### Current state of Quantum Computers

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Van: "Nicolaas Vroom" Onderwerp: Current state of Quantum Computers Datum: dinsdag 17 juni 2003 10:38
 1 "Nicolaas Vroom" Current state of Quantum Computers dinsdag 17 juni 2003 10:38 2 "Sam Wormley" Re: Current state of Quantum Computers dinsdag 17 juni 2003 13:58 3 "Gregory L. Hansen" Re: Current state of Quantum Computers dinsdag 17 juni 2003 16:48 4 "Laurel Amberdine" Re: Current state of Quantum Computers woensdag 18 juni 2003 1:46 5 "Nicolaas Vroom" Re: Current state of Quantum Computers woensdag 18 juni 2003 12:34 6 "Gregory L. Hansen" Re: Current state of Quantum Computers woensdag 18 juni 2003 15:43 7 "Nicolaas Vroom" Re: Current state of Quantum Computers vrijdag 20 juni 2003 10:51

### 1 Just what is quantum computation ?

Van: "Nicolaas Vroom"
Onderwerp: Current state of Quantum Computers
Datum: dinsdag 17 juni 2003 10:38

Reading about quantum logic and quantum computers I am becoming more and more convinced that building a working QC is very difficult.

First one definition:
A quantum machine is a device which consists of Qubits and Quantum Logic and which performs quantum computations. A quantum machine is only capabable to solve one problem. (Different input register values will give diff. results) You can also call this a special purpose QC. A quantum computer (QC) is like a quantum machine with the extra capability that it incorporates some form of instructions. A QC is capable to solve different problems. You can also call this a general purpose QC.

In order to be called quantum computations, qubits and quantum logic should exploit the concept of superposition and entanglement For an excellent introduction See Nature 20 Feb 2003 pages 796-797 and pages 823-826.
A separate issue is parallelisme. The first problem is what is superposition and entanglement. Accordingly to the article (Free interpretation) in Nature an array of Qubits in superposition looks very much like an array of classical oscillators each vibrating at its own frequency. In the article this behaviour is called Quantum oscillations.

In case of entanglement those classical oscillators are becomining linked or coupled and the overall behaviour becomes more erratic or unpredictable. However
1. each moment the array of Qubits is in a particular state (*)
2. not all states have the same probability
3. the sequence of states is pseudo random.

(*) It is important to remark that each qubit has three states: 1, 0 or indeterminate (going from 0 to 1 or reverse) IMO when one qubit is indeterminate the whole state of the quantum machine is indeterminate.

Point 1 is in conflict with the classical meaning of what superposition is as reflected in the sentence:
Before measuring the cat is in superposition of states of both live and dead.

One of the major benefits of quantum computions (i.e. why it will outperform classical logic) is because it performs many computations in parallel.

Consider the following example

x = p*q mod n.
On a classical machine in order to solve this problem you need an multiplier, a divider, a second multiplier and a subtractor. On a classical computer you need four instructions.

If you want to consider parallelisme than the example becomes:

x(j) = p(j)*q(j) mod n(j)
i.e. there are j sets of four variables (reg: p,q,n and x) To implement this on a clasical computer is easy.
To implement this on a quantum computer is IMO impossible. How do you take care that the quantum computer selects the right set of variables ?
The issue is synchronisation between the different registers. In a classical computer this is no problem. In a quantum machine this feature does not exist.

Of course you can claim that the reg p is in a superposition of j states (or should I say entangled) and so are the reg's: q,n and x
But how do you know that all the values of x are correct ?

This can be aggravated when a register (all input registers) is in such a short period in a certain state that there is not enough time to calculate x.

On important concept of Shor's Algorithm is periodicity in order to calculate f(x) = a^x mod n. To demonstrate this periodicity on a classical computer is easy because the variable x is each cylce incremented with one. On a quantum machine to demonstate this periodicity (physical) is difficult because the variable x is in a superposition of states and the order is pseudo random i.e. certain values of x are more likely and others are not. To increase x is IMO no solution.

In stead of periodicity you can also try to count a certain value of f(x) within a certain fixed period. The problem is that for each fixed period the number of occurences can differ making such a methode also highly unreliable.

The above objections are serious for a quantum machine. For a Quantum Computer they are worse.

Any comments ? Or is the future not so bleak as I see it ?

### 2 Just what is quantum computation ?

Van: "Sam Wormley"
Onderwerp: Re: Current state of Quantum Computers
Datum: dinsdag 17 juni 2003 13:58

Nicolaas Vroom wrote:
 > Reading about quantum logic and quantum computers I am becoming more and more convinced that building a working QC is very difficult.

A successful solid-state quantum computer will have to `entangle' quantum bits - or `qubits' - over macroscopic distances. However, entanglement in solid-state systems has only been observed on the micrometre scale so far. Now, Andrew Berkley and colleagues from the University of Maryland have entangled two solid-state superconducting qubits over a distance of 0.7 mm - a thousand times greater than ever before (A J Berkley et al. 2003 Sciencexpress 1084528 ).

### 3 Just what is quantum computation ?

Van: "Gregory L. Hansen"
Onderwerp: Re: Current state of Quantum Computers
Datum: dinsdag 17 juni 2003 16:48

In article <3EEF0243.22BC9A78@mchsi.com>, Sam Wormley wrote:
 > Nicolaas Vroom wrote:
 >> Reading about quantum logic and quantum computers I am becoming more and more convinced that building a working QC is very difficult.
 > A successful solid-state quantum computer will have to `entangle' quantum bits - or `qubits' - over macroscopic distances. However, entanglement in solid-state systems has only been observed on the micrometre scale so far. Now, Andrew Berkley and colleagues from the University of Maryland have entangled two solid-state superconducting qubits over a distance of 0.7 mm - a thousand times greater than ever before (A J Berkley et al. 2003 Sciencexpress 1084528 ).

And the only thing I can think of to do with quantum computers, once they're built, is to read encrypted mail.

-- "Is that plutonium on your gums?"
"Shut up and kiss me!"
-- Marge and Homer Simpson

### 4 Just what is quantum computation ?

Van: "Laurel Amberdine"
Onderwerp: Re: Current state of Quantum Computers
Datum: woensdag 18 juni 2003 1:46

On Tue, 17 Jun 2003 14:48:57 +0000 (UTC), Gregory L. Hansen wrote:
 > In article <3EEF0243.22BC9A78@mchsi.com>, Sam Wormley wrote:
 >> Nicolaas Vroom wrote:
 >>> Reading about quantum logic and quantum computers I am becoming more and more convinced that building a working QC is very difficult.
 >> A successful solid-state quantum computer will have to `entangle' quantum bits - or `qubits' - over macroscopic distances. However, entanglement in solid-state systems has only been observed on the micrometre scale so far. Now, Andrew Berkley and colleagues from the University of Maryland have entangled two solid-state superconducting qubits over a distance of 0.7 mm - a thousand times greater than ever before (A J Berkley et al. 2003 Sciencexpress 1084528 ).
 > And the only thing I can think of to do with quantum computers, once they're built, is to read encrypted mail.

No doubt they'll be made illegal then. (In the US.)

-Laurel

### 5 Just what is quantum computation ?

Van: "Nicolaas Vroom"
Onderwerp: Re: Current state of Quantum Computers
Datum: woensdag 18 juni 2003 12:34

"Gregory L. Hansen" schreef in bericht news:bcn9op\$650\$9@hood.uits.indiana.edu...
 > In article <3EEF0243.22BC9A78@mchsi.com>, Sam Wormley wrote:
 > > Nicolaas Vroom wrote:
 > >> Reading about quantum logic and quantum computers I am becoming more and more convinced that building a working QC is very difficult.
 > > A successful solid-state quantum computer will have to `entangle' quantum bits - or `qubits' - over macroscopic distances. However, entanglement in solid-state systems has only been observed on the micrometre scale so far. Now, Andrew Berkley and colleagues from the University of Maryland have entangled two solid-state superconducting qubits over a distance of 0.7 mm - a thousand times greater than ever before (A J Berkley et al. 2003 Sciencexpress 1084528 ).
 > And the only thing I can think of to do with quantum computers, once they're built, is to read encrypted mail.

Do you think that a quantum computer is capable to calculate:

x = p*q mod n ?
When ? When superposition is involved ? When entanglement is involved ?

It seems to me that the issue of quantum computers is more or less for 100% solved in the mathematical world and that we have taken the first hurdle out of many hurdles, (unaware of how many there are) in the physical world.

### 6 Just what is quantum computation ?

Van: "Gregory L. Hansen"
Onderwerp: Re: Current state of Quantum Computers
Datum: woensdag 18 juni 2003 15:43

In article , Nicolaas Vroom wrote:
 > "Gregory L. Hansen" schreef in bericht news:bcn9op\$650\$9@hood.uits.indiana.edu...
 >> In article <3EEF0243.22BC9A78@mchsi.com>, Sam Wormley wrote:
 >> > Nicolaas Vroom wrote:
 >> >> Reading about quantum logic and quantum computers I am becoming more and more convinced that building a working QC is very difficult.
 >> > A successful solid-state quantum computer will have to `entangle' quantum bits - or `qubits' - over macroscopic distances. However, entanglement in solid-state systems has only been observed on the micrometre scale so far. Now, Andrew Berkley and colleagues from the University of Maryland have entangled two solid-state superconducting qubits over a distance of 0.7 mm - a thousand times greater than ever before (A J Berkley et al. 2003 Sciencexpress 1084528 ).
 >> And the only thing I can think of to do with quantum computers, once they're built, is to read encrypted mail.
 > Do you think that a quantum computer is capable to calculate: x = p*q mod n ? When ? When superposition is involved ? When entanglement is involved ?

Shor's algorithm.

It's the most common practical application mentioned when writers write of quantum computing. It's pretty much the only practical application mentioned, at least that I can recall.

 > It seems to me that the issue of quantum computers is more or less for 100% solved in the mathematical world and that we have taken the first hurdle out of many hurdles, (unaware of how many there are) in the physical world.

It's an interesting technical problem, but do we really care that much about factoring numbers?

-- "Is that plutonium on your gums?"
"Shut up and kiss me!"
-- Marge and Homer Simpson

### 7 Just what is quantum computation ?

Van: "Nicolaas Vroom" Onderwerp: Re: Current state of Quantum Computers Datum: vrijdag 20 juni 2003 10:51

"Gregory L. Hansen" schreef in bericht news:bcpq9a\$oi\$1@hood.uits.indiana.edu...
 > In article , Nicolaas Vroom wrote:

 > > Do you think that a quantum computer is capable to calculate: x = p*q mod n ? When ? When superposition is involved ? When entanglement is involved ?
 > Shor's algorithm. It's the most common practical application mentioned when writers write of quantum computing. It's pretty much the only practical application mentioned, at least that I can recall.

This article explains Shor's algorithm in 11 steps. The article is in agreement with my statement mentioned below. At step 6 they write:
" Due to quantum parallelism this will take only one step" At step 8 they write: "This step is performed by the quantum computer in one step through quantum parallelism" They do not write what quantum parallelisme physical is and or how you demonstrate that quantum parallelisme is involved.

To see what is involved in step 6 go to:
https://www.nicvroom.be/shor.htm#ref3 In that example only 4+4 Qubits are involved. For a real example consisting of 100 digits the whole "matrix" becomes gargantuan. In the matrix hardware parallelisme is involved but that is not the same parallelisme as meant in the two sentences above.

Quantum parallelisme is something closely related to superposition and entanglement. Consider a register of 4 Qubits. IF the definition of entanglement (superposition) means that that register when entangled is in 16 states simultaneous than quantum parallelisme means that 16 computations are performed simultaneous However I doubt if both definitions are physical true. IMO a reg. can not be in 16 states simultaneous nor can you perform those computations simultaneous. Mathematical may be there is no problem but physical there definite is one.

All in all I have great problems with the above mentioned step 6 and step 8.

 > > It seems to me that the issue of quantum computers is more or less for 100% solved in the mathematical world and that we have taken the first hurdle out of many hurdles, (unaware of how many there are) in the physical world.
 > It's an interesting technical problem, but do we really care that much about factoring numbers?

IF you can use a quantum computer to solve ONE problem which outperforms a classical computer than that would be a big succes.

Again a big IF.

Nick

Created: 26 June 2003

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