Fold-transversal surface code cultivation

2025/09/05 by Kaavya Sahay, Sahay, Kaavya, Pei-Kai Tsai +11 · 5 citations
Engineering · #Advanced Surface Polishing Techniques #FOS: Physical sciences #Manufacturing Process and Optimization #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2509.05212

openalex publication_date 2025/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

Magic state cultivation is a state-of-the-art protocol to prepare ultra-high fidelity non-Clifford resource states for universal quantum computation. It offers a significant reduction in spacetime overhead compared to traditional magic state distillation techniques. Cultivation protocols involve measuring a transversal logical Clifford operator on an initial small-distance code and then rapidly growing to a larger-distance code. In this work, we present a new cultivation scheme in which we measure the fold-transversal Hadamard of the unrotated surface code, and leverage unitary techniques to grow within the surface code family. Using both stabilizer and state vector simulations we find that this approach achieves the lowest known spacetime overhead for magic state cultivation. Practical implementation of our protocol is best suited to architectures with non-local connectivity, showing the strength of architectures where such connectivity is readily available.

Citations

• Lower-depth local encoding circuits for the surface code
• Cultivating T states on the surface code with only two-qubit gates
• Leveraging erasure errors in logical qubits with metastable ¹⁷¹Yb atoms
• A Unitary Encoder for Surface Codes
• How to factor 2048 bit RSA integers with less than a million noisy qubits
• Resource Analysis of Low-Overhead Transversal Architectures for Reconfigurable Atom Arrays
• Demonstration of low-overhead quantum error correction codes
• Clifford and Non-Clifford Splitting in Quantum Circuits: Applications and ZX-Calculus Detection Procedure
• Magic State Injection with Erasure Qubits
• Efficient Magic State Cultivation on the Surface Code
• Magic state cultivation: growing T states as cheap as CNOT gates
• Efficient soft-output decoders for the surface code
• Yoked surface codes
• A Race Track Trapped-Ion Quantum Processor
• Cleaner magic states with hook injection
• Relaxing Hardware Requirements for Surface Code Circuits using Time-dynamics
• Magic state injection on the rotated surface code
• Universal quantum computation with ideal Clifford gates and noisy ancillas
• Topological quantum memory
• Quantum codes on a lattice with boundary
• Fault-tolerant quantum computation by anyons

Cited by

• Minimizing the Number of Code Switching Operations in Fault-Tolerant Quantum Circuits
• INJEQT: Improved Magic-State Injection Protocol for Fault-Tolerant Quantum Extractor Architectures
• Efficient magic state cultivation with lattice surgery
• Demonstration of a Logical Architecture Uniting Motion and In-Place Entanglement
• How to simulate magic state cultivation with around 8 Clifford terms on average

Related

• Efficient Magic State Cultivation on \mathbbRP²
• Efficient Magic State Cultivation on the Surface Code
• Cultivating T states on the surface code with only two-qubit gates
• Constant depth magic state cultivation with Clifford measurements by gauging
• Generating logical magic states with the aid of non-Abelian topological order