many different definitions of computational universality for various types of dynamical systems have flourished since Turing's work. We propose a general definition of universality that applies to arbitrary discrete time symbolic dynamical…

Quantum measurement is universal for quantum computation. This universality allows alternative schemes to the traditional three-step organisation of quantum computation: initial state preparation, unitary transformation, measurement. In…

We present here a scheme that relates seemingly two different kinds of physical impossibilities of quantum information processing. We derive, exact flipping of three arbitrary states not lying in one great circle is not possible with…

A rather easy yet rigorous proof of a version of G\"odel's first incompleteness theorem is presented. The version is "each recursively enumerable theory of natural numbers with 0, 1, +, *, =, logical and, logical not, and the universal…

Quantum measurement is universal for quantum computation. This universality allows alternative schemes to the traditional three-step organisation of quantum computation: initial state preparation, unitary transformation, measurement. In…

Multiway Turing machines (also known as nondeterministic Turing machines or NDTMs) with explicit, simple rules are studied. Even very simple rules are found to generate complex behavior, characterized by complex multiway graphs, that can be…

Metastability is a spurious mode of operation in digital signals, where an electrical signal fails to settle into a stable state within a specified time, leading to uncertainty and potentially failing downstream hardware. A system that…

Models of computation operating over the real numbers and computing a larger class of functions compared to the class of general recursive functions invariably introduce a non-finite element of infinite information encoded in an arbitrary…

We experimentally demonstrate that it is impossible to simulate quantum bipartite correlations with a deterministic universal Turing machine. Our approach is based on the Normalized Information Distance (NID) that allows the comparison of…

We analyze to what extent it is possible to copy arbitrary states of a two-level quantum system. We show that there exists a "universal quantum copying machine", which approximately copies quantum mechanical states in such a way that the…

The paper offers a mathematical formalization of the Turing test. This formalization makes it possible to establish the conditions under which some Turing machine will pass the Turing test and the conditions under which every Turing machine…

We define a subclass of quantum Turing machine (QTM) named SR-QTM, which halts deterministically and has deterministic tape head position. A quantum state transition diagram (QSTD) is proposed to describe SR-QTM. With the help of QSTD, we…

We prove the Extended Church-Turing Thesis: Every effective algorithm can be efficiently simulated by a Turing machine. This is accomplished by emulating an effective algorithm via an abstract state machine, and simulating such an abstract…

Universal memcomputing machines (UMMs) [IEEE Trans. Neural Netw. Learn. Syst. 26, 2702 (2015)] represent a novel computational model in which memory (time non-locality) accomplishes both tasks of storing and processing of information. UMMs…

This paper describes the formal verification of two Turing machines using the program verifier Dafny. Both machines are deciders, so we prove total correctness. They are typical first examples of Turing machines used in any course of…

In the 1960's Gisbert Hasenjaeger built Turing Machines from electromechanical relays and uniselectors. Recently, Glaschick reverse engineered the program of one of these machines and found that it is a universal Turing machine. In fact,…