Scalable and fault-tolerant preparation of encoded k-uniform states

Published

March 18, 2025

Author(s)

Shayan Majidy, Madelyn Cain, Nishad Maskara, Dominik Hangleiter, Michael Gullans

Abstract

k-uniform states are valuable resources in quantum information, enabling tasks such as teleporta- tion, error correction, and accelerated quantum simulations. However, verifying k-uniformity is as difficult as measuring code distances, and devising fault-tolerant preparation protocols adds further complexity. To address these challenges, we present a scalable, fault-tolerant method for preparing encoded k-uniform states, and we illustrate our approach using surface and color codes. We first present a technique to determine k-uniformity directly from a stabilizer tableau. We then identify a family of Clifford circuits that ensures both fault tolerance and scalability in preparing these states. Building on the encoded k-uniform states, we introduce a hybrid physical–logical strategy that retains some of the error-protection benefits of logical qubits while lowering the overhead for implementing arbitrary gates compared to fully logical algorithms. We show that this hybrid approach can outperform fully physical implementations for resource-state preparation, as demonstrated by explicit constructions of k-uniform states.

Citation

Physical Review A (Atomic, Molecular and Optical Physics)

Pub Type

Journals

Keywords

Quantum computing, quantum error correction, quantum algorithms

Citation

Majidy, S. , Cain, M. , Maskara, N. , Hangleiter, D. and Gullans, M. (2025), Scalable and fault-tolerant preparation of encoded k-uniform states, Physical Review A (Atomic, Molecular and Optical Physics) (Accessed April 25, 2025)