Success-or-Draw: A Strategy Allowing Repeat-Until-Success in Quantum Computation

TL;DR

This paper introduces a novel 'success-or-draw' structure enabling repeat-until-success strategies in quantum algorithms, overcoming measurement disturbance issues, with a universal construction and optimization approach.

Contribution

It proposes a new probabilistic transformation framework called success-or-draw, allowing repeat-until-success in quantum computation, and provides a universal construction and optimization method.

Findings

Universal success-or-draw structure applicable to any probabilistic transformation.

Semidefinite programming approach for optimal success-or-draw protocols.

Detailed analysis of inverting general unitary operations.

Abstract

Repeat-until-success strategy is a standard method to obtain success with a probability which grows exponentially in the number of iterations. However, since quantum systems are disturbed after a quantum measurement, it is not straightforward how to perform repeat-until-success strategies in certain quantum algorithms. In this paper, we propose a new structure for probabilistic higher-order transformation named success-or-draw, which allows a repeat-until-success implementation. For that we provide a universal construction of success-or-draw structure which works for any probabilistic higher-order transformation on unitary operations. We then present a semidefinite programming approach to obtain optimal success-or-draw protocols and analyze in detail the problem of inverting a general unitary operation.