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Quantum low-density parity-check (qLDPC) codes are a promising construction for drastically reducing the overhead of fault-tolerant quantum computing (FTQC) architectures. However, all of the known hardware implementations of these codes…

In this short review, I draw attention to new developments in the theory of fault tolerance in quantum computation that may give concrete direction to future work in the development of superconducting qubit systems. The basics of quantum…

Quantum Physics · Physics 2015-05-13 David P. DiVincenzo

The stabilization of a quantum computer by repeated error correction can be reduced almost entirely to repeated preparation of blocks of qubits in quantum codeword states. These are multi-particle entangled states with a high degree of…

Quantum Physics · Physics 2007-05-23 Andrew M. Steane

Quantum computers will require encoding of quantum information to protect them from noise. Fault-tolerant quantum computing architectures illustrate how this might be done but have not yet shown a conclusive practical advantage. Here we…

Quantum Physics · Physics 2019-03-01 Robin Harper , Steven T. Flammia

Vast numbers of qubits will be needed for large-scale quantum computing due to the overheads associated with error correction. We present a scheme for low-overhead fault-tolerant quantum computation based on quantum low-density parity-check…

Quantum Physics · Physics 2022-05-24 Lawrence Z. Cohen , Isaac H. Kim , Stephen D. Bartlett , Benjamin J. Brown

Quantum error correction requires the detection of errors by reliable measurements of suitable multi-qubit correlation operators. Here, we experimentally demonstrate a fault-tolerant weight-4 parity check measurement scheme. An additional…

Quantum computers hold the promise of solving computational problems which are intractable using conventional methods. For fault-tolerant operation quantum computers must correct errors occurring due to unavoidable decoherence and limited…

Practical quantum computing will require error rates that are well below what is achievable with physical qubits. Quantum error correction offers a path to algorithmically-relevant error rates by encoding logical qubits within many physical…

Quantum Physics · Physics 2025-04-08 Rajeev Acharya , Igor Aleiner , Richard Allen , Trond I. Andersen , Markus Ansmann , Frank Arute , Kunal Arya , Abraham Asfaw , Juan Atalaya , Ryan Babbush , Dave Bacon , Joseph C. Bardin , Joao Basso , Andreas Bengtsson , Sergio Boixo , Gina Bortoli , Alexandre Bourassa , Jenna Bovaird , Leon Brill , Michael Broughton , Bob B. Buckley , David A. Buell , Tim Burger , Brian Burkett , Nicholas Bushnell , Yu Chen , Zijun Chen , Ben Chiaro , Josh Cogan , Roberto Collins , Paul Conner , William Courtney , Alexander L. Crook , Ben Curtin , Dripto M. Debroy , Alexander Del Toro Barba , Sean Demura , Andrew Dunsworth , Daniel Eppens , Catherine Erickson , Lara Faoro , Edward Farhi , Reza Fatemi , Leslie Flores Burgos , Ebrahim Forati , Austin G. Fowler , Brooks Foxen , William Giang , Craig Gidney , Dar Gilboa , Marissa Giustina , Alejandro Grajales Dau , Jonathan A. Gross , Steve Habegger , Michael C. Hamilton , Matthew P. Harrigan , Sean D. Harrington , Oscar Higgott , Jeremy Hilton , Markus Hoffmann , Sabrina Hong , Trent Huang , Ashley Huff , William J. Huggins , Lev B. Ioffe , Sergei V. Isakov , Justin Iveland , Evan Jeffrey , Zhang Jiang , Cody Jones , Pavol Juhas , Dvir Kafri , Kostyantyn Kechedzhi , Julian Kelly , Tanuj Khattar , Mostafa Khezri , Mária Kieferová , Seon Kim , Alexei Kitaev , Paul V. Klimov , Andrey R. Klots , Alexander N. Korotkov , Fedor Kostritsa , John Mark Kreikebaum , David Landhuis , Pavel Laptev , Kim-Ming Lau , Lily Laws , Joonho Lee , Kenny Lee , Brian J. Lester , Alexander Lill , Wayne Liu , Aditya Locharla , Erik Lucero , Fionn D. Malone , Jeffrey Marshall , Orion Martin , Jarrod R. McClean , Trevor Mccourt , Matt McEwen , Anthony Megrant , Bernardo Meurer Costa , Xiao Mi , Kevin C. Miao , Masoud Mohseni , Shirin Montazeri , Alexis Morvan , Emily Mount , Wojciech Mruczkiewicz , Ofer Naaman , Matthew Neeley , Charles Neill , Ani Nersisyan , Hartmut Neven , Michael Newman , Jiun How Ng , Anthony Nguyen , Murray Nguyen , Murphy Yuezhen Niu , Thomas E. O'Brien , Alex Opremcak , John Platt , Andre Petukhov , Rebecca Potter , Leonid P. Pryadko , Chris Quintana , Pedram Roushan , Nicholas C. Rubin , Negar Saei , Daniel Sank , Kannan Sankaragomathi , Kevin J. Satzinger , Henry F. Schurkus , Christopher Schuster , Michael J. Shearn , Aaron Shorter , Vladimir Shvarts , Jindra Skruzny , Vadim Smelyanskiy , W. Clarke Smith , George Sterling , Doug Strain , Marco Szalay , Alfredo Torres , Guifre Vidal , Benjamin Villalonga , Catherine Vollgraff Heidweiller , Theodore White , Cheng Xing , Z. Jamie Yao , Ping Yeh , Juhwan Yoo , Grayson Young , Adam Zalcman , Yaxing Zhang , Ningfeng Zhu

We present a native three-qubit entangling gate that exploits engineered interactions to realize control-control-target and control-target-target operations in a single coherent step. Unlike conventional decompositions into multiple…

Quantum Physics · Physics 2025-08-15 Xuexin Xu , Siyu Wang , Radhika Joshi , Rihan Hai , Mohammad H. Ansari

The surface code is one of the most promising candidates for combating errors in large scale fault-tolerant quantum computation. A fault-tolerant decoder is a vital part of the error correction process---it is the algorithm which computes…

Quantum Physics · Physics 2015-09-15 Fern H. E. Watson , Hussain Anwar , Dan E. Browne

Quantum low-density parity-check (qLDPC) codes can achieve high encoding rates and good code distance scaling, providing a promising route to low-overhead fault-tolerant quantum computing. However, the long-range connectivity required to…

In a modern error corrected quantum memory or circuit, parallelization of gate operations is severely restricted due to issues like cross-talk. Hence, there are enough idle qubits not undergoing gate operations either during the computation…

Quantum Physics · Physics 2025-02-17 Sai Sanjay Narayanan , Smita Bagewadi , Avhishek Chatterjee

Scalable and fault-tolerant quantum computation will require error correction. This will demand constant measurement of many-qubit observables, implemented using a vast number of CNOT gates. Indeed, practically all operations performed by a…

Quantum Physics · Physics 2018-10-16 Andreas Peter , Daniel Loss , James R. Wootton

Quantum error correcting codes have been developed to protect a quantum computer from decoherence due to a noisy environment. In this paper, we present two methods for optimizing the physical implementation of such error correction schemes.…

Mesoscale and Nanoscale Physics · Physics 2009-10-31 Guido Burkard , Daniel Loss , David P. DiVincenzo , John A. Smolin

Quantum error correction is widely believed to be essential for large-scale quantum computation, but the required qubit overhead remains a central challenge. Quantum low-density parity-check codes can substantially reduce this overhead…

Quantum Physics · Physics 2026-05-13 Chen Zhao , Casey Duckering , Andi Gu , Nishad Maskara , Hengyun Zhou

A key requirement for an effective Quantum Error Correction (QEC) scheme is that the physical qubits have error rates below a certain threshold. The value of this threshold depends on the details of the specific QEC scheme, and its…

Quantum Physics · Physics 2026-02-09 Gözde Üstün , Andrea Morello , Simon Devitt

A scalable and programmable quantum computer holds the potential to solve computationally intensive tasks that classical computers cannot accomplish within a reasonable time frame, achieving quantum advantage. However, the vulnerability of…

Quantum Physics · Physics 2025-03-04 Younghun Kim , Martin Sevior , Muhammad Usman

The construction of topological error correction codes requires the ability to fabricate a lattice of physical qubits embedded on a manifold with a non-trivial topology such that the quantum information is encoded in the global degrees of…

Quantum Physics · Physics 2017-10-18 James M. Auger , Hussain Anwar , Mercedes Gimeno-Segovia , Thomas M. Stace , Dan E. Browne

Quantum error correction will be a necessary component towards realizing scalable quantum computers with physical qubits. Theoretically, it is possible to perform arbitrarily long computations if the error rate is below a threshold value.…

Quantum computing holds the promise of solving classically intractable problems. Enabling this requires scalable and hardware-efficient quantum processors with vanishing error rates. This perspective manuscript describes how bosonic codes,…