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Fault-tolerant quantum computing based on surface code has emerged as an attractive candidate for practical large-scale quantum computers to achieve robust noise resistance. To achieve universality, magic states preparation is a commonly…

The distillation of magic states is an often-cited technique for enabling universal quantum computing once the error probability for a special subset of gates has been made negligible by other means. We present a routine for magic-state…

Quantum Physics · Physics 2012-04-20 Adam M. Meier , Bryan Eastin , Emanuel Knill

We present numerical simulation results for the 7-to-1 and 15-to-1 state distillation circuits, constructed using transversal CNOTs acting on multiple surface code patches. The distillation circuits are decoded iteratively using the method…

Quantum Physics · Physics 2026-01-28 Kwok Ho Wan

Magic state distillation plays an important role in universal fault-tolerant quantum computing, and its overhead is one of the major obstacles to realizing fault-tolerant quantum computers. Hence, many studies have been conducted to reduce…

Quantum Physics · Physics 2025-08-22 Yutaka Hirano , Tomohiro Itogawa , Keisuke Fujii

Fault-tolerant implementation of non-Clifford gates is a major challenge for achieving universal fault-tolerant quantum computing with quantum error-correcting codes. Magic state distillation is the most well-studied method for this but…

Quantum Physics · Physics 2026-01-09 Seok-Hyung Lee , Felix Thomsen , Nicholas Fazio , Benjamin J. Brown , Stephen D. Bartlett

We propose a new family of error detecting stabilizer codes with an encoding rate 1/3 that permit a transversal implementation of the pi/8-rotation $T$ on all logical qubits. The new codes are used to construct protocols for distilling…

Quantum Physics · Physics 2012-11-30 Sergey Bravyi , Jeongwan Haah

Magic state distillation is a resource intensive subroutine that consumes noisy input states to produce high-fidelity resource states that are used to perform logical operations in practical quantum-computing architectures. The resource…

Quantum Physics · Physics 2022-05-17 Shraddha Singh , Andrew S. Darmawan , Benjamin J. Brown , Shruti Puri

Magic state distillation (MSD) is an essential element for universal fault-tolerant quantum computing, which distills a high-fidelity magic state from noisy magic states using ideal (error-corrected) Clifford operations. For ideal Clifford…

Quantum Physics · Physics 2025-06-23 Tomohiro Itogawa , Yugo Takada , Yutaka Hirano , Keisuke Fujii

Despite significant overhead reductions since its first proposal, magic state distillation is often considered to be a very costly procedure that dominates the resource cost of fault-tolerant quantum computers. The goal of this work is to…

Quantum Physics · Physics 2019-12-04 Daniel Litinski

Preparing high-fidelity logical magic states is crucial for fault-tolerant quantum computation. Among prior attempts to reduce the substantial cost of magic state preparation, magic state cultivation (MSC), a recently proposed protocol for…

Quantum Physics · Physics 2025-03-25 Zi-Han Chen , Ming-Cheng Chen , Chao-Yang Lu , Jian-Wei Pan

Magic state distillation enables universal fault-tolerant quantum computation by implementing non-Clifford gates via the preparation of high-fidelity magic states. However, it comes at the cost of substantial logical-level overhead in both…

Quantum Physics · Physics 2026-05-27 Diego Ruiz , Jérémie Guillaud , Christophe Vuillot , Mazyar Mirrahimi

We present magic state factory constructions for producing $|CCZ\rangle$ states and $|T\rangle$ states. For the $|CCZ\rangle$ factory we apply the surface code lattice surgery construction techniques described by Fowler et al. to the…

Quantum Physics · Physics 2019-05-01 Craig Gidney , Austin G. Fowler

We show that using qutrits rather than qubits leads to a substantial reduction in the overhead cost associated with an approach to fault-tolerant quantum computing known as magic state distillation. We construct a family of $[[9m-k, k,…

Quantum Physics · Physics 2025-06-18 Shiroman Prakash , Tanay Saha

Magic state distillation is a key component of fault-tolerant quantum computation, as it enables the implementation of non-Clifford gates such as the $T$ gate and the $CCZ$ gate via gate teleportation. However, conventional distillation…

Quantum Physics · Physics 2026-05-22 Tomohiro Itogawa , Yutaka Hirano , Yutaro Akahoshi , Keisuke Fujii

The standard approach to fault-tolerant quantum computation is to store information in a quantum error correction code, such as the surface code, and process information using a strategy that can be summarized as distill-then-synthesize. In…

Quantum Physics · Physics 2026-05-01 Earl T. Campbell , Mark Howard

One of the leading quantum computing architectures is based on the two-dimensional (2D) surface code. This code has many advantageous properties such as a high error threshold and a planar layout of physical qubits where each physical qubit…

Quantum Physics · Physics 2019-12-06 Michael Vasmer , Dan E. Browne

Magic State Distillation is considered to be one of the promising methods for supplying the non-Clifford resources required to achieve universal fault tolerance. Conventional MSD protocols implemented in surface codes often require multiple…

Quantum Physics · Physics 2026-02-25 Shifan Xu , Kun Liu , Patrick Rall , Zhiyang He , Yongshan Ding

Magic state distillation uses special codes to suppress errors in input states, which are often tailored to a Clifford-twirled error model. We present detailed measurement sequences for magic state distillation protocols which can suppress…

Quantum Physics · Physics 2021-01-27 Jeongwan Haah , Matthew B. Hastings

Magic state distillation (MSD) is a cornerstone of fault-tolerant quantum computing, enabling non-Clifford gates via state injection into stabilizer circuits. However, the substantial overhead of current MSD protocols remains a major…

Quantum Physics · Physics 2026-05-26 Muhammad Erew , Moshe Goldstein , Yaron Oz , Haim Suchowski

Magic state distillation plays a crucial role in fault-tolerant quantum computation and represents a major bottleneck. In contrast to traditional logical-level distillation, physical-level distillation offers significant overhead reduction…

Quantum Physics · Physics 2025-10-29 Yutaka Hirano , Riki Toshio , Tomohiro Itogawa , Keisuke Fujii
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