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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

Developing space- and time-efficient logical magic state preparation protocols will likely be an essential step towards building a large-scale fault-tolerant quantum computer. Motivated by this need, we introduce a scalable method for…

Quantum Physics · Physics 2026-05-26 Samyak Surti , Lucas Daguerre , Isaac H. Kim

Preparing high-fidelity logical states is a central challenge in fault-tolerant quantum computing, yet existing approaches struggle to balance control complexity against resource overhead. Here, we present a complete framework for the…

Measurement-based quantum computing (MBQC) is a promising alternative to traditional circuit-based quantum computing predicated on the construction and measurement of cluster states. Recent work has demonstrated that MBQC provides a more…

Quantum Physics · Physics 2020-07-15 Michael Newman , Leonardo Andreta de Castro , Kenneth R. Brown

Fault-tolerant quantum computation using two-dimensional topological quantum error correcting codes can benefit from multi-qubit long-range operations. By using simple commutation rules, a quantum circuit can be transpiled into a sequence…

In many architectures for fault tolerant quantum computing universality is achieved by a combination of Clifford group unitary operators and preparation of suitable nonstabilizer states, the so-called magic states. Universality is possible…

Quantum Physics · Physics 2011-06-28 Earl T. Campbell

Quantum logic gates must perform properly when operating on their standard input basis states, as well as when operating on complex superpositions of these states. Experiments using superconducting qubits have validated the truth table for…

Contemporary quantum computers have relatively high levels of noise, making it difficult to use them to perform useful calculations, even with a large number of qubits. Quantum error correction is expected to eventually enable…

Fast, reliable logical operations are essential for realizing useful quantum computers. By redundantly encoding logical qubits into many physical qubits and using syndrome measurements to detect and correct errors, one can achieve low…

Quantum error correction represents a significant advancement in large-scale quantum computing. However, achieving fault-tolerant implementations of non-Clifford logical gates with reduced overhead remains a challenge in the popular surface…

Quantum Physics · Physics 2025-07-29 Zhi-Cheng He , Zheng-Yuan Xue

As quantum devices continue to scale, distributed quantum computing emerges as a promising strategy for executing large-scale tasks across modular quantum processors. A central challenge in this paradigm is verifying the correctness of…

Fault-tolerant architectures aim to reduce the noise of a quantum computation. Despite such architectures being well studied a detailed understanding of how noise is transformed in a fault-tolerant primitive such as magic state injection is…

Quantum Physics · Physics 2025-06-25 Nicholas Fazio , Robin Harper , Stephen D. Bartlett

A promising approach to achieving scalable fault-tolerant quantum computation is the use of quantum error correction (QEC) codes augmented with magic states i.e. resource states produced via distillation, cultivation, or $R_z$ synthesis and…

Quantum Physics · Physics 2026-05-11 Aditi Awasthi , Sayam Sethi , Sahil Khan , Gokul Subramanian Ravi , Jonathan Mark Baker

Quantum computation provides great speedup over its classical counterpart for certain problems. One of the key challenges for quantum computation is to realize precise control of the quantum system in the presence of noise. Control of the…

Quantum Physics · Physics 2015-11-30 Xing Rong , Jianpei Geng , Fazhan Shi , Ying Liu , Kebiao Xu , Wenchao Ma , Fei Kong , Zhen Jiang , Yang Wu , Jiangfeng Du

A set of stabilizer operations augmented by some special initial states known as 'magic states', gives the possibility of universal fault-tolerant quantum computation. However, magic state preparation inevitably involves nonideal operations…

Various quantum applications can be reduced to estimating expectation values, which are inevitably deviated by operational and environmental errors. Although errors can be tackled by quantum error correction, the overheads are far from…

Quantum Physics · Physics 2020-02-19 Shuaining Zhang , Yao Lu , Kuan Zhang , Wentao Chen , Ying Li , Jing-Ning Zhang , Kihwan Kim

In certain approaches to quantum computing the operations between qubits are non-deterministic and likely to fail. For example, a distributed quantum processor would achieve scalability by networking together many small components;…

Quantum Physics · Physics 2013-05-29 Ying Li , Sean D. Barrett , Thomas M. Stace , Simon C. Benjamin

High-fidelity control of quantum bits is paramount for the reliable execution of quantum algorithms and for achieving fault-tolerance, the ability to correct errors faster than they occur. The central requirement for fault-tolerance is…

Topological color codes are widely acknowledged as promising candidates for fault-tolerant quantum computing. Neither a two-dimensional nor a three-dimensional topology, however, can provide a universal gate set $\{$H, T, CNOT$\}$, with the…

Quantum Physics · Physics 2024-06-26 Friederike Butt , Sascha Heußen , Manuel Rispler , Markus Müller

In this paper we study reusable magic states. These states are a special subset of the standard magic states. Once distilled, reusable magic states can be used, repeatedly, to apply some unitary U. Given this property, reusable magic states…

Quantum Physics · Physics 2012-05-24 Jonas T. Anderson