Complexity Limitations on Quantum Computation

Lance Fortnow, John Rogers
<span title="">1999</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="" style="color: black;">Journal of computer and system sciences (Print)</a> </i> &nbsp;
We use the powerful tools of counting complexity and generic oracles to help understand the limitations of the complexity of quantum computation. We show several results for the probabilistic quantum class BQP: BQP is low for PP, i.e., PP BQP =PP; There exists a relativized, world, where P=BQP and the polynomial-time hierarchy is infinite; There exists a relativized world, where BQP does not have complete sets; There exists a relativized world, where P=BQP, but P{UP & coUP and one-way functions
more &raquo; ... exist. This gives a relativized answer to an open question of Simon.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="">doi:10.1006/jcss.1999.1651</a> <a target="_blank" rel="external noopener" href="">fatcat:2pkcasoih5enzg3lvd7e2b7ayi</a> </span>
<a target="_blank" rel="noopener" href="" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href=""> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / </button> </a>