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 |
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.
The following document explains:
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:
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:
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 https://www.nicvroom.be/shor.htm
for more details.
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 https://www.nicvroom.be/shor.htm
for more details.
"Nicolaas Vroom"
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
"MorituriMax"
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.
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.
The reason why my question is important becomes clear
if you want to calculate the following:
Now suppose there is no floating point arithmatic available
but only integer arithmatic.
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.
I agree
Nicolaas Vroom
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.
A standard single processor DC does not have the capability
to perform calculations 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)
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
"Nicolaas Vroom"
Along the same line is it possible to use
unitary logic based on two entangled states.
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.
Back to my home page Contents of This Document
1 Quantum Computers and Loops
Van: "Nicolaas Vroom"
Onderwerp: Quantum Computers and Loops
Datum: dinsdag 7 oktober 2003 12:14
For i = 1 to 100
Total = Total + A(i)
Next i
IMO you can not use loops in a QC.
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
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.
Suppose you want to calculate 13/5 and your
divider uses subtraction.
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:
3 Quantum Computers and Floating Point
Van: "MorituriMax"
Onderwerp: Re: Quantum Computers and Floating Point
Datum: woensdag 15 oktober 2003 21:22
>
4 Quantum Computers and Floating Point
Van: "Nicolaas Vroom"
Onderwerp: Re: Quantum Computers and Floating Point
Datum: donderdag 16 oktober 2003 10:00
>
"Nicolaas Vroom"
> >
> >
is very complex.
>
If you want to implement floating point arithmatic this becomes
much more complex.
Using floating point the result is 0.25
Next you calculate 424 * 0.25 and the result is 106
The only way to calculate 424 * 64 / 256
is first to calculate 424 * 64 = 27136
and then 27136 / 256 = 106.
>
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
5 Quantum Computers and Parallelism
Van: "Nicolaas Vroom"
Onderwerp: Re: Quantum Computers and Parallelism
Datum: zaterdag 25 oktober 2003 20:21
Does that mean that those calculations are performed
at the same time ?
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.
IMO it is wrong to claim that those 8 states exists
in parallel (Or is this wrong ?)
5 Quantum Computers and Parallelism
Van: "Nicolaas Vroom"
Onderwerp: Re: Quantum Computers and FFT
Datum: zondag 2 november 2003 12:04
>
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.
A Hadamard operation based on 3 Qubits
results in 8 entangled states.
i.e 000, 001, 010,011,100,101,110 and 111
>
Nicolaas Vroom
See https://www.nicvroom.be/shor.htm
for more details.
Created: 26 September 2003