Subject: Your brain and quant-ph/0003084 v3
Date: Tue, 25 Mar 2003 14:48:00 +0000
From: Dimi Chakalov <dchakalov@surfeu.at>
To: a.steane1@physics.ox.ac.uk
CC: dyakonov@LPM.univ-montp2.fr

Dear Andrew,

Regarding "the nature of entanglement involving more than two parties", perhaps you may wish to see how your brain stores values in a highly qualified (and in this case totally useful) sense,

http://members.aon.at/chakalov/Vecchi.html

It can "represent and manipulate correlations directly, rather than indirectly through a manipulation of the correlated entities." We call it 'context',

http://members.aon.at/chakalov/Penrose.html#NB

It's UNspeakable and real,

http://members.aon.at/chakalov/Bassi.html#NB

http://members.aon.at/chakalov/Feedback.html#NB

and is right above your neck.

I'm curious, are EPSRC and the Research Training and Development and Human Potential Programs of the European Union aware of this possibility?

Best regards,

Dimi
--
Dimiter G. Chakalov
35 Sutherland St
London SW1V 4JU
http://members.aon.at/chakalov

====

Subject: Re: Your brain and quant-ph/0003084 v3
Date: Thu, 03 Apr 2003 19:16:31 +0300
From: Dimi Chakalov <dchakalov@surfeu.at>
To: a.steane1@physics.ox.ac.uk
CC: kak@ee.lsu.edu, dyakonov@lpm.univ-montp2.fr
 

P.S. I spotted some puzzling omissions in your recent "Quantum Computing and Error Correction", quant-ph/0304016 (please see below). It seems to me that you have completely ignored the devastating critics by many colleagues of yours, such as Subhash Kak, "Can Qubit Errors Be Corrected?"

http://xxx.lanl.gov/abs/quant-ph/0206144
http://members.aon.at/chakalov/right.html#Kak

and Michel Dyakonov, "Quantum computing: a view from the enemy camp",

http://xxx.lanl.gov/abs/cond-mat/0110326
http://members.aon.at/chakalov/right.html#Dyakonov

Moreover, your "hierarchical quantum computer" still faces the challenge of reconciling QM with STR, which is well-known since 1931 but persistently ignored by "quantum computing" community. John Bell was fully aware of these pitfalls. See

http://members.aon.at/chakalov/Frasca.html#NB

Your tutorial introduction to error correction didn't explain how one could keep the precious entangled state alive and kicking for a *finite* time interval during which you can time the sequence of events of error correction, as read by your good old wristwatch. Please take a good look at your Fig. 1 and tell me how would you position the sequence of error correction events in your reference frame, and then try to map this same sequence onto the "duration" of your entangled state,

http://members.aon.at/chakalov/Lloyd.html#2

Perhaps it would be a good idea if you report your results in Nature, as you already did on a bit different occasion.

You can read this email also at

http://members.aon.at/chakalov/Steane.html#NB

I wish you best of luck.

Dimi

--
A. M. Steane, Quantum Computing and Error Correction, Wed, 2 Apr 2003 15:02:52 GMT,
http://xxx.lanl.gov/abs/quant-ph/0304016

Comments: 12 pages, a very simple tutorial introduction to error correction, with emphasis on avoiding misconceptions regarding the treatment of noise

"The success of QEC methods in practice will depend on our having the correct understanding of noise in open quantum systems.
...

"The first quantum error correcting codes were discovered independently by Shor [4] and Steane [5]. ([5] A. M. Steane. Error correcting codes in quantum theory. Phys. Rev. Lett., 77:793-797, 1996.)
...

"Exactly what is meant by a quantum error correcting code will become apparent.
...

"As a numerical example, consider the [[127, 29, 15]] code. Let us suppose we employ this code to store a general 29-qubit state in a collection of 127 two-level atoms, and we envisage that the excited state of each atom is subject to spontaneous decay with a lifetime of 1 second. If the sequence of operations required for syndrome extraction can be completed in 1 millisecond, then the error probability per atom is of order p = 10^-3. The probability that an uncorrectable error occurs is approximately (3np)^8/8! = 10^-8. Therefore we could repeatedly correct the state for 10^5 s = 1 day before the fidelity of the stored state falls to a half, despite the fact that during such a process every one of the atoms will have decayed on average about 50,000 times!
...

"I propose that the best construction for a quantum computer is a *hierarchical* one, as illustrated in figure 2. The most important role of the parallelism and communication inside the computer is to get the syndromes out as quickly as possible, so that qubits are not left accumulating noise for too long before they are corrected."

=====

Subject: Re: Is Quantum Computation Possible?
Date: Wed, 25 Jun 2003 23:38:45 +0300
From: Dimi Chakalov <dchakalov@surfeu.at>
To: Andrew Steane <a.steane1@physics.ox.ac.uk>
CC: m.plenio@ic.ac.uk, o.rudolph@ic.ac.uk, p.knight@ic.ac.uk,
     laflamme@iqc.ca, dalvit@lanl.gov, dziarmaga@k-t.lanl.gov,
     knill@lanl.gov, barnum@lanl.gov, fizra@univ.gda.pl,
     artur.ekert@qubit.org, preskill@theory.caltech.edu,
     lkgrover@lucent.com
 

On Mon, 11 Feb 2002 14:21:04 -0000, Message-ID:
<35666012DF4CD411BE940090279FA240010099FF@
ppnt41.physics.ox.ac.uk>, Andrew Steane wrote:

[snip]

> However, the relativity of simultaneity is not an issue here,
> because all the operations at different time-steps in the error
> correction network can be arranged to be separated from one
> another in a time-like way.

During the past sixteen months, I've been trying to understand how could you separate the error correction events in a time-like way while keeping the entangled state alive and unchanged. Perhaps you tacitly imply some sort of non-perturbative continuous measurement that could "communicate" with the entangled state in a time-like way. Sounds like a miracle to me.

Again, may I ask you to look at Fig. 1 from your "Quantum Computing and Error Correction", quant-ph/0304016,

http://members.aon.at/chakalov/Steane.html#below

"Figure 1: Example of quantum error correction which illustrates the main features. A single qubit is encoded into three, and these are sent down the noisy channel. The receiver introduces further qubits (the ancilla) and uses them to extract a syndrome by applying controlled-not gates and then measuring the ancilla bits. The received state can then be corrected. Finally, the single qubit of information may be re-extracted (decoded) from the three."

Here's a time-like sequence:

t_1: A single qubit is encoded into three.

t_2: These are sent down the noisy channel.

t_3: The receiver introduces further qubits (the ancilla).

t_4: It uses them to extract a syndrome by applying controlled-not gates.

t_5: Then measures the ancilla bits.

t_6: Then the received state can be corrected.

t_7: Finally, the single qubit of information may be re-extracted (decoded) from the three.

t_8: Everybody are happy and relaxed: no errors were made during this particular error correction process.

Please write down the Hamiltonian and explain this miracle. Perhaps you may wish to consult Martin Plenio, I believe he is also eager to manipulate the entangled state locally, in line with STR.

My doubts can be read at

http://members.aon.at/chakalov/Steane.html#note

Some prerequisites at

http://members.aon.at/chakalov/Zurek.html#note

Looking forward to hearing from you,

Regards,

Dimi
http://members.aon.at/chakalov
--
Dead matter makes quantum jumps; the living-and-quantum matter is smarter.

======

Subject: Re: Is Quantum Computation Possible?
Date: Thu, 26 Jun 2003 21:11:17 +0300
From: Dimi Chakalov <dchakalov@surfeu.at>
To: Andrew Steane <a.steane1@physics.ox.ac.uk>
CC: m.plenio@ic.ac.uk, o.rudolph@ic.ac.uk, p.knight@ic.ac.uk,
     laflamme@iqc.ca, dalvit@lanl.gov, dziarmaga@k-t.lanl.gov,
     knill@lanl.gov, barnum@lanl.gov, fizra@univ.gda.pl,
     artur.ekert@qubit.org, preskill@theory.caltech.edu,
     lkgrover@lucent.com

On Thu, 26 Jun 2003 12:45:13 +0100, Andrew Steane wrote:
>
> You asked me to write down the Hamiltonian.

Yes I did. Thank you very much.

> The quantum network (figure 1) is a diagrammatic representation
> of the Hamiltonian.
> Various quantum gates are introduced as a function of time. Each
> quantum gate means a Hamiltonian to achieve the relevent rotation
> of the qubits in their Hilbert space is switched on for the time
> needed to complete the gate. Two-qubit gates involve coupling
> between separate quantum systems: this coupling can be slow
> enough to obey all the standard rules of causality and no
> faster-than-light information transfer.

If we're talking about entangled state(s), I'm afraid "slow enough" is poetry.

> The complete Hamiltonian is thus a function of time of the
> following form.
>
> Let T_tg(t) be the `top hat' function which is zero for t<tg, then 1
> for  tg <= t < tg+tau,  then zero for t > tg+tau. Here, tau is the
> duration of a gate and tg is the time the gate starts.
>
> Let C_a,b be the Hamiltonian which gives the action of the
> controlled not  gate between qubits a and b.
>
> Then
> H(t) = T_1 C_1,2 + T_2 C_1,3 + Hn + T_100 C_1,4 + T_101
> C_2,4 + T_102  C_1,5 + T_103 C_3,5
>
> where I gave the times (subscripts to T function) in units of tau,
> Hn is the Hamiltonian describing the noise,
> and in this example I assumed the channel takes up 97 time steps.
>
> I have not yet included the measurements.

This is *the* crucial point in my note at

http://members.aon.at/chakalov/Steane.html#miracle

> You can deal with those two ways.
> Either use a von-Neuman projection, in which the time taken for
> the various entangled qubits to be projected can be long enough to
> allow time-like communication if you like, or you can replace each
> measurement by a controlled-not gate to another quantum system.

I will definitely use a von-Neumann projection to get "the classical information provided by the measurement" (see below).

Replacing each measurement by a controlled-not gate to another quantum system is *not* an option. It's a mess.

> The corrective operation is either done by using the classical
> information provided by the measurement, or you could use
> quantum gates to do that as well (it would require Toffoli gate
> from bits 4 and 5 to bit 1, followed by repreparation of bits 2 and 3
> in zero state).
>
> If your worry is that this assumes the quantum logic operations are
> perfect, then we have to go to fault-tolerant methods which are
> more complicated.

NB: I worry about using a von-Neumann projection that must be (1) "slow enough to obey all the standard rules of causality" and (2) deliver the classical information instantaneously.

These two requirements form an outstanding challenge, to say the least. I have no idea how are you going to make it, Andrew.

Besides, why invent the wheel? Perhaps we have the same gadgets right above our neck.

Wishing you all the best,

Dimi
http://members.aon.at/chakalov
--
We haven't the money, so we've got to think!
Lord Rutherford, 1962 Brunel Lecture, 14 February 1962

======

Subject: quant-ph/0307062 vs. STR
Date: Wed, 09 Jul 2003 14:57:52 +0300
From: Dimi Chakalov <dchakalov@surfeu.at>
To: Marco Pravia <praviam@mit.edu>
CC: bartlett@ics.mq.edu.au, rudolpht@bell-labs.com,
     lkgrover@lucent.com, ulf@st-andrews.ac.uk,
     schmuel@informatics.bangor.ac.uk
 

Dear Dr. Pravia,

In your "Robust Control of Quantum Information", quant-ph/0307062, you and your colleagues wrote:

"The common goal is to preserve or manipulate a quantum system so that the effective evolution over a control sequence is precisely the desired process."

I'm wondering how would you cope with STR,

http://members.aon.at/chakalov/Steane.html#reply

As to NMR quantum computing, I'm curious whether you are aware of the opinion of Sam Braunstein who is the chief NAY-sayer against liquid-state NMR, see e.g.,

http://www.sees.bangor.ac.uk/~schmuel/news98/pt00.html

I will appreciate the opinion of your colleagues as well.

Regards,

Dimiter G. Chakalov
http://members.aon.at/chakalov
--
Dead matter makes quantum jumps; the living-and-quantum matter is smarter.

======

Note: The problems of error correction in "quantum computing" are not confined to 'noise reduction', as in A. Steane's quant-ph/0304016 above or in the review article by Emanuel H. Knill et al., "Introduction to Quantum Error Correction", quant-ph/0207170.

Robert Alicki <fizra@univ.gda.pl> (Institute of Theoretical Physics and Astrophysics at Gdansk, Poland) published today a very clear, down-to-earth article, entitled: "Remarks on the nature of quantum computation", quant-ph/0306103. He explained the inevitable problem of error correction, stressing that there are various types of errors, and we can not eliminate all of them. One of the cases that can not be eliminated is the compilation of errors in the final measurement of the output: the probability of correct identification of the output state for the whole register falls down exponentially (Ibid., Eq. 9). This is not an engineering obstacle. The problem is of theoretical origin.

My objection is also theoretical: look at Fig 1 in A. Steane's article, and write down the sequence of error correction events. They are uniquely ordered within a finite time interval, as read by a clock. However, to even talk about an entangled state spanned over a finite time interval, we need a theory of Lorentz-invariant nonlocality. This problem is known since 1931 and has been particularly stressed by John Bell. Sorry.

Here comes the good news: all we need is a human brain, as I tried to explain above.

Look at the definition of 'information' in Sec. 27 of E. Knill's quant-ph/0207170 of 28 July 2002: "Something that can be recorded, communicated and computed with. Information is fungible, which implies that its meaning can be identified regardless of the particulars of the physical realization. Thus, information in one realization (such as ink on a sheet of paper) can be easily transferred to another (for example, spoken words)."

What makes the information in the human brain "fungible"? We call it 'context'. It refers to a holistic state of the human brain. The fact that the human brain does not suffer from causal anomalies, closed time curves, etc., means that its holistic state obeys the laws of special relativity theory. Only we don't know how. This is what we need to understand and explore. Not "quantum computing". No need to 'invent the wheel'. It is right above our neck.

I thank Andrew Steane for his thoughtful reply. It is a great pleasure to communicate with a person who keeps an open mind and never gives up. In plain English, "If qubits spontaneously relax whenever there is a 100-way entanglement, then quantum computing will be practically impossible", said Andrew Steane on Tue, 12 Feb 2002 17:35:03 -0000. Qui vivra, verra.
 
 

Dimi Chakalov
Tuesday, June 17, 2003
Latest update: Thursday, June 26, 2003