Magic state cultivation: growing T states as cheap as CNOT gates

TL;DR

This paper introduces a method called magic state cultivation that efficiently produces high-fidelity T states within surface code patches, potentially reducing or eliminating the need for further magic state distillation.

Contribution

It presents a novel cultivation technique that grows T states gradually, using comparable resources to a CNOT gate, and achieves lower logical error rates with fewer qubit-rounds than previous methods.

Findings

Achieves logical error rates as low as 2e-9 at certain noise levels.

Uses an order of magnitude fewer qubit-rounds than prior approaches.

Strongly responds to physical noise improvements, reducing the need for distillation.

Abstract

We refine ideas from Knill 1996, Jones 2016, Chamberland 2020, Gidney 2023+2024, Bombin 2024, and Hirano 2024 to efficiently prepare good $|T\rangle$ states. We call our construction "magic state cultivation" because it gradually grows the size and reliability of one state. Cultivation fits inside a surface code patch and uses roughly the same number of physical gates as a lattice surgery CNOT gate of equivalent reliability. We estimate the infidelity of cultivation (from injection to idling at distance 15) using a mix of state vector simulation, stabilizer simulation, error enumeration, and Monte Carlo sampling. Compared to prior work, cultivation uses an order of magnitude fewer qubit-rounds to reach logical error rates as low as $2 \cdot 10^{-9}$ when subjected to $10^{-3}$ uniform depolarizing circuit noise. Halving the circuit noise to $5 \cdot 10^{-4}$ improves the achievable logical error rate to $4 \cdot 10^{-11}$. Cultivation's efficiency and strong response to improvements in physical noise suggest that further magic state distillation may never be needed in practice.