Related papers: On the completeness of quantum computation models
Recently Quantum Computation has generated a lot of interest due to the discovery of a quantum algorithm which can factor large numbers in polynomial time. The usefulness of a quantum com puter is limited by the effect of errors. Simulation…
To date, work on formalizing connectionist computation in a way that is at least Turing-complete has focused on recurrent architectures and developed equivalences to Turing machines or similar super-Turing models, which are of more…
Axioms are presented which encapsulate the properties satisfied by categories of games which form the basis of results on full abstraction for PCF and other programming languages, and on full completeness for various logics and type…
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 show that the common theory of all modules over a tubular algebra (over a recursive algebraically closed field) is decidable. This result supports a long standing conjecture of Mike Prest which says that a finite-dimensional algebra…
This paper demonstrates the relativity of Computability and Nondeterministic; the nondeterministic is just Turing's undecidable Decision rather than the Nondeterministic Polynomial time. Based on analysis about TM, UM, DTM, NTM, Turing…
We report a new limitation on the ability of physical systems to perform computation -- one that is based on generalizing the notion of memory, or storage space, available to the system to perform the computation. Roughly, we define memory…
Experimental science usually relies on laboratory procedures that, after finitely many steps, terminate with numerical reports on physical quantities. This paper argues that such procedures can be understood as algorithmic once the…
I provide an alternative way of seeing quantum computation. First, I describe an idealized classical problem solving machine that, thanks to a many body interaction, reversibly and nondeterministically produces the solution of the problem…
The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones polynomial and arise in Witten-Chern-Simons…
The notion of quantum Turing machines is a basis of quantum complexity theory. We discuss a general model of multi-tape, multi-head Quantum Turing machines with multi final states that also allow tape heads to stay still.
We present a scalable, robust approach to creating quantum programs of arbitrary size and complexity. The approach is based on the true abstraction of the problem. The quantum program is expressed in terms of a high-level model together…
Computational complexity characterizes the usage of spatial and temporal resources by computational processes. In the classical theory of computation, e.g. in the Turing Machine model, computational processes employ only local space and…
Simulation of quantum systems that provide intrinsically fault-tolerant quantum computation is shown to preserve fault tolerance. Errors committed in the course of simulation are eliminated by the natural error-correcting features of the…
A universal Turing machine is a powerful concept - a single device can compute any function that is computable. A universal spin model, similarly, is a class of physical systems whose low energy behavior simulates that of any spin system.…
We identify "proper quantum computation" with computational processes that cannot be efficiently simulated on a classical computer. For optical quantum computation, we establish "no-go" theorems for classes of quantum optical experiments…
We say that a set is exhaustible if it admits algorithmic universal quantification for continuous predicates in finite time, and searchable if there is an algorithm that, given any continuous predicate, either selects an element for which…
The formalism of quantum theory over discrete systems is extended in two significant ways. First, quantum evolutions are generalized to act over entire network configurations, so that nodes may find themselves in a quantum superposition of…
We develop a sound and complete equational theory for the functional quantum programming language QML. The soundness and completeness of the theory are with respect to the previously-developed denotational semantics of QML. The completeness…
The string-net condensate is a new class of materials which exhibits the quantum topological order. In order to answer the important question, "how useful is the string-net condensate in quantum information processing?", we consider the…