Will computers ever solve chess?

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Avatar of JesusFixesAll
Chess is a game of options. I believe that there will always be a valid option for good moves. This should be true in spite of who moves first.
In nature, many animals have greater success in not moving first. They study and wait patiently. Their win is countering with a faster &/or better move.
Good question. God’s blessings friend. _Dr. G 😎
Avatar of Elroch
btickler wrote:
Elroch wrote:

Part 2: a toy example to indicate how the algorithm should work

Suppose a game has two possible positions P and Q  and two possible outcomes W and L.  We represent the position by just 1 qubit where P is true and Q is false and the outcome by a another state entangled with the position state and having three values - Undetermined, Win and Loss.

Suppose P is the initial position of the game.

So we can start with an entangled state which is a superposition of two states indicating the position P is 

PU + QU

Applying our algorithm for which positions have a result on the board we find Q is a win. The state becomes

PU + QW

Note that although this is entangled, the value conditional on the position is definite. The value conditional on position P it is U, and the value conditional on the position being Q is W.

Next we apply our algorithm that finds the legal moves in each position. It happens that there is a single legal move from P that reaches Q.  We can then update the conditional value of P to get the state:

PW + QW

As the value of the initial position is now determined, the game has been solved.

Of course most games would require repetition of the inner steps and there would be as many entangled states as there are positions, but the updates are in parallel.

That last sentence is the key, though.  If they solve the destructive read issue, then I will revise my stance... but I don't how they can...doesn't physics preclude it?  Like trying to determine where an electron is fixes it's location, observing the qubits results before the process ends kills the entire results "matrix" (I'm sure there's a different term in quantum computing circles).

I am not sure. The problem likely comes down to the no cloning theorem, so you have to be very careful how you transform the state, containing superimposed information at every stage. I tentatively hypothesise that if you can express it in a way where every step is reversible - i.e. unitary transformations - that would suffice. I have not done that above (rather assumed that it would be possible instead).

Avatar of DuskPikachu

I think the computer should always be able to find the best moves in a position by calculating all the possible responses and so on, but I think it would take a very long time for it to calculate everything.

Correct me if I have missed something though.

Avatar of Elroch

Just the content of the previous 7000+ posts.

Avatar of tygxc

#7006
Per GM Sveshnikov it takes 5 years of computer time with human input
No need to calculate all black moves: 1 is enough if it leads to a table base draw
No need to calculate all white moves: reasonable moves e.g. 4 is enough

Avatar of DiogenesDue
tygxc wrote:

#7006
Per GM Sveshnikov it takes 5 years of computer time with human input
No need to calculate all black moves: 1 is enough if it leads to a table base draw
No need to calculate all white moves: reasonable moves e.g. 4 is enough

None of these are true.  You've just decided to hitch your wagon to a dead guy that made a completely unsupported claim.

Here's the state of the thread:

Chess will not be solved in our lifetimes, nor in the foreseeable future of expected technology advances.  People can posit otherwise, but right now it's science fiction.  If they make some very big breakthroughs in quantum computing, then the long term future may change, but not the present/short term future.  Quantum computers can't even play Pong as things sit now, much less solve chess.

Avatar of tygxc

#7009
Your state is not the state of the thread.
Being dead is no reason to be wrong. Einstein, Newton... all dead.
The profession of GM Sveshnikov was to analyse chess, and in this century also the elder GM use engines to do so.
Facts and figures support the truth of his claim.
You can have a different opinion but you are the one who provides no support .

Avatar of Elroch
btickler wrote:
Elroch wrote:
btickler wrote:
Elroch wrote:

It is a different programming paradigm, but I believe in principle entirely general. One interesting property of quantum computing is reversibility: it is essential that all quantum gates are reversible for it to work.

If by different paradigm you mean like Turing's Enigma breaker, that has to crank through the entire process and either succeeds in one pass or fails, then I would agree.  But 10^44.5 is a large process to do in one shot , and it's a fundamentally iterative process evaluating backwards from mate.  You cannot "evaluate" each single position standalone, that would be like solving chess another 10^44.5 times over.  So you need to carry information states from one subprocess to another...ergo the problem for quantum computers.

I would liken it to a massive pattern of dominoes tipping over.  One shot to do it right, no stopping, and no having certain dominoes wait for others to do their tipping.  It's unidirectional in nature.  The pattern falls and then you see what you got in the end.  It's a tremendous limitation compared to traditional programming.

Edit:  ...and sure enough, as soon as I Googled "quantum computers like dominoes", I found this...

...and this.

Maybe I should be in quantum computing.  It seems like an incredibly frustrating way to program though, much like real domino pattern builders.  It's well suited to massively parallel tasks, but not iterative ones.

My starting point is the intuitive concept to deal in parallel with all of the possibilities as superpositions of states. To represent 10^44.5 positions you need over 10^50 classical bits of storage, but not necessarily more than 147 qubits (a practical representation is likely to require more than this, but less than 1000).

Then you need to add another couple of entangled qubits to represent the value of the positions. We need these qubits to be in conditionally definite states - i.e. at any time in the process, the conditional value of the value qubits given any specific position qubit representation is one of the following possibilities: "undetermined", "white win", "black win" or "draw" without any superposition.  The algorithm manipulating the entangled state will be changing these entangled values from "undetermined" to other values.

The initialisation applies an algorithm to positions that determines if it is a result (a checkmate on the board).

A key part of the algorithm is to determine the set of positions reachable by a legal move from a given position and generating the set of value bits associated with those positions. Only when the value is determined for all of these moves can the value be determined for the given position (just like for tablebase construction, but this needs to work in parallel).

So as time passes more and more of the position values (as represented in the entangled value bits) become definite. One of two things can happen. Either the initial position becomes determined, or it doesn't. 

I haven't bothered to try to address drawing rules here, thinking more of a variation of chess with all the drawing rules omitted except stalemate (a more elegant rule set, but one that permits infinite games that are only resolvable at huge depths related to the size of the equivalence classes of positions with reversible paths between them).  I am sure there are ways to add 50/75 move rules to be more relevant to normal chess (and more practical to compute).

You can't run it all in parallel, because you have to check past results as the tree expands backwards.  You can't check or pass along those results because quantum computing is a "destructive read" technology.  When you check the answer, you destroy the answer, like eating a coded message after you read it.

Either that or every single process has to calculate completely standalone and so there will be countless evaluations of the same positions that are heading toward different endstate checkmates, and each possible checkmate will have to calculate the entire tree.  That vastly increases the 10^44+ we're dealing with as the goal.

"One of two things can happen. Either the initial position becomes determined, or it doesn't."

Yes .  I believe you are agreeing with me on this point.

I have come to a different conclusion -  that the problems are practical rather than it being possible they are fundamental.

All you need (easy to say) is a reversible operators for each of the steps I illustrated and then to apply those steps to the massively superimposed state dealing with all positions repeatedly. While I only described the parts of the state that are of use, every destructive operation can be replaced by one that is reversible - it adds extra inputs and outputs to preserve enough to reconstruct the original state.

For example an NAND gate is destructive. What we want is a gate which provides NAND outputs on one line, but has other lines which make it reversible. Because NAND has output 1 for 3 different states of the inputs, this is impossible with a 2 output gate, but there is a 3 input, 3 output gate called the CCNOT or the Toffoli gate which achieves this.  This is the simplest universal, reversible quantum gate and suffices (in principle) to efficiently implement all quantum computations (including ours).

Avatar of TheUltraTrap

I think computers might solve chess at some point, not soon, but I believe chess is a draw with perfect play from both sides

Avatar of Chessflyfisher

Yes.

Avatar of Wits-end

With all the self-appointed brainiacs in this thread you’d think it would have already been accomplished. I mean no offense, but all the arguments are very subjective…. And boring. 

Avatar of IMKeto
Wits-end wrote:

With all the self-appointed brainiacs in this thread you’d think it would have already been accomplished. I mean no offense, but all the arguments are very subjective…. And boring. 

Have no fear!  The site has had a few members that claim to have solved chess, and have solved how to beat the strongest engines.  The only problem is they dont disclose their knowledge, refuse to play anyone, and...well...you get it.

Avatar of Elroch
IMBacon wrote:
Wits-end wrote:

With all the self-appointed brainiacs in this thread you’d think it would have already been accomplished. I mean no offense, but all the arguments are very subjective…. And boring. 

Have no fear!  The site has had a few members that claim to have solved chess, and have solved how to beat the strongest engines.  The only problem is they dont disclose their knowledge, refuse to play anyone, and...well...you get it.

Very poor analogy.

If anyone not participating has been following the discussion they would know that there are no quantum computers big enough to solve chess. Indeed it is an open question whether there ever will be. But we (some of us) have been discussing the question of whether such a computer could be programmed to solve chess. I have my view, but would not claim the question is undeniably answered.

Avatar of DiogenesDue
Elroch wrote:

Very poor analogy.

If anyone not participating has been following the discussion they would know that there are no quantum computers big enough to solve chess. Indeed it is an open question whether there ever will be. But we (some of us) have been discussing the question of whether such a computer could be programmed to solve chess. I have my view, but would not claim the question is undeniably answered.

Which analogy?  Pong? wink.png

That one was not supposed to be a solid analogy, just a humorous statement that illustrates that quantum computing is still in its infancy, for all the potential it has.  I've been programming since I taught myself as a kid, and I am all for quantum computing, but it's not there, even with Toblerone gates (yes, that was more humor, and yes, I knew about the gates, in fact I posted the same table of gates in another thread where Blueemu and I were trying to educate tygxc...).

The existence of the Toffoli gate should actually make my point.  Quantum computing will have to do backflips to emulate conventional programming logic and to get around limitations. 

"Here's a new kind of abacus:  it is awesome, but you need to know how to use it...you can't flip the beads back and forth with your finger, you have to throw it in the air as fast as you can several times until it lands on the ground with the right answer...yes, it will let you know when it has the right answer..."

I guess one *could* formulate even more precise analogies, but once you incorporate a double slit experiment or something then we've lost 85% of the people reading.

Avatar of tygxc

#6998
"not necessarily more than 147 qubits"
#7015
"there are no quantum computers big enough to solve chess"

Google operates a 72 qubit quantum computer at Bristlecone
https://thenextweb.com/news/google-reclaims-quantum-computer-crown-with-72-qubit-processor 
DWave is already at 5000 qubit annealing
https://www.hpcwire.com/2019/02/27/d-wave-previews-next-gen-platform-debuts-pegasus-topology-targets-5000-qubits/ 

Avatar of DiogenesDue
tygxc wrote:

#6998
"not necessarily more than 147 qubits"
#7015
"there are no quantum computers big enough to solve chess"

Google operates a 72 qubit quantum computer at Bristlecone
https://thenextweb.com/news/google-reclaims-quantum-computer-crown-with-72-qubit-processor 
DWave is already at 5000 qubit annealing
https://www.hpcwire.com/2019/02/27/d-wave-previews-next-gen-platform-debuts-pegasus-topology-targets-5000-qubits/ 

So...in your world, a preview of a plan (not even a working test model mind you) is the same as "already at 5000 qubits"?  Or maybe you aren't even reading what you post.  Hint:  it's a fluff marketing piece with no actual content or real achievement being announced of any kind.  A couple pages that all say "this company is going to do something they haven't even started yet, invest some money!"

This kind of massive overreaching is right in line with all your claims, so I guess it's not really surprising.

Avatar of tygxc

#7015
The method you describe is overambitious: an attempt to strongly solve chess, i.e. generate a 32 men table base. Weakly solving like checkers is enough and requires far less positions.
However, the 72 qubit computer of google at Bristlecone suffices to generate a 9 men or even 10 or 11 men tablebase.
First initiate all positions as U. Then seed the known 7 men table base results W/D/L. Then apply your method to generate the 8 men table base. Then use this to generate the 9 men table base.
men            positions   qubits
32               4,41E+33   112
31               9,13E+38   129
30               2,52E+42   141
29               4,98E+44   148
28               6,32E+45   152
27               1,73E+45   150
26               1,63E+44   147
25               1,18E+43   143
24               7,73E+41   139
23               4,60E+40   135
22               2,51E+39   131
21               1,26E+38   127
20               5,79E+36   122
19               2,46E+35   118
18               9,59E+33   113
17               3,45E+32   108
16               1,14E+31   103
15               3,42E+29    98
14               9,37E+27    93
13               2,32E+26    88
12               5,18E+24    82
11                1,03E+23   76
10                1,81E+21   71
9                  2,77E+19   65
8                  3,64E+17   58
7  4037164893744720  52
6      36641451949418  45
5          261516365480  38
4              1376431148  30
3                    4750192  22
2                          8064  13
Total              8,73E+45 153

Please note that 94.67% of these positions is illegal, less than 1 in a million is sensible, and are not yet compressed for symmetry by a factor 8 like syzygy.

Avatar of Elroch
btickler wrote:
Elroch wrote:

Very poor analogy.

If anyone not participating has been following the discussion they would know that there are no quantum computers big enough to solve chess. Indeed it is an open question whether there ever will be. But we (some of us) have been discussing the question of whether such a computer could be programmed to solve chess. I have my view, but would not claim the question is undeniably answered.

Which analogy?  Pong?

[snip]

Seems to be a misunderstanding. I was responding to the immediately previous post, not yours. Now edited to include quote.

Avatar of Elroch
tygxc wrote:

#6998
"not necessarily more than 147 qubits"
#7015
"there are no quantum computers big enough to solve chess"

Google operates a 72 qubit quantum computer at Bristlecone
https://thenextweb.com/news/google-reclaims-quantum-computer-crown-with-72-qubit-processor 
DWave is already at 5000 qubit annealing
https://www.hpcwire.com/2019/02/27/d-wave-previews-next-gen-platform-debuts-pegasus-topology-targets-5000-qubits/ 

Note: my understanding of the issues is at a level where you should check everything I say. happy.png

The 147 qubits was the absolute lower limit for the representation of a general chess position. It is the nature of quantum devices that the state of such a device could be the superimposition of all positions. While it is easy for me to provide such a lower limit based on simple counting (done by others) this is merely the starting point.

Unfortunately the computational power of a real quantum computer is not determined merely by the number of qubits. This is because they are not perfect: noise reduces their capabilities in a way that IBM has quantified using "quantum volume", combining the number of qubits and the noise level in a way which indicates computing power (by indicating the size of the quantum circuit that can be implemented successfully).  This is analogous to the way the capacity of a communication channel and the noise level can be combined to calculate the maximum bit rate of communication.

Here is how to measure quantum volume for real!

As I write, the largest quantum volume achieved is 1024, and I believe this means the maximum size of quantum circuit that can be implemented is a square array of 10 x 10 two qubit gates.  This is more relevant to the limits on quantum computing that the impressive qubit counts from DWave (undoubtedly with a fair amount of noise that doesn't matter so much for some applications).

UPDATE: IonQ has claimed it will achieve a quantum volume of 2^22 which (by I infer from the simpler examples) means a quantum circuit of 22 x 22 quantum gates.  However, there has been no confirmation of this - they are probably more interested in their IPO as the first publicly traded quantum computing company. Their roadmap is ambitious, aiming to get to quantum volume of 2^1024 by 2028.

How big solving chess would require is far from clear to me, but it seems highly likely it would be around that level or higher. Both in terms of the capacity for representation and the capacity for computation seem in the right ball park. I suspect there will be other higher priority tasks queued up to harness the worlds most powerful computer.

Avatar of tygxc

#7021
In 2022 IBM plans to release its 433-qubit Quantum Osprey system.