Quantum Computers and Loops

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1 "Nicolaas Vroom" Quantum Computers and Loops dinsdag 7 oktober 2003 12:14
2 "Nicolaas Vroom" Re: Quantum Computers and Floating Point woensdag 15 oktober 2003 21:01
3 "MorituriMax" Re: Quantum Computers and Floating Point woensdag 15 oktober 2003 21:22
4 "Nicolaas Vroom" Re: Quantum Computers and Floating Point donderdag 16 oktober 2003 10:00
5 "Nicolaas Vroom" Re: Quantum Computers and Parallelism zaterdag 25 oktober 2003 20:21
6 "Nicolaas Vroom" Re: Quantum Computers and FFT zondag 2 november 2003 12:04


1 Quantum Computers and Loops

Van: "Nicolaas Vroom"
Onderwerp: Quantum Computers and Loops
Datum: dinsdag 7 oktober 2003 12:14

Question: Is it possible to use loops in a Quantum Computer using the advantages of Quantum Computers and or Quantum mechanics i.e. superposition and entanglement.

Loops are for example used in Digital Computers if you want to add an array of numbers.

   For i = 1 to 100
       Total = Total + A(i)
   Next i
IMO you can not use loops in a QC.

The following document explains:
Lecture Notes on Quantum Computation. Cornell University. Spring 2002. N. David Mermin.
http://www.ccmr.cornell.edu/~mermin/qcomp/CS483.html
Studying the examples IMO now where you can find loops. http://www.ccmr.cornell.edu/~mermin/qcomp/chap3.pdf

The reason why you cannot loops IMO is because the easiest way to implement any loop is to use synchronisation pulses.

For example if you want to perform a certain calculation which require loops:
With the first pulse you calculate the output state as a function of the input state using QC (unitary) logic.
With the second pulse you copy the output state into the input state (registers)
With the third pulse you calculate the output state as a function of the input state using QC (unitary) logic.
etc until some ending condition is reached.

The problem I see is that you loose superposition.

The solution is to implement all functionality to perform all the n loops in QC (unitary) logic such that you can perform your calculation semi instantaneous i.e. without a loop.

To give an example:
Suppose you want to calculate 13/5 and your divider uses subtraction.

In cycle 1 you subtract 13 - 5. The result = 8
In cycle 2 you subtract 8 - 5. The result = 3
In cycle 3 you subtract 3 - 5 The result = -2
Cycle 3 is too much, because the result is negative. The final result of 13/5 is the value of the previous cycle counter i.e. 2 and the rest value is 3. (13 Mod 5 = 3)

If you can not implement this calculation, by using a loop structure, because it does not support superposition than you have to implement the subtraction logic at least 3 times in hardware.

If you want to perform many divisions you can imagine that you needs lots of hardware and this approach becomes complete unpractical. specific if the numbers become larger.

Nicolaas Vroom See http://users.pandora.be/nicvroom/shor.htm for more details.

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2 Quantum Computers and Floating Point

Van: "Nicolaas Vroom"
Onderwerp: Re: Quantum Computers and Floating Point
Datum: woensdag 15 oktober 2003 21:01

> Nicolaas Vroom wrote:

Question: Is it possible to use Floating Point Logic in a QC using the advantages of Quantum Computers and or Quantum mechanics i.e. superposition and entanglement.

I have great doubts. To implement operations like ADD SUB MUL and DIV is very complex.

Floating Point Logic requires a mantissa and an exponent. See http://research.microsoft.com/~hollasch/cgindex/coding/ieeefloat.html

Nicolaas Vroom See http://users.pandora.be/nicvroom/shor.htm for more details.

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3 Quantum Computers and Floating Point

Van: "MorituriMax"
Onderwerp: Re: Quantum Computers and Floating Point
Datum: woensdag 15 oktober 2003 21:22

"Nicolaas Vroom" wrote in message news:NIhjb.79968$ZX1.4237340@phobos.telenet-ops.be...
>

Question: Is it possible to use Floating Point Logic in a QC using the advantages of Quantum Computers and or Quantum mechanics i.e. superposition and entanglement.

I have great doubts. To implement operations like ADD SUB MUL and DIV is very complex.

Don't you think the very existence of quantum computers might offset it, as the concept of creating and using quantum bits seems to me to be much more complex than ADD SUB MUL or DIV operations..

If they can implement the use of quantum mechanics in a computer, then I wouldn't put it beyond the abilities of those same people to allow the thing to perform operations much more complex than what you describe.

Thanks

next "Nicolaas Vroom" posting 4


4 Quantum Computers and Floating Point

Van: "Nicolaas Vroom"
Onderwerp: Re: Quantum Computers and Floating Point
Datum: donderdag 16 oktober 2003 10:00

"MorituriMax" schreef in bericht news:y0ijb.54168$7_1.44675@twister.austin.rr.com...
> "Nicolaas Vroom" wrote in message news:NIhjb.79968$ZX1.4237340@phobos.telenet-ops.be...
> >

Question: Is it possible to use Floating Point Logic in a QC using the advantages of Quantum Computers and or Quantum mechanics i.e. superposition and entanglement.

I have great doubts. To implement operations like ADD SUB MUL and DIV

May be I should have added: "With floating point arithmatic" to make my point more clearly.

> > is very complex.
>

Don't you think the very existence of quantum computers might offset it, as the concept of creating and using quantum bits seems to me to be much more complex than ADD SUB MUL or DIV operations..

The concept of using quantum bits if you stick to integer arithmatic with unitary logic is relative simple.
If you want to implement floating point arithmatic this becomes much more complex.

The reason why my question is important becomes clear if you want to calculate the following:

424 * 64 / 256
Suppose you want to calculate 64 / 256 first.
Using floating point the result is 0.25 Next you calculate 424 * 0.25 and the result is 106

Now suppose there is no floating point arithmatic available but only integer arithmatic.
The only way to calculate 424 * 64 / 256 is first to calculate 424 * 64 = 27136 and then 27136 / 256 = 106.

Now suppose you want to calculate 424 * 64 * 64 / (256 * 256)

My point is that the intermediate results become gargantuan which is a nuisance and a serious drawback.

> If they can implement the use of quantum mechanics in a computer, then I wouldn't put it beyond the abilities of those same people to allow the thing to perform operations much more complex than what you describe.

I agree

> Thanks

Nicolaas Vroom


5 Quantum Computers and Parallelism

Van: "Nicolaas Vroom"
Onderwerp: Re: Quantum Computers and Parallelism
Datum: zaterdag 25 oktober 2003 20:21

One of the main advantages of Quantum Computers (QC) is to perform many (millions of) calculations in parallel.

For some reading see: http://www.aps.org/apsnews/0698/069808.html http://www.cs.caltech.edu/~westside/quantum-intro.html

One question is: what is the definition of parallel.
Does that mean that those calculations are performed at the same time ?

A standard single processor DC does not have the capability to perform calculations in parallel.
Only a multi processor DC has the capability to perform calculations in parallel. An analog computer (AC) has the capability to perform computations in parallel. The reason is because an AC is built with all the necessary hardware (Integrators, summers, multipliers) to solve all the differential equations at once i.e. in parallel.

In order for an QC to operate in parallel is it enough that the QC is built with unitary logic ?

In many QC applications starting point is an input register of for example 3 QUbits. Next there is an Hadamard operation Next there is a matrix of unitary logic. The final result is stored in an output register of for example 3 QUbits.

If the Hadamard operation works on 3 QUbits than the Hadamard operation represents 8 entangled states ( 000, 001, 010, 011, 100, 101,110 and 111)
IMO it is wrong to claim that those 8 states exists in parallel (Or is this wrong ?)

If this is true than it is only correct to say that the whole matrix of unitary logic is perfomed in parallel but not the 8 possible caculations based on the 8 entangled states ? Is that correct ?

Still there is an additional CONSTRAINT. Each unitary logic operation will take some time that means the output state will only be correct based on an input state after a certain delay time. The total delay time is a function of the maximum number of unitary operations inbetween input and output. Is that correct ?

Nicolaas Vroom


5 Quantum Computers and Parallelism

Van: "Nicolaas Vroom"
Onderwerp: Re: Quantum Computers and FFT
Datum: zondag 2 november 2003 12:04

"Nicolaas Vroom" schreef in bericht wrote news:uexgb.63047$dW3.2885681@phobos.telenet-ops.be...
> Question: Is it possible to use loops in a Quantum Computer using the advantages of Quantum Computers and or Quantum mechanics i.e. superposition and entanglement.

Along the same line is it possible to use unitary logic based on two entangled states.
A Hadamard operation based on 3 Qubits results in 8 entangled states. i.e 000, 001, 010,011,100,101,110 and 111

For example is it possible to add those 8 entangled states. The result should be 28 i.e. 5 Qubits.

If it is possible than how do you test (measure ?) it ?

If it is not possible to use unitary logic based on two (or more ?) entangled states (error free ?) than FFT IMO becomes very difficult to realize.

> Nicolaas Vroom See http://users.pandora.be/nicvroom/shor.htm for more details.


Created: 26 September 2003

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