Related papers: Irreversibility in the Halting Problem of Quantum …
The state function of a quantum object is undetermined with respect to its phase. This indeterminacy does not matter if it is global, but what if the components of the state have unknown relative phases? Can useful computations be performed…
We study effects of the physical realization of quantum computers on their logical operation. Through simulation of physical models of quantum computer hardware, we analyse the difficulties that are encountered in programming physical…
Quantum computers promise to efficiently solve not only problems believed to be intractable for classical computers, but also problems for which verifying the solution is also considered intractable. This raises the question of how one can…
The halt scheme for quantum Turing machines, originally proposed by Deutsch, is reformulated precisely and is proved to work without spoiling the computation. The ``conflict'' pointed out recently by Myers in the definition of a universal…
This paper considers the problem of robust stability for a class of uncertain quantum systems subject to unknown perturbations in the system coupling operator. A general stability result is given for a class of perturbations to the system…
We prove that there is no algorithm to tell whether an arbitrarily constructed Quantum Turing Machine has same time steps for different branches of computation. We, hence, can not avoid the notion of halting to be probabilistic in Quantum…
Significant advances in the development of computing devices based on quantum effects and the demonstration of their use to solve various problems have rekindled interest in the nature of the "quantum computational advantage." Although…
A major challenge to the control of infinite dimensional quantum systems is the irreversibility which is often present in the system dynamics. Here we consider systems with discrete-spectrum Hamiltonians operating over a Schwartz space…
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,…
The quantum computer is supposed to process information by applying unitary transformations to the complex amplitudes defining the state of N qubits. A useful machine needing N=1000 or more, the number of continuous parameters describing…
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…
The method of using concepts and insight from quantum information theory in order to solve problems in reversible classical computing (introduced in Ref. [1]) have been generalized to irreversible classical computing. The method have been…
An outstanding problem in quantum computing is the calculation of entanglement, for which no closed-form algorithm exists. Here we solve that problem, and demonstrate the utility of a quantum neural computer, by showing, in simulation, that…
Quantum computing is a new model of computation, based on quantum physics. Quantum computers can be exponentially faster than conventional computers for problems such as factoring. Besides full-scale quantum computers, more restricted…
Determining whether a quantum state is separable or entangled is a problem of fundamental importance in quantum information science. This is a brief review in which we consider the problem for states in infinite dimensional Hilbert spaces.…
The Turing machine halting problem can be explained by several factors, including arithmetic logic irreversibility and memory erasure, which contribute to computational uncertainty due to information loss during computation. Essentially,…
The physics of many closed, conservative systems can be described by both classical and quantum theories. The dynamics according to classical theory is symplectic and admits linear instabilities which would initially seem at odds with a…
Irreversibility, despite being a necessary condition for thermalization, still lacks a sound understanding in the context of isolated quantum many-body systems. In this work we approach this question by studying the behavior of generic…
One-to-one reversible automata are introduced. Their applicability to a modelling of the quantum mechanical measurement process is discussed.
The fundamental dynamics of quantum particles is neutral with respect to the arrow of time. And yet, our experiments are not: we observe quantum systems evolving from the past to the future, but not the other way round. A fundamental…