The non-algorithmic side of the mind

The existence of a non-algorithmic side of the mind, conjectured by Penrose on the basis of G\"odel's first incompleteness theorem, is investigated here in terms of a quantum metalanguage. We suggest that, besides human ordinary thought, which can be formalized in a computable, logical language, there is another important kind of human thought, which is Turing-non-computable. This is methatought, the process of thinking about ordinary thought. Metathought can be formalized as a metalanguage, which speaks about and controls the logical language of ordinary thought. Ordinary thought has two computational modes, the quantum mode and the classical mode, the latter deriving from decoherence of the former. In order to control the logical language of the quantum mode, one needs to introduce a quantum metalanguage, which in turn requires a quantum version of Tarski Convention T.

http://arxiv.org/abs/1205.1820

Order of magnitude advance in QC: "The ion-crystal used is poised to create one of the most powerful computers ever developed,"

Previous efforts at realizing a quantum simulator have had problems with decoherence and other systemic errors past 10~ qubits. This advance is roughly 10 ten times more than the previous record. Quantum simulators are used to model systems such that parameters that could not be physically varied in the original system can be with the modeled analogue parameters. That is the computation that they are referring to when they say a computer the size of the universe would be needed to perform the calculations.

For instance, the quantum behaviour of these hundred so spin qubits mimicks the behaviour found in numerous mesoscale systems, particularly lattices. In those systems, varying the lattice length and / or other parameters describing the system is often physically impossible or otherwise restrictively difficult, and completely impossible to simulate with a computer. By creating an analogue, pseudo-variations can be performed that give insight into the underlying structure and lead to a better understanding of the original lattice.

From the arXiv paper below the news story: a tunable parameter that mimicks various physical couplings.

That is, by adjusting the single experimental parameter μR we can mimic a continuum of physical couplings including important special cases: a = 0 is infinite range, a = 1 is monopole-monopole (Coulomb-like), a = 2 is monopole-dipole and a = 3 is dipole-dipole. Note that a = 0 results in the so-called Jˆz interaction that gives rise to spin-
squeezing and is used in quantum logic gates (see Supple-
mentary Information) [27]. In addition, tuning μR also permits
access to both antiferromagnetic (AFM, μR > ω1 ) and ferro-
magnetic (FM, ω2 μR < ω1 ) couplings [13].

http://sydney.edu.au/news/84.html?newsstoryid=9081

"The system we have developed has the potential to perform calculations that would require a supercomputer larger than the size of the known universe - and it does it all in a diameter of less than a millimetre," said Dr Biercuk.
"The projected performance of this new experimental quantum simulator eclipses the current maximum capacity of any known computer by an astonishing 10 to the power of 80. That is 1 followed by 80 zeros, in other words 80 orders of magnitude, a truly mind-boggling scale."
The work smashes previous records in terms of the number of elements working together in a quantum simulator, and therefore the complexity of the problems that can be addressed

Most recent paper from author:
http://arxiv.org/abs/1204.5789

Engineered 2D Ising interactions on a trapped-ion quantum simulator with hundreds of spins

(Submitted on 25 Apr 2012) 

The presence of long-range quantum spin correlations underlies a variety of physical phenomena in condensed matter systems, potentially including high-temperature superconductivity. However, many properties of exotic strongly correlated spin systems (e.g., spin liquids) have proved difficult to study, in part because calculations involving N-body entanglement become intractable for as few as N~30 particles. Feynman divined that a quantum simulator - a special-purpose "analog" processor built using quantum particles (qubits) - would be inherently adept at such problems. In the context of quantum magnetism, a number of experiments have demonstrated the feasibility of this approach. However, simulations of quantum magnetism allowing controlled, tunable interactions between spins localized on 2D and 3D lattices of more than a few 10's of qubits have yet to be demonstrated, owing in part to the technical challenge of realizing large-scale qubit arrays. Here we demonstrate a variable-range Ising-type spin-spin interaction J_ij on a naturally occurring 2D triangular crystal lattice of hundreds of spin-1/2 particles (9Be+ ions stored in a Penning trap), a computationally relevant scale more than an order of magnitude larger than existing experiments. We show that a spin-dependent optical dipole force can produce an antiferromagnetic interaction J_ij ~ 1/d_ij^a, where a is tunable over 0<a<3; d_ij is the distance between spin pairs. These power-laws correspond physically to infinite-range (a=0), Coulomb-like (a=1), monopole-dipole (a=2) and dipole-dipole (a=3) couplings. Experimentally, we demonstrate excellent agreement with theory for 0.05<a<1.4. This demonstration coupled with the high spin-count, excellent quantum control and low technical complexity of the Penning trap brings within reach simulation of interesting and otherwise computationally intractable problems in quantum magnetism.

Related:
http://arxiv.org/abs/1204.5917

Prospects for Spin-Based Quantum Computing 

Experimental and theoretical progress toward quantum computation with spins in quantum dots (QDs) is reviewed, with particular focus on QDs formed in GaAs heterostructures, on nanowire-based QDs, and on self-assembled QDs. We report on a remarkable evolution of the field where decoherence, one of the main challenges for realizing quantum computers, no longer seems to be the stumbling block it had originally been considered. General concepts, relevant quantities, and basic requirements for spin-based quantum computing are explained; opportunities and challenges of spin-orbit interaction and nuclear spins are reviewed. We discuss recent achievements, present current theoretical proposals, and make several suggestions for further experiments.