From: Stuart Hameroff <

To: JACK SARFATTI <

Sent: Sun, July 17, 2011 9:05:04 AM

Subject: Re: topological quantum memories - mechanism for tubulin consciousness?

Dear Jack

Thanks for bringing this up. Here's the story.

In 1998 after the Royal Society meeting on

quantum computing, John Preskill gave a talk about topological

quantum error correction on an orthogonal grid. The quantum

algorithm could run along one axis, and quantum error correction

codes on the other, repeatedly intersecting and correcting any

decoherence.

I asked whether this could work on a hexagonal lattice, thinking

of the microtubule A lattice (which has Fibonacci geometry). Preskill

replied, sure, why not? Roger Penrose remarked, how interesting it

would be if the Fibonacci geometry enabled quantum error correction.

Kitaev, Preskill and others generalized the error correction to

topological quantum computing, with pathways of bits/qubits (rather

than states of individual bits/qubits) conveying information. In a 2002

paper (Conduction Pathways In Microtubules, biological quantum computation

and consciousness, Stuart Hameroff, Alex Nip, Mitchell Porter and Jack

Tuszynski,Biosystems 2002, 64(1-3):149-168, on my website under

publications, microtubule biology) we suggested that microtubules

perform topological quantum computing using the Fibonacci pathways

of tubulins as qubits. This reduces the overall information capacity

but greatly enhances resistance to decoherence.

More recemtly, Travis Craddock, Jack Tuszynski and I have looked at the

intra-tubulin pathways which could support the mesoscopic/macroscopic

conduction and found quantum channels of non-polar electron clouds in

aromatic amino acids. This was mentioned in the Google workshop talk

you cited, and in the paper by Roger and me in the forthcoming book

Consciousness and the Universe (you have a paper in it as well).

Anirban Bandyopadhyay has evidence for warm temperature resonances

which correspond with the different pathways, and people are talking

about Fibonacci anyons in topological quantum computing. (I dont know

about the fractional charge supposedly required for anyons.)

So what you have referred to as caged qubits may be caged (in the

sense they are isolated from polar environments)

quantum channels, giving mesoscopic/macroscopic quantum states the

length of microtubules.

The Berkeley quantum photosynthesis group has suggested quantum

coherence as a generalized biological feature. See

http://arxiv.org/PS_cache/arxiv/pdf/1106/1106.2911v1.pdf

The role of the pigment chromophores in the FMO complex

they see as quantum conveyors may be played by non-polar amino acid

electron clouds in microtubules, as Travis Craddock has shown, all

at biological temperature and conditions.

Quantum biology, and quantum consciousness, are heating up!

cheers

Stu

Stuart Hameroff MD

Anesthesiology, Psychology and Center for Consciousness Studies

The University of Arizona, Tucson, Arizona

www.quantumconsciousness.org

Quoting JACK SARFATTI <

> Clarifying the Tubulin bit/qubit - Defending the Penrose-Hameroff ...

>

>

> www.youtube.com/watch?v=LXFFbxoHp3s

> 46 min - Oct 28, 2010 - Uploaded by GoogleTechTalks

> Google Workshop om error n Quantum Biology Clarifying the tubulin

> bit/qubit - Defending the Penrose-Hameroff Orch OR Model of Quantum

> ...

> ?

> YouTube - Quantum Consciousness - Criticism of the Penrose ...

>

>

> www.youtube.com/watch?v=Oqz2frRRpyk

> 9 min - Jul 25, 2010 - Uploaded by PianoIsTheRemedy

> Long article with pictures on Hameroff's Tubulin Theory:

> http://rds.yahoo.com/ _ylt=A0oG7_o6PU5MfWQBDblXNyoA;_ylu ...

> More videos for hameroff tubulin »

> [PDF] Penrose-Hameroff Quantum Tubulin Electrons, Chiao Gravity Antennas ...

> www.valdostamuseum.org/hamsmith/QMINDpaper.pdf

> File Format: PDF/Adobe Acrobat - Quick View

> analogous to tubulin caged electrons. Tegmark has criticized

> Penrose-Hameroff quantum consciousness, based on thermal decoherence

> of any such quantum ...

> Bringing Order through Disorder: Localization of Errors in

> Topological Quantum Memories

> James R. Wootton and Jiannis K. Pachos

> School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT,

> United Kingdom

> (Received 1 March 2011; published 14 July 2011)

>

> Anderson localization emerges in quantum systems when randomized

> parameters cause the exponential suppression of motion. Here we

> consider this phenomenon in topological models and establish its

> usefulness for protecting topologically encoded quantum information.

> For concreteness we employ the toric code. It is known that in the

> absence of a magnetic field this can tolerate a finite initial

> density of anyonic errors, but in the presence of a field anyonic

> quantum walks are induced and the tolerable density becomes zero.

> However, if the disorder inherent in the code is taken into account,

> we demonstrate that the induced localization allows the topological

> quantum memory to regain a finite critical anyon density and the

> memory to remain stable for arbitrarily long times. We anticipate

> that disorder inherent in any physical realization of topological

> systems will help to strengthen the fault tolerance of quantum

> memories.

>

> Topological quantum memories are many-body interacting systems that

> can serve as error-correcting codes [1]. These models possess

> degenerate ground state manifolds in which quantum information may be

> encoded. The size of the model and its energy gap then protect this

> information, preventing local perturbations from splitting the

> degeneracy and hence causing errors [2?5]. However, the dynamic

> effects of perturbations when excitations are present are a serious

> problem for the stability of the memory [6], especially for nonzero

> temperature [7]. Several promising schemes have been proposed [8,9]

> that suggest ways to combat this problem with their own merits and

> drawbacks. In particular, in Ref. [9] it is shown that disorder can

> aid the stability of topological phases. Here we shed new light on

> the issue by showing that disorder in topological memories can induce

> Anderson localization [10]. This exponentially suppresses the dynamic

> effects of perturbations on exited states and allows the memory to

> remain stable.

>

> In the definition of a topological memory, we require the following

> conditions. First, the stored information is encoded within a

> degenerate ground state of a system. Second, we require that the

> memory can be left exposed to some assumed noise model for

> arbitrarily long times without active monitoring or manipulations.

> Finally, measurement of the system after errors have occurred

> extracts both the (now noisy) contents of the memory and an error

> syndrome, allowing a one-off error correction step to be performed to

> retrieve the original stored information.

>

> In topological memories, errors create anyonic excitations. Logical

> errors correspond to the propagation of these anyons around

> topologically nontrivial paths on the surface of the system. While

> the anyons are normally static, a kinetic term emerges in the

> presence of a spurious magnetic field [6]. If this can act unchecked,

> even a single pair of anyons will cause a logical error after a time

> linear with the system size L. This means that the memory is not

> resilient against any nonzero density of anyons initially present in

> the system. We demonstrate that randomness in the couplings of the

> code causes anyons to remain well localized in their initial

> positions. This enables the topological memory to successfully store

> quantum information for arbitrarily long times as long as the

> distribution of anyons is below a critical value. Hence, topological

> quantum memories can be made fault-tolerant against the dynamical

> effects of local perturbations.

>

>

>

> Since disorder will be inherent in any experimental realization of

> topological systems, e.g., with Josephson junctions [14], the effect

> described here is expected to play a significant role in their

> behavior. Localization will also protect against Hamiltonian pertur-

> bations in other topological models, including those of non-Abelian

> anyons. The prospect of purposefully engi- neering disorder into

> topological systems to benefit from further localization effects, for

> both coherent and incoher- ent errors, is a subject of continuing

> study.

Leeds, Leeds LS2 9JT,

> United Kingdom

> (Received 1 March 2011; published 14 July 2011)

>

> Anderson localization emerges in quantum systems when randomized

> parameters cause the exponential suppression of motion. Here we

> consider this phenomenon in topological models and establish its

> usefulness for protecting topologically encoded quantum information.

> For concreteness we employ the toric code. It is known that in the

> absence of a magnetic field this can tolerate a finite initial

> density of anyonic errors, but in the presence of a field anyonic

> quantum walks are induced and the tolerable density becomes zero.

> However, if the disorder inherent in the code is taken into account,

> we demonstrate that the induced localization allows the topological

> quantum memory to regain a finite critical anyon density and the

> memory to remain stable for arbitrarily long times. We anticipate

> that disorder inherent in any physical realization of topological

> systems will help to strengthen the fault tolerance of quantum

> memories.

>

> Topological quantum memories are many-body interacting systems that

> can serve as error-correcting codes [1]. These models possess

> degenerate ground state manifolds in which quantum information may be

> encoded. The size of the model and its energy gap then protect this

> information, preventing local perturbations from splitting the

> degeneracy and hence causing errors [2?5]. However, the dynamic

> effects of perturbations when excitations are present are a serious

> problem for the stability of the memory [6], especially for nonzero

> temperature [7]. Several promising schemes have been proposed [8,9]

> that suggest ways to combat this problem with their own merits and

> drawbacks. In particular, in Ref. [9] it is shown that disorder can

> aid the stability of topological phases. Here we shed new light on

> the issue by showing that disorder in topological memories can induce

> Anderson localization [10]. This exponentially suppresses the dynamic

> effects of perturbations on exited states and allows the memory to

> remain stable.

>

> In the definition of a topological memory, we require the following

> conditions. First, the stored information is encoded within a

> degenerate ground state of a system. Second, we require that the

> memory can be left exposed to some assumed noise model for

> arbitrarily long times without active monitoring or manipulations.

> Finally, measurement of the system after errors have occurred

> extracts both the (now noisy) contents of the memory and an error

> syndrome, allowing a one-off error correction step to be performed to

> retrieve the original stored information.

>

> In topological memories, errors create anyonic excitations. Logical

> errors correspond to the propagation of these anyons around

> topologically nontrivial paths on the surface of the system. While

> the anyons are normally static, a kinetic term emerges in the

> presence of a spurious magnetic field [6]. If this can act unchecked,

> even a single pair of anyons will cause a logical error after a time

> linear with the system size L. This means that the memory is not

> resilient against any nonzero density of anyons initially present in

> the system. We demonstrate that randomness in the couplings of the

> code causes anyons to remain well localized in their initial

> positions. This enables the topological memory to successfully store

> quantum information for arbitrarily long times as long as the

> distribution of anyons is below a critical value. Hence, topological

> quantum memories can be made fault-tolerant against the dynamical

> effects of local perturbations.

>

>

>

> Since disorder will be inherent in any experimental realization of

> topological systems, e.g., with Josephson junctions [14], the effect

> described here is expected to play a significant role in their

> behavior. Localization will also protect against Hamiltonian pertur-

> bations in other topological models, including those of non-Abelian

> anyons. The prospect of purposefully engi- neering disorder into

> topological systems to benefit from further localization effects, for

> both coherent and incoher- ent errors, is a subject of continuing

> study.