Quantum Computing with black-box Subroutines

TL;DR

This paper investigates the limitations of executing unknown quantum subroutines as black boxes, revealing fundamental restrictions and proposing methods to mitigate these issues in quantum algorithms like factoring.

Contribution

It demonstrates the impossibility of executing unknown quantum subroutines and introduces a method to improve quantum factoring algorithms by reducing their complexity.

Findings

Impossible to execute unknown quantum subroutines as black boxes

Proposed method enhances quantum factoring algorithms

Reduces the complexity and input-specific tailoring needed

Abstract

Modern programming relies on our ability to treat preprogrammed functions as black boxes - we can invoke them as subroutines without knowing their physical implementation. Here we show it is generally impossible to execute an unknown quantum subroutine. This, as a special case, forbids applying black-box subroutines conditioned on an ancillary qubit. We explore how this limits many quantum algorithms - forcing their circuit implementation to be individually tailored to specific inputs and inducing failure if these inputs are not known in advance. We present a method to avoid this situation for certain computational problems. We apply this method to enhance existing quantum factoring algorithms; reducing their complexity, and the extent to which they need to be tailored to factor specific numbers. Thus, we highlight a natural property of classical information that fails in the advent of quantum logic; and simultaneously demonstrate how to mitigate its effects in practical situations.