# Computational Power of Infinite Quantum Parallelism

@article{Ziegler2005ComputationalPO, title={Computational Power of Infinite Quantum Parallelism}, author={Martin Ziegler}, journal={International Journal of Theoretical Physics}, year={2005}, volume={44}, pages={2059-2071} }

Recent works have independently suggested that quantum mechanics might permit procedures that fundamentally transcend the power of Turing Machines as well as of ‘standard’ Quantum Computers. These approaches rely on and indicate that quantum mechanics seems to support some infinite variant of classical parallel computing.We compare this new one with other attempts towards hypercomputation by separating (1) its %principal computing capabilities from (2) realizability issues. The first are shown…

## 19 Citations

### Effective Physical Processes and Active Information in Quantum Computing

- Physics, Computer Science
- 2007

The idea of “effective physical process” is proposed as the essentially physical notion of computation as the possibility to realize quantum oracles is reachable and computation is led back to the logic of physical world.

### Quantum computation and a universal quantum computer.

- Computer Science, Physics
- 2012

The core and primary focus of this thesis is the theoretical construction of a machine that can compute every computable function, that is, a universal (i.e.programmable) quantum computer.

### Physically-relativized Church-Turing Hypotheses: Physical foundations of computing and complexity theory of computational physics

- PhilosophyAppl. Math. Comput.
- 2009

### Computational Complexity of Geometric Quantum Logic ∗

- Mathematics

We propose a new approach towards the question of whether the equational theory of ortholattices related to Quantum Mechanics is decidable or not: By determining the growth of the algorithmic…

### Complete set of circuit equations for stabilizer quantum mechanics

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- 2014

We find a sufficient set of equations between quantum circuits from which we can derive any other equation between stabilizer quantum circuits. To establish this result, we rely upon existing work on…

### On the existence of truly autonomic computing systems and the link with quantum computing

- Computer Science, PhilosophyArXiv
- 2004

NAFL supports a link between autonomic and quantum computing, with the AM existing as a metamathematical entity, and allows quantum algorithms to access truly random elements and thereby supports non-standard models of quantum (hyper-) computation that permit infinite parallelism.

### On More or Less Appropriate Notions of 'Computation'

- Computer ScienceSouth Afr. Comput. J.
- 2018

This paper presents some arguments about which notions of “computation” may be considered “reasonably acceptable” for the authors' own historic era, and emphasizes that every science-philosophical notion has its own long-term historical semantics which cannot be fixed once and forever.

### Understanding topological quantum error-correction codes using classical spin models

- Computer Science, Physics
- 2012

This thesis numerically calculates – for the first time – the error threshold of several topological error-correction codes via large-scale Monte Carlo simulations, which denotes the maximum tolerable error rate for reliable error correction.

### Alternative theories in quantum foundations

- Physics
- 2016

Abstraction is an important driving force in theoretical physics. New insights often accompany the creation of physical frameworks which are both comprehensive and parsimonious. In particular, the…

## References

SHOWING 1-10 OF 49 REFERENCES

### Classical physics and the Church--Turing Thesis

- PhysicsJACM
- 2003

In this article, it is observed that there is fundamental tension between the Extended Church--Turing Thesis and the existence of numerous seemingly intractable computational problems arising from classical physics.

### Quantum Algorithm for Hilbert's Tenth Problem

- PhysicsArXiv
- 2001

It is argued that computability, and with it the limits of Mathematics, ought to be determined not solely by Mathematics itself but also by Physical Principles.

### Computing the non-computable

- Mathematics, Computer ScienceArXiv
- 2002

It is argued that computability, and thus the limits of mathematics, ought to be determined not solely by mathematics itself but also by physical principles.

### Physical Hypercomputation and the Church–Turing Thesis

- PhilosophyMinds and Machines
- 2004

It is argued that the existence of the device does not refute the Church–Turing thesis, but nevertheless may be a counterexample to Gandy's thesis.

### Hypercomputation: computing more than the Turing machine

- Computer ScienceArXiv
- 2002

Much of the work that has been done on hypercomputation is surveyed, explaining how such non-classical models fit into the classical theory of computation and comparing their relative powers.

### Reflections on quantum computing

- Mathematics, Computer ScienceComplex.
- 2000

In this rather speculative note three problems pertaining to the power and limits of quantum computing are posed and partially answered: a) when are quantum speedups possible?, b) is fixed-point…

### Transcending the Limits of Turing Computability

- Computer Science
- 2003

This paper will discuss the solutions of the Infinite Merchant Problem, a decision problem equivalent to the Halting Problem, based on results obtained in \cite{Coins,acp}.

### The Fundamental Physical Limits of Computation.

- Computer Science
- 1985

One of us has shown that it is possi ble to build a reversible Turing machine, for Alan M. Turing's device can per form any computation that can be per formed by a modern computer.

### Non-Turing Computations Via Malament–Hogarth Space-Times

- Computer Science
- 2001

It is argued that there are several distinguished Church–Turing-type theses (not only one) and validity of some of these theses depend on the background physical theory the authors choose to use, and if they choose classical general relativity theory as their background theory, then certain forms of the Church-Turing thesis cease to be valid.

### The Broad Conception of Computation

- Philosophy
- 1997

A myth has arisen concerning Turing's article of 1936, namely that Turing set forth a fundamental principle concerning the limits of what can be computed by machine; this supposed principle is sometimes incorrectly termed the Church-Turing thesis.