Implementing Logical Operators using Code Rewiring

• URL: http://arxiv.org/abs/2210.14074v2
• Date: Tue, 2 May 2023 11:05:07 GMT
• Title: Implementing Logical Operators using Code Rewiring
• Authors: Darren Banfield, Alastair Kay
• Abstract summary: We describe a method to use measurements and correction operations in order to implement the Clifford group in a stabilizer code. In particular this provides a method to implement a logical Hadamard-type gate within the 15-qubit Reed-Muller quantum code.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We describe a method to use measurements and correction operations in order to implement the Clifford group in a stabilizer code, generalising a result from [Bombin,2011] for topological subsystem colour codes. In subsystem stabilizer codes of distance at least $3$ the process can be implemented fault-tolerantly. In particular this provides a method to implement a logical Hadamard-type gate within the 15-qubit Reed-Muller quantum code by measuring and correcting only three observables. This is an alternative to the method proposed by [Paetznick and Reichardt, 2013] to generate a set of gates which is universal for quantum computing for this code. The construction is inspired by the description of code rewiring from [Colladay and Mueller, 2018].

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