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A logical qubit is a two-dimensional subspace of a higher dimensional system, chosen such that it is possible to detect and correct the occurrence of certain errors.
A limited memory algorithm for bound constrained optimization
Richard H Byrd, Peihuang Lu, Jorge Nocedal, and Ciyou Zhu · 1995
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Derivatives of the Matrix Exponential and Their Computation
I Najfeld and T F Havel · 1995
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Arbitrary Control of a Quantum Electromagnetic Field
C K Law and J H Eberly · 1996
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Encoding a qubit in an oscillator
Daniel Gottesman, Alexei Kitaev, and John Preskill · 2001
Earlier work this paper cites.
Realization of quantum error correction
J Chiaverini, D Leibfried, T Schaetz, MD Barrett, RB Blakestad, J Britton, WM Itano, JD Jost, E Knill, C Langer, et al · 2004
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Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms
Navin Khaneja, Timo Reiss, Cindie Kehlet, Thomas Schulte-Herbrüggen, and Steffen J Glaser · 2005
Earlier work this paper cites.
Synthesizing arbitrary quantum states in a superconducting resonator
Max Hofheinz, H Wang, M Ansmann, Radoslaw C Bialczak, Erik Lucero, M Neeley, A D O’Connell, D Sank, J Wenner, John M Martinis, and Andrew N Cleland · 2009
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Second order gradient ascent pulse engineering
P de Fouquieres, SG Schirmer, SJ Glaser, and Ilya Kuprov · 2011
Earlier work this paper cites.
Scalable and Robust Randomized Benchmarking of Quantum Processes
Easwar Magesan, Jay M Gambetta, and Joseph Emerson · 2011
Earlier work this paper cites.
Optimal control methods for rapidly time-varying Hamiltonians
F Motzoi, Jay M Gambetta, S T Merkel, and F K Wilhelm · 2011
Earlier work this paper cites.
Experimental Implementation of Encoded Logical Qubit Operations in a Perfect Quantum Error Correcting Code
Jingfu Zhang, Raymond Laflamme, and Dieter Suter · 2012
Earlier work this paper cites.
Efficient Measurement of Quantum Gate Error by Interleaved Randomized Benchmarking
Easwar Magesan, Jay M Gambetta, Blake R Johnson, Colm A Ryan, Jerry M Chow, Seth T Merkel, Marcus P da Silva, George A Keefe, Mary B Rothwell, Thomas A Ohki, Mark B Ketchen, and M Steffen · 2012
Cited alongside, same era.
Deterministically Encoding Quantum Information Using 100-Photon Schrödinger Cat States
Brian Vlastakis, Gerhard Kirchmair, Zaki Leghtas, Simon E Nigg, Luigi Frunzio, Steven M Girvin, Mazyar Mirrahimi, Michel H Devoret, and Robert J Schoelkopf · 2013
Cited alongside, same era.
Observation of quantum state collapse and revival due to the single-photon kerr effect
Gerhard Kirchmair, Brian Vlastakis, Zaki Leghtas, Simon E Nigg, Hanhee Paik, Eran Ginossar, Mazyar Mirrahimi, Luigi Frunzio, Steven M Girvin, and Robert J Schoelkopf · 2013
Cited alongside, same era.
Quantum computations on a topologically encoded qubit
D Nigg, M Müller, E A Martinez, P Schindler, M Hennrich, T Monz, M A Martin-Delgado, and R Blatt · 2014
Cited alongside, same era.
Dynamically protected cat-qubits: a new paradigm for universal quantum computation
Mazyar Mirrahimi, Zaki Leghtas, Victor V Albert, Steven Touzard, Robert J Schoelkopf, Liang Jiang, and Michel H Devoret · 2014
State preservation by repetitive error detection in a superconducting quantum circuit
J Kelly, R Barends, Austin G Fowler, A Megrant, E Jeffrey, T C White, D Sank, J Y Mutus, B Campbell, Yu Chen, Z Chen, B Chiaro, A Dunsworth, I C Hoi, C Neill, P J J O’Malley, C Quintana, P Roushan, A Vainsencher, J Wenner, Andrew N Cleland, and John M Martinis · 2015
Later among the works it cites.
Detecting bit-flip errors in a logical qubit using stabilizer measurements
D Ristè, S Poletto, M Z Huang, A Bruno, V Vesterinen, O P Saira, and L DiCarlo · 2015
Later among the works it cites.
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
Later among the works it cites.
Universal control of an oscillator with dispersive coupling to a qubit
Stefan Krastanov, Victor V Albert, Chao Shen, Chang-Ling Zou, Reinier W Heeres, Brian Vlastakis, Robert J Schoelkopf, and Liang Jiang · 2015
Later among the works it cites.
Cavity State Manipulation Using Photon-Number Selective Phase Gates
Reinier W Heeres, Brian Vlastakis, Eric Holland, Stefan Krastanov, Victor V Albert, Luigi Frunzio, Liang Jiang, and Robert J Schoelkopf · 2015
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Cited alongside, same era.
Deterministic Hadamard gate for microwave cat-state qubits in circuit QED
Simon E Nigg · 2014
Cited alongside, same era.
High-fidelity spin entanglement using optimal control
Florian Dolde, Ville Bergholm, Ya Wang, Ingmar Jakobi, Boris Naydenov, Sébastien Pezzagna, Jan Meijer, Fedor Jelezko, Philipp Neumann, Thomas Schulte-Herbrüggen, Jacob Biamonte, and Jörg Wrachtrup · 2014
Cited alongside, same era.
Tracking photon jumps with repeated quantum non-demolition parity measurements
L Sun, A Petrenko, Z Leghtas, B Vlastakis, G Kirchmair, KM Sliwa, A Narla, M Hatridge, S Shankar, J Blumoff, L Frunzio, M Mirrahimi, Devoret M H, and R J Schoelkopf · 2014
Cited alongside, same era.
Adaptive Hybrid Optimal Quantum Control for Imprecisely Characterized Systems
D J Egger and F K Wilhelm · 2014
Cited alongside, same era.
Optimal Quantum Control Using Randomized Benchmarking
J Kelly, R Barends, B Campbell, Y Chen, Z Chen, B Chiaro, A Dunsworth, Austin G Fowler, I C Hoi, E Jeffrey, A Megrant, J Mutus, C Neill, P J J O’Malley, C Quintana, P Roushan, D Sank, A Vainsencher, J Wenner, T C White, Andrew N Cleland, and John M Martinis · 2014
Cited alongside, same era.
Quantum error correction for quantum memories
Barbara M Terhal · 2015
Cited alongside, same era.
Later among the works it cites.
Accurate and Robust Unitary Transformations of a High-Dimensional Quantum System
B E Anderson, H Sosa-Martinez, C A Riofrío, Ivan H Deutsch, and Poul S Jessen · 2015
Later among the works it cites.
Extending the lifetime of a quantum bit with error correction in superconducting circuits
Nissim Ofek, Andrei Petrenko, Reinier Heeres, Philip Reinhold, Zaki Leghtas, Brian Vlastakis, Yehan Liu, Luigi Frunzio, SM Girvin, Liang Jiang, M Mirrahimi, M H Devoret, and R J Schoelkopf · 2016
Closest in time.
Repeated quantum error correction on a continuously encoded qubit by real-time feedback
J Cramer, N Kalb, M A Rol, B Hensen, M S Blok, M Markham, D J Twitchen, R Hanson, and T H Taminiau · 2016
Closest in time.
New Class of Quantum Error-Correcting Codes for a Bosonic Mode
Marios H Michael, Matti Silveri, R T Brierley, Victor V Albert, Juha Salmilehto, Liang Jiang, and Steven M Girvin · 2016
Closest in time.
Quantum memory with millisecond coherence in circuit qed
Matthew Reagor, Wolfgang Pfaff, Christopher Axline, Reinier W. Heeres, Nissim Ofek, Katrina Sliwa, Eric Holland, Chen Wang, Jacob Blumoff, Kevin Chou, Michael J. Hatridge, Luigi Frunzio, Michel H. Devoret, Liang Jiang, and Robert J. Schoelkopf · 2016
Closest in time.