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In this work we introduce two code families, which we call the heavy hexagon code and heavy square code.
Triangular color codes on trivalent graphs with flag qubits
Christopher Chamberland, Aleksander Kubica, Theodore J. Yoder, and Guanyu Zhu · 1911
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Paths, trees, and flowers
Jack Edmonds · 1965
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Quantum codes on a lattice with boundary
S. B. Bravyi and A. Yu. Kitaev · 1998
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Projective plane and planar quantum codes
Michael H. Freedman and David A. Meyer · 2001
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Topological quantum memory
Eric Dennis, Alexei Kitaev, Andrew Landhal, and John Preskill · 2002
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Stabilizer formalism for operator quantum error correction
David Poulin · 2005
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Quantum Error Correcting Subsystem Codes From Two Classical Linear Codes
Dave Bacon and Andrea Casaccino · 2006
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Subsystem fault tolerance with the bacon-shor code
Panos Aliferis and Andrew W. Cross · 2007
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Demonstration of two-qubit algorithms with a superconducting quantum processor
L DiCarlo, J M Chow, J M Gambetta, Lev S Bishop, B R Johnson, D I Schuster, J Majer, A Blais, L Frunzio, S M Girvin, and R J Schoelkopf · 2009
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Fully microwave-tunable universal gates in superconducting qubits with linear couplings and fixed transition frequencies
Chad Rigetti and Michel Devoret · 2010
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Topological order with a twist: Ising anyons from an abelian model
H. Bombin · 2010
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Quantum computation with Turaev-Viro codes
Robert Koenig, Greg Kuperberg, and Ben W Reichardt · 2010
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Simple all-microwave entangling gate for fixed-frequency superconducting qubits
Jerry M. Chow, A. D. Córcoles, Jay M. Gambetta, Chad Rigetti, B. R. Johnson, John A. Smolin, J. R. Rozen, George A. Keefe, Mary B. Rothwell, Mark B. Ketchen, and M. Steffen · 2011
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Surface code quantum computing with error rates over 1
David S. Wang, Austin G. Fowler, and Lloyd C. L. Hollenberg · 2011
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Surface codes: Towards practical large-scale quantum computation
Austin G. Fowler, Matteo Mariantoni, John M. Martinis, and Andrew N. Cleland · 2012
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Proof of finite surface code threshold for matching
Austin G. Fowler · 2012
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Superconducting quantum circuits at the surface code threshold for fault tolerance
R. Barends, J. Kelly, A. Megrant, A. Veitia, D. Sank, E. Jeffrey, T. C. White, J. Mutus, A. G. Fowler, B. Campbell, et al · 2014
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Qubit architecture with high coherence and fast tunable coupling
Yu Chen, C. Neill, P. Roushan, N. Leung, M. Fang, R. Barends, J. Kelly, B. Campbell, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, A. Megrant, J. Y. Mutus, P. J. J. O’Malley, C. M. Quintana, D. Sank, A. Vainsencher, J. Wenner, T. C. White, Michael R. Geller, A. N. Cleland, and John M. Martinis · 2014
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Implementing a strand of a scalable fault-tolerant quantum computing fabric
Jerry M. Chow, Jay M. Gambetta, Easwar Magesan, David W. Abraham, Andrew W. Cross, B R Johnson, Nicholas A. Masluk, Colm A. Ryan, John A. Smolin, Srikanth J. Srinivasan, and M Steffen · 2014
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Low-distance surface codes under realistic quantum noise
Yu Tomita and Krysta M. Svore · 2014
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Quantum error correction for quantum memories
Barbara M. Terhal · 2015
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Demonstration of a quantum error detection code using a square lattice of four superconducting qubits
A. D. Córcoles, Easwar Magesan, Srikanth J. Srinivasan, Andrew W. Cross, M. Steffen, Jay M. Gambetta, and Jerry M. Chow · 2015
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Superconducting Through-Silicon Vias for Quantum Integrated Circuits
Mehrnoosh Vahidpour, William O’Brien, Jon Tyler Whyland, Joel Angeles, Jayss Marshall, Diego Scarabelli, Genya Crossman, Kamal Yadav, Yuvraj Mohan, Catvu Bui, Vijay Rawat, Russ Renzas, Nagesh Vodrahalli, Andrew Bestwick, and Chad Rigetti · 2017
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Flag fault-tolerant error correction with arbitrary distance codes
Christopher Chamberland and Michael E. Beverland · 2018
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Flag fault-tolerant error correction, measurement, and quantum computation for cyclic CSS codes
Theerapat Tansuwannont, Christopher Chamberland, and Debbie Leung · 2018
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Ben W. Reichardt · 2018
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Universal gate for fixed-frequency qubits via a tunable bus
David C. McKay, Stefan Filipp, Antonio Mezzacapo, Easwar Magesan, Jerry M. Chow, and Jay M. Gambetta · 2016
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Procedure for systematically tuning up cross-talk in the cross-resonance gate
Sarah Sheldon, Easwar Magesan, Jerry M. Chow, and Jay M. Gambetta · 2016
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Demonstration of weight-four parity measurements in the surface code architecture
Maika Takita, A. D. Córcoles, Easwar Magesan, Baleegh Abdo, Markus Brink, Andrew Cross, Jerry M. Chow, and Jay M. Gambetta · 2016
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Constructions and noise threshold of hyperbolic surface codes
N. P. Breuckmann and B. M. Terhal · 2016
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Experimental demonstration of fault-tolerant state preparation with superconducting qubits
Maika Takita, Andrew W. Cross, A. D. Córcoles, Jerry M. Chow, and Jay M. Gambetta · 2017
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Building logical qubits in a superconducting quantum computing system
Jay M. Gambetta, Jerry M. Chow, and Matthias Steffen · 2017
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The surface code with a twist
Theodore J. Yoder and Isaac H. Kim · 2017
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Easwar Magesan and Jay M. Gambetta · 2018
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IBM Q 5 Yorktown backend specification V1.1.0, https://ibm.biz/qiskit-yorktown , 2018
IBMQ · 2018
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Fault-Tolerant Quantum Computing in the Pauli or Clifford Frame with Slow Error Diagnostics
Christopher Chamberland, Pavithran Iyer, and David Poulin · 2018
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Instantaneous braids and Dehn twists in topologically ordered states
Guanyu Zhu, Ali Lavasani, and Maissam Barkeshli · 2018
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Fault-tolerant magic state preparation with flag qubits
Christopher Chamberland and Andrew W. Cross · 2019
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