Scott Aaronson&#x27;s answer on MO indicates it was known under &quot;suitable popular derandomization assumptions&quot; [1].<p>[1] <a href="http:&#x2F;&#x2F;mathoverflow.net&#x2F;a&#x2F;32312" rel="nofollow">http:&#x2F;&#x2F;mathoverflow.net&#x2F;a&#x2F;32312</a>