Amit Hagar

A recent proposal to solve the halting problem with the quantum adiabatic algorithm is criticized and found wanting. Contrary to other physical hypercomputers, where one believes that a physical process “computes” a (recursive-theoretic) non-computable function simply because one believes the physical theory that presumably governs or describes such process, believing the theory (i.e., quantum mechanics) in the case of the quantum adiabatic “hypercomputer” is tantamount to acknowledging that the hypercomputer cannot perform its task.

Among the alternatives of non-relativistic quantum mechanics (NRQM) there are those that give different predictions than quantum mechanics in yet-untested circumstances, while remaining compatible with current empirical findings. In order to test these predictions, one must isolate one’s system from environmental induced decoherence, which, on the standard view of NRQM, is the dynamical mechanism that is responsible for the ‘apparent’ collapse in open quantum systems. But while recent advances in condensed-matter physics may lead in the near future to experimental setups that will allow one to test the two hypotheses, namely genuine collapse vs. decoherence, hence make progress toward a solution to the quantum measurement problem, those philosophers and physicists who are advocating an information-theoretic approach to the foundations of quantum mechanics are still unwilling to acknowledge the empirical character of the issue at stake. Here I argue that in doing so they are displaying an unwarranted double standard. r 2007 Elsevier Ltd. All rights reserved.

Relying on the universality of quantum mechanics and on recent results known as the “threshold theorems,” quantum information scientists deem the question of the feasibility of large‐scale, fault‐tolerant, and computationally superior quantum computers as purely technological. Reconstructing this question in statistical mechanical terms, this article suggests otherwise by questioning the physical significance of the threshold theorems. The skepticism it advances is neither too strong (hence is consistent with the universality of quantum mechanics) nor too weak (hence is independent of technological contingencies). *Received June 2009; revised August 2009. †To contact the author, please write to: Department of History and Philosophy of Science, College of Arts and Sciences, Indiana University, Bloomington, IN 47405; e‐mail: [email protected].