A 3D lattice defect and efficient computations in topological MBQC

TL;DR

This paper presents a fault-tolerant 3D cluster state approach for measurement-based quantum computation, introducing lattice defects and rebit encoding to implement gates efficiently and improve circuit performance.

Contribution

It introduces lattice defects and rebit encoding in 3D cluster states for fault-tolerant MBQC, enabling topological gate implementation and circuit optimization.

Findings

Topological implementation of Hadamard gate

Efficient phase gate via rebit encoding

Improved circuit performance and verification

Abstract

We describe an efficient, fully fault-tolerant implementation of Measurement-Based Quantum Computation (MBQC) in the 3D cluster state. The two key novelties are (i) the introduction of a lattice defect in the underlying cluster state and (ii) the use of the Rudolph-Grover rebit encoding. Concretely, (i) allows for a topological implementation of the Hadamard gate, while (ii) does the same for the phase gate. Furthermore, we develop general ideas towards circuit compaction and algorithmic circuit verification, which we implement for the Reed-Muller code used for magic state distillation. Our performance analysis highlights the overall improvements provided by the new methods.