Abstract

Classical computation is modular. It exploits plug n’ play architectures which allow us to use pre-fabricated circuits without knowing their construction. This bestows advantages such as allowing parts of the computational process to be outsourced, and permitting individual circuit components to be exchanged and upgraded. Here, we introduce a formal framework to describe modularity in the quantum regime. We demonstrate a ‘no-go’ theorem, stipulating that it is not always possible to make use of quantum circuits without knowing their construction. This has significant consequences for quantum algorithms, forcing the circuit implementation of certain quantum algorithms to be rebuilt almost entirely from scratch after incremental changes in the problem—such as changing the number being factored in Shor’s algorithm. We develop a workaround capable of restoring modularity, and apply it to design a modular version of Shor’s algorithm that exhibits increased versatility and reduced complexity. In doing so we pave the way to a realistic framework whereby ‘quantum chips’ and remote servers can be invoked (or assembled) to implement various parts of a more complex quantum computation.

Highlights

  • - A software methodology for compiling quantum programs Thomas Häner, Damian S Steiger, Krysta Svore et al

  • In doing so we pave the way to a realistic framework whereby ‘quantum chips’ and remote servers can be invoked to implement various parts of a more complex quantum computation

  • By supplying different comparison functions, we may adapt such a program to sort a sequence of data by any number of different parameters

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Summary

January 2018

We apply this methodology to design two new quantum algorithms—modular DQC1 and modular factoring The former can evaluate the normalized modulus of the trace of a completely unknown physical process, and the latter can perform the full functionality of factoring with a polynomial reduction in the number of elementary gates over Shor’s algorithm. Both algorithms exhibit the full advantages of modularity—greatly reducing the extent to which their circuits need to be tailored to specific inputs. We illustrate that the diversity of conclusions about whether this is possible naturally emerges from different implicit assumptions about how the unknown unitary is physically realized

Framework
Constraints on modularity
Building modular quantum algorithms
Modularity with partial knowledge
Discussion
Full Text
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