Does Google's new quantum computer mean we will soon have a more powerful AlphaZero? According to a paper published in Nature Google has developed a quantum computer.


  Abstract
  
  The promise of quantum computers is that certain computational tasks
  might be executed exponentially faster on a quantum processor than on
  a classical processor. A fundamental challenge is to build a
  high-fidelity processor capable of running quantum algorithms in an
  exponentially large computational space. Here we report the use of a
  processor with programmable superconducting qubits to create quantum
  states on 53 qubits, corresponding to a computational state-space of
  dimension 2^53 (about 10^16). 
  
  Measurements from repeated experiments sample the resulting
  probability distribution, which we verify using classical simulations.
  Our Sycamore processor takes about 200 seconds to sample one instance
  of a quantum circuit a million times—our benchmarks currently indicate
  that the equivalent task for a state-of-the-art classical
  supercomputer would take approximately 10,000 years. This dramatic
  increase in speed compared to all known classical algorithms is an
  experimental realization of quantum supremacy for this specific
  computational task, heralding a much-anticipated computing paradigm.


On a cautionary note, Google's central claim, that they have performed in 200 seconds computation that would take current state-of-the-art supercomputers 10,000 years is disputed by IBM in a blog post which claims that:


  We argue that an ideal simulation of the same task can be performed on
  a classical system in 2.5 days and with far greater fidelity. This is
  in fact a conservative, worst-case estimate, and we expect that with
  additional refinements the classical cost of the simulation can be
  further reduced.


3 minutes 20 seconds to perform what would take 2.5 days is still pretty impressive and presumably up-scaling would produce (exponentially) better results. 

Note that quantum computing is not so well suited to linear processing, such as would typically be used to generate tablebases, but is ideally suited to highly parallel processes like those used in AlphaZero.

Does this advance mean we can look forward to a vastly improved AlphaZero?
TLDR: No

Reasoning: Quantum Computers in the short to medium term only have some very specific things efficiently (factoring and discrete log and a few others). The algorithm google showed "quantum supremecy" on is basically simulating a random quantum circuit to generate random numbers, which is


about as favorable an algorithm as you could imagine
completely useless as an algorithm since there are plenty of simpler random number generators
probably not even quantum supremecy achieved IBM paper


For general tasks, quantum computers achieve a quadratic speedup assuming a large enough quantum computer (compared to exponential or more speedup for the demonstrated problem). Furthermore, to even run a basic chess evaluation function on a quantum computer you would need at least an order of magnitude more qbits than state of the art (probably way more, but I'm hedging).

Overall, quantum computers now are at about the same stage as computers were in the 1800s. It will be a while before they are useful for anything, and chess is highly unlikely to be something they are ever used for seriously.