This project on quantum computation is supported by NSF's Science, Technology, and Society program. It is also fund by the joint initiative with Mathematical and Physical Sciences Directorate: Research at the Interface of the Mathematical and Physical Sciences and Society. In quantum computation, algorithms exist that can solve problems more efficiently than any known classical algorithms. While the laws of quantum mechanics are error-free, computers (physical objects that are subject to the laws of physics) are subject to imprecision that can cause a mismatch between what they are supposed to do and what they actually do. The elimination of such errors has become a predominant goal.
A worldwide quest for the realization of a large scale computationally superior quantum computer that is fault-tolerant is currently taking place. Optimists suppose that under a certain threshold of errors, an arbitrary long fault-tolerant quantum computation can be achieved with only moderate overhead in computational cost. Pessimists object that there are fundamental (as opposed to merely technological) reasons why large scale quantum computers will never be computationally superior to classical ones no matter what innovations are introduced. Since a complete characterization of actual errors is itself an intractable task, arguments for and against the feasibility of such machines invite philosophical scrutiny.
This project aims to gain further insights for the debate by reformulating the problem within statistical mechanics. The reformulation is suggested by many similarities that exist between the foundations of statistical mechanics (particularly the debate on the origins of thermodynamic irreversibility) and the foundations of quantum mechanics (and the analogous debate on its universal applicability). On this view, rather than an active attempt to shield the quantum computer from external noise, fault-tolerant quantum computing should be portrayed as a passive attempt to prepare computationally superior quantum states that are noise-resilient. Skepticism about the feasibility of a large scale computationally superior quantum computer could then be vindicated by demonstrating how to connect the putative scarcity of such computational superior noise-resilient states with the computational cost involved in locating them.
The pedagogical component of this project aims to expose humanities students to the exciting transition in the meaning of notions such as "computation" and "complexity," which have left their cradle, mathematical logic, and have migrated into physics with the advancement of technology. The goal of this component is achieved by devising a new upper-level undergraduate course in the humanities and a corresponding compendium (that will be placed online) in which the historical and the philosophical foundations of this transition are discussed.
