Methodology for bus layout for topological quantum error correcting codes

TL;DR

This paper presents a scalable optimization framework for designing optimal qubit layouts in 2D quantum error correction codes, using linear programming techniques tailored for practical quantum computing architectures.

Contribution

It introduces a novel linear programming-based method to optimize qubit layouts for topological quantum error correcting codes, applicable to realistic hardware constraints.

Findings

Framework successfully applied to surface and Fibonacci codes

Provides scalable solutions for qubit layout optimization

Reduces complex design problems to binary linear programs

Abstract

Most quantum computing architectures can be realized as two-dimensional lattices of qubits that interact with each other. We take transmon qubits and transmission line resonators as promising candidates for qubits and couplers; we use them as basic building elements of a quantum code. We then propose a simple framework to determine the optimal experimental layout to realize quantum codes. We show that this engineering optimization problem can be reduced to the solution of standard binary linear programs. While solving such programs is a NP-hard problem, we propose a way to find scalable optimal architectures that require solving the linear program for a restricted number of qubits and couplers. We apply our methods to two celebrated quantum codes, namely the surface code and the Fibonacci code.