Projective Measurements: Topological Quantum Computing with an Arbitrary Number of Qubits

TL;DR

This paper introduces a measurement-based approach to extend topological quantum computing to multiple qubits, enabling universal quantum gates and demonstrating high-fidelity operations with scalable architectures.

Contribution

It proposes incorporating projective measurements into topological quantum computing to achieve universality and demonstrates high-fidelity, scalable quantum operations through simulations.

Findings

Achieved over 99% fidelity in five-qubit random circuits.

Demonstrated scalability with a ten-qubit system.

Fidelity remains high under moderate disorder.

Abstract

Topological quantum computing promises intrinsic fault tolerance by encoding quantum information in non-Abelian anyons, where quantum gates are implemented via braiding. While braiding operations are robust against local perturbations, a critical yet often overlooked challenge arises when scaling beyond two qubits: the naive extension of braiding based gates fails to support even the full Clifford group. To overcome this limitation, we incorporate projective measurements that enable transitions between different qubit encodings, thus restoring computational universality. We perform many-body simulations of braiding dynamics augmented with measurement-based switching, explicitly preparing the Bell state and GHZ state for systems of two and five qubits, respectively. Furthermore, we execute a random unitary circuit on five qubits, achieving a fidelity exceeding 99%. We analyze the circuit's robustness by studying its fidelity dependence on total braid duration and static potential disorder. Our results show that the fidelity remains above 99% for moderate disorder, underscoring the intrinsic fault tolerance of the architecture. Finally, we demonstrate a random circuit on a ten qubit system to showcase the scalability of our techniques.