user3405: The theory is that there are more that 10^40 positions, and a computer that works with an atomic scale has to be impossibly large(As in galaxy-scale large), and well beyond our current level of knowledge.
But now, quantum computers will soon be available. This computer can have 2^n, instead of n bytes of space, because of quantum states. With this new large place for tablebases, will chess  be solved? Of course, this will take more breakthroughs in the future, but will we see 8 piece databases in the following years?
Many questions on the possibility of solving chess revolve on the fact that we don't have enough computer space to fill them. Will quantum computers change the status quo? 

user2789: I'm not an expert on quantum computation but my understanding is that quantum computers are not expected to be useful for chess.
Quantum algorithms are very good at finding needles in haystacks: the three big quantum algorithms are Shor's factorization algorithm, Grover's database lookup algorithm and the Deutsch–Jozsa algorithm, which essentially determines whether a long list of numbers is either all zeroes, all ones or half of each.
All of these problems can be seen as examples of "I've hidden something: you must find it quickly." In factorization, I've "hidden" the prime factors and you must find them; in database lookup, I've hidden an entry with a given key in a large unsorted table and you must find it; in the problem solved by Deutsch–Jozsa, I might have placed a large number of zeroes in a table of ones but, with a classical algorithm, when you've looked at half the table and seen only ones, you might have just been unlucky and looked at the "wrong" half.  Note also that all of these problems could be solved quickly by an unrealistically parallel classical computer: you could try all the factors in parallel, look at all the database entries in parallel and look at all the values in the zero-one table in parallel.
Solving chess isn't even slightly like any of these problems. It's a fundamentally sequential activity. Whether or not my move is any good depends on what you do in response. Whether or not your response is any good depends on what I do in response to that. And so on.  You might imagine you can do the first ply of the search by taking a superposition of the possible moves.  But then what do you do at the second ply? You can't just take the superposition of all the positions we could be in after two ply because that has forgotten the tree structure. For example, consider this very artificial position, with white to move:
[FEN "1k6/ppp5/5Q2/7q/8/8/PPP5/1K6 w - - 0 2"]

If we forget the tree structure, Black is very happy. He says, "In two ply, the best position I can be in is that I deliver checkmate!"  This is true but, of course, White will never allow that, since White's best move is one that prevents Black from checkmating (or doing anything else).  Chess isn't about figuring out the best move you can possibly make in N ply: it's about figuring out the best move that your opponent will allow you to play in N ply. Quantum computers don't seem to be good at this back-and-forth, give-and-take reasoning. We don't even know how to solve chess with an unrealistically parallel classical computer.

3405: <p>The theory is that there are more that 10^40 positions, and a computer that works with an atomic scale has to be impossibly large(As in galaxy-scale large), and well beyond our current level of knowledge.</p>

<p>But now, quantum computers will soon be available. This computer can have 2^n, instead of n bytes of space, because of quantum states. With this new large place for tablebases, will chess  be solved? Of course, this will take more breakthroughs in the future, but will we see 8 piece databases in the following years?</p>

<p>Many questions on the possibility of solving chess revolve on the fact that we don't have enough computer space to fill them. Will quantum computers change the status quo? </p>
 2789: <p>I'm not an expert on quantum computation but my understanding is that quantum computers are <em>not</em> expected to be useful for chess.</p>

<p>Quantum algorithms are very good at finding needles in haystacks: the three big quantum algorithms are <a href="https://en.wikipedia.org/wiki/Shor%27s_algorithm" rel="noreferrer">Shor's factorization algorithm</a>, <a href="https://en.wikipedia.org/wiki/Grover%27s_algorithm" rel="noreferrer">Grover's database lookup algorithm</a> and the <a href="https://en.wikipedia.org/wiki/Deutsch%E2%80%93Jozsa_algorithm" rel="noreferrer">Deutsch&ndash;Jozsa algorithm</a>, which essentially determines whether a long list of numbers is either all zeroes, all ones or half of each.
All of these problems can be seen as examples of "I've hidden something: you must find it quickly." In factorization, I've "hidden" the prime factors and you must find them; in database lookup, I've hidden an entry with a given key in a large unsorted table and you must find it; in the problem solved by Deutsch&ndash;Jozsa, I might have placed a large number of zeroes in a table of ones but, with a classical algorithm, when you've looked at half the table and seen only ones, you might have just been unlucky and looked at the "wrong" half.  Note also that all of these problems could be solved quickly by an unrealistically parallel classical computer: you could try all the factors in parallel, look at all the database entries in parallel and look at all the values in the zero-one table in parallel.</p>

<p>Solving chess isn't even slightly like any of these problems. It's a fundamentally sequential activity. Whether or not my move is any good depends on what you do in response. Whether or not your response is any good depends on what I do in response to that. And so on.  You might imagine you can do the first ply of the search by taking a superposition of the possible moves.  But then what do you do at the second ply? You can't just take the superposition of all the positions we could be in after two ply because that has forgotten the tree structure. For example, consider this very artificial position, with white to move:</p>

<pre><code>[FEN "1k6/ppp5/5Q2/7q/8/8/PPP5/1K6 w - - 0 2"]
</code></pre>

<p>If we forget the tree structure, Black is very happy. He says, "In two ply, the best position I can be in is that I deliver checkmate!"  This is true but, of course, White will never allow that, since White's best move is one that prevents Black from checkmating (or doing anything else).  Chess isn't about figuring out the best move you can possibly make in N ply: it's about figuring out the best move that your opponent will allow you to play in N ply. Quantum computers don't seem to be good at this back-and-forth, give-and-take reasoning. We don't even know how to solve chess with an unrealistically parallel classical computer.</p>
