That is not how PCB autorouters work - at least, not any autorouter that expects to route more than a couple of tracks in the lifetime of the designer.
However, it is not far off the way quantum computers work, because they try all combinations simultaneously.
Practical quantum computers have to have a lot of error correction in order to overcome the effects of decoherence. My late colleague Roger Koch was really big on quantum ECC.
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC Optics, Electro-optics, Photonics, Analog Electronics 160 North State Road #203 Briarcliff Manor NY 10510 hobbs at electrooptical dot net http://electrooptical.net
Yes, quite!
That was my thought - can they be used to find not just *a* solution, but the One True exact best "global optimum" in a design problem.
-- John Devereux
On 01/09/2015 16:13, Rob wrote: > Martin Brown wrote: >> On 31/08/2015 22:49, Syd Rumpo wrote: >>> On 31/08/2015 20:35, Phil Hobbs wrote: >>> >>> >>> >>>> If the interactions between qubits are small, a single quantum state of >>>> the whole system is the product of states of the individual qubits. >>>> (This is just separation of variables as in elementary PDEs.) >>> >>> What form does this product take? >> >> The solution wavefunction ends up in the register you read back. > > What I think is a much more interesting question: how do you program > a quantum computer? How does it store its instructions, and how are > they sequenced?
I think the short answer is for now they build whatever they can make (or simulate) and then play with it to develop algorithms, determine their speed for quantum vs classical and proofs of correctness.
I think at the moment just getting one to cohere for long enough to study it on nearly trivial computations is near state of the art (in the open literature). I am still trying to find the material I found about a decade ago but in the meantime for those with a mathematical bent the best introduction I have found so far is at:
Increment 01_ to 02_ etc in the obvious way. Enjoy!
-- Regards, Martin Brown
You would hope that over the allowed range of parameters they should find a global optimum but the algorithms published so far claim only to be approximate optimal solutions (at least so far as I can see).
NIST maintains a list of the algorithms developed so far:
And approximate optimisation is amongst them.
Isn't that what the D-wave kit is supposed to do? Although there is still a lot of controversy about whether or not it is truly a quantum machine implementation.
-- Regards, Martin Brown
As long as you maintain coherence across the whole system, then you will be able to get an optimal solution. For many quantum algorithms, this is absolutely necessary - after all, /approximately/ factoring an integer is not going to be very helpful!
D-Wave machines are not "traditional" quantum machines. They exploit some quantum behaviour - but arguably so do conventional computers in the way their semiconductor gates work. In particular, in D-Wave's systems the qubits are not all interconnected - they have a certain influence with their neighbours that reduces over distance. This lets them get a lot more bits that stay stable for a lot longer than "true" quantum computers, but it also means that they don't calculate over the whole range of states, and will at best find a reasonable approximate answer rather than an optimal answer.
Hi,
The simplest quantum system has two states per qubit:
If logic is still used in the quantum computer system, this is equivalent to going from a one dimensional logic ie normal binary or trinary logic, to a 2 dimensional logic for a two state quantum system.
In one dimensional logic, the number of logic levels can go from binary, trinary, all the way up to analog computing, it is the same for a two state "quantum" computing system, the logic levels can also be discretized at binary, trinary etc (optionally independently per state) or be used up to analog per state.
If binary logic is used in a two state quantum system, then on the quantum 2 state "Bloch sphere" (shows the values of each of the two states in a qbit), a quantum 2 state Not gate for example should just return the X and Y values describing a point on the Bloch sphere that is furthest away from the X and Y values of the input qbit to the quantum 2 state Not gate.
For a quantum 2 state And gate with two qbit inputs (two states each), the output of the And gate should be the correlation between the two inputs for each of the 2 state inputs, ie.
X1Y1 AND X2Y2 = X3Y3 Where X3Y3 = (correlation between X1 and X2)(correlation between Y1 and Y2)
That is one way possibly to make a quantum And gate I think.
The important part is that quantum systems are just a specific implementation of 2 state or higher logic, where each variable has 2 states (or more) ie the Bloch sphere for a 2 state qbit, and the superpositions of 2 state logic give a lot more computing power than the superpositions of one state logic, ie one state binary or trinary.
The implementation details of practically making a quantum computer (what you were asking I think) is the hard part I guess! :)
cheers, Jamie
Hi,
I think each of the two input variables that will be added together can be stored in a single two state qbit, with each state quantized to at least 10 levels in your example. The qbit can feed into an accumulator to do the addition, which could be just half of a two state qbit that has a higher quantization ie 2^10 levels could accumulate to 1024. This is just theory I don't know how practically it could be done but might involve some duct tape.
cheers, Jamie
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