Optimal Fusion Strategies for Quantum Computation

arXiv (Cornell University)

Abstract

Logical fusions are important for a number of tasks in quantum information, such as quantum error correction and quantum repeaters. In the photonic setting one must contend with the fact that physical fusions can fail, i.e. individual qubits are measured in a user-controlled product state basis with some probability, which can lead to a failure on the logical level. The choice of failure basis of each qubit is known as a fusion strategy, and finding good fusion strategies is important for optimizing performance of fusion-based quantum computation. Here we provide a complete characterization when $k=1$ qubits are encoded, and in particular characterize those codes and fusion strategies such that all but one physical fusion can fail, i.e.~\emph{perfect fusion strategies}. In doing so, we recover previously known perfect fusion strategies, and find perfect fusion strategies for quantum parity-check codes, answering an open question. We furthermore show that perfect fusion strategies are generic: random $[[n, 1, d]]$ graph codes admit a perfect fusion strategy with probability exponentially close to $1$. Additionally we motivate the study of a new graph parameter, namely the maximum degree of a graph at a given vertex taken over all LC-equivalent graphs, by giving a new operationally meaningful interpretation of it.

Authors 5

1. Kenneth Goodenough

   University of Siegen

   Affiliation as printed

   Naturwissenschaftlich-Technische Fakultät , Universität Siegen , Walter-Flex-Straße 3 , 57068 Siegen , Germany

2. Andrew Landahl

   University of New Mexico · Sandia National Laboratories

   Affiliation as printed

   Microsystems Engineering, Science and Applications , Sandia National Laboratories , Albuquerque , NM , 87185 , USA

   QNM -I , Center for Quantum Information and Control , Department of Physics and Astronomy , University of New Mexico , Albuquerque , NM , 87131 , USA

3. Joon Lee Aachen

   Leiden University

   Affiliation as printed

   LIACS , Leiden University

4. Antonio Russo

   Sandia National Laboratories

   Affiliation as printed

   Center for Computing Research , Sandia National Laboratories , Albuquerque , NM , 87185 , USA

5. Kevin Thompson

   Sandia National Laboratories

   Affiliation as printed

   Center for Computing Research , Sandia National Laboratories , Albuquerque , NM , 87185 , USA