The Experts below are selected from a list of 50331 Experts worldwide ranked by ideXlab platform
Christopher Chamberland - One of the best experts on this subject based on the ideXlab platform.
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fault tolerant bosonic Quantum Error correction with the surface gottesman kitaev preskill code
Physical Review A, 2020Co-Authors: Kyungjoo Noh, Christopher ChamberlandAbstract:The performance of the circuit-based surface-GKP bosonic Quantum Error correction code under noise due to finite squeezing of the GKP states and photon losses is investigated. The authors show under what conditions fault-tolerant Quantum Error correction is possible with the surface-GKP code.
Raymond Laflamme - One of the best experts on this subject based on the ideXlab platform.
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Quantum Error correction decoheres noise
Physical Review Letters, 2018Co-Authors: Stefanie Beale, Raymond Laflamme, Kenneth R Brown, Joel J Wallman, Mauricio GutierrezAbstract:Typical studies of Quantum Error correction assume probabilistic Pauli noise, largely because it is relatively easy to analyze and simulate. Consequently, the effective logical noise due to physically realistic coherent Errors is relatively unknown. Here, we prove that encoding a system in a stabilizer code and measuring Error syndromes decoheres Errors, that is, causes coherent Errors to converge toward probabilistic Pauli Errors, even when no recovery operations are applied. Two practical consequences are that the Error rate in a logical circuit is well quantified by the average gate fidelity at the logical level and that essentially optimal recovery operators can be determined by independently optimizing the logical fidelity of the effective noise per syndrome.
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Experimental Quantum Error Correction
Physical Review Letters, 1998Co-Authors: David G. Cory, Emanuel Knill, Raymond Laflamme, Wojciech H. Zurek, Mark D. Price, W. Maas, Timothy F. Havel, Shyamal SomarooAbstract:Quantum Error correction is required to compensate for the fragility of the state of a Quantum computer. We report the first experimental implementations of Quantum Error correction and confirm the expected state stabilization. A precise analysis of the decay behavior is performed in alanine and a full implementation of the Error correction procedure is realized in trichloroethylene. In NMR computing, however, a net improvement in the signal to noise would require very high polarization. The experiment implemented the three-bit code for phase Errors using liquid state NMR.
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theory of Quantum Error correcting codes
Physical Review A, 1997Co-Authors: Emanuel Knill, Raymond LaflammeAbstract:Quantum Error correction will be necessary for preserving coherent states against noise and other unwanted interactions in Quantum computation and communication. We develop a general theory of Quantum Error correction based on encoding states into larger Hilbert spaces subject to known interactions. We obtain necessary and sufficient conditions for the perfect recovery of an encoded state after its degradation by an interaction. The conditions depend only on the behavior of the logical states. We use them to give a recovery-operator-independent definition of Error-correcting codes. We relate this definition to four others: the existence of a left inverse of the interaction, an explicit representation of the Error syndrome using tensor products, perfect recovery of the completely entangled state, and an information theoretic identity. Two notions of fidelity and Error for imperfect recovery are introduced, one for pure and the other for entangled states. The latter is more appropriate when using codes in a Quantum memory or in applications of Quantum teleportation to communication. We show that the Error for entangled states is bounded linearly by the Error for pure states. A formal definition of independent interactions for qubits is given. This leads to lower bounds on the number of qubits required to correct e Errors and a formal proof that the classical bounds on the probability of Error of e-Error-correcting codes applies to e-Error-correcting Quantum codes, provided that the interaction is dominated by an identity component.
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perfect Quantum Error correcting code
Physical Review Letters, 1996Co-Authors: Raymond Laflamme, Cesar Miquel, Juan Pablo Paz, Wojciech H. ZurekAbstract:We present a Quantum Error correction code which protects a qubit of information against general one qubit Errors. To accomplish this, we encode the original state by distributing Quantum information over five qubits, the minimal number required for this task. We describe a circuit which takes the initial state with four extra qubits in the state {vert_bar}0{r_angle} to the encoded state. It can also be converted into a decoder by running it backward. The original state of the encoded qubit can then be restored by a simple unitary transformation. {copyright} {ital 1996 The American Physical Society.}
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perfect Quantum Error correcting code
Physical Review Letters, 1996Co-Authors: Raymond Laflamme, Cesar Miquel, Juan Pablo Paz, Wojciech H. ZurekAbstract:We present a Quantum Error correction code which protects a qubit of information against general one qubit Errors. To accomplish this, we encode the original state by distributing Quantum information over five qubits, the minimal number required for this task. We describe a circuit which takes the initial state with four extra qubits in the state $|0〉$ to the encoded state. It can also be converted into a decoder by running it backward. The original state of the encoded qubit can then be restored by a simple unitary transformation.
Kyungjoo Noh - One of the best experts on this subject based on the ideXlab platform.
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fault tolerant bosonic Quantum Error correction with the surface gottesman kitaev preskill code
Physical Review A, 2020Co-Authors: Kyungjoo Noh, Christopher ChamberlandAbstract:The performance of the circuit-based surface-GKP bosonic Quantum Error correction code under noise due to finite squeezing of the GKP states and photon losses is investigated. The authors show under what conditions fault-tolerant Quantum Error correction is possible with the surface-GKP code.
Yaakov S. Weinstein - One of the best experts on this subject based on the ideXlab platform.
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syndrome measurement order for the 7 1 3 Quantum Error correction code
arXiv: Quantum Physics, 2013Co-Authors: Yaakov S. WeinsteinAbstract:In this work we explore the accuracy of Quantum Error correction depending of the order of the implemented syndrome measurements. CSS codes require bit-flip and phase flip-syndromes be measured separately. To comply with fault tolerant demands and to maximize accuracy this set of syndrome measurements should be repeated allowing for flexibility in the order of their implementation. We examine different possible orders of Shor state and Steane state syndrome measurements for the [[7,1,3]] Quantum Error correction code. We find that the best choice of syndrome order, determined by the fidelity of the state after noisy Error correction, will depend on the Error environment. We also compare the fidelity when syndrome measurements are done with Shor states versus Steane states and find that Steane states generally, but not always, lead to final states with higher fidelity. Together, these results allow a Quantum computer programmer to choose the optimal syndrome measurement scheme based on the system's Error environment.
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Encoding an arbitrary state in a [7,1,3] Quantum Error correction code
Quantum Information Processing, 2013Co-Authors: Sidney D. Buchbinder, Channing L. Huang, Yaakov S. WeinsteinAbstract:We calculate the fidelity with which an arbitrary state can be encoded into a [7, 1, 3] Calderbank-Shor-Steane Quantum Error correction code in a non-equiprobable Pauli operator Error environment with the goal of determining whether this encoding can be used for practical implementations of Quantum computation. The determination of usability is accomplished by applying ideal Error correction to the encoded state which demonstrates the correctability of Errors that occurred during the encoding process. We also apply single-qubit Clifford gates to the encoded state and determine the accuracy with which these gates can be implemented. Finally, fault tolerant noisy Error correction is applied to the encoded states allowing us to compare noisy (realistic) and perfect Error correction implementations. We find the encoding to be usable for the states $${|0\rangle, |1\rangle}$$ , and $${|\pm\rangle = |0\rangle\pm|1\rangle}$$ . These results have implications for when non-fault tolerant procedures may be used in practical Quantum computation and whether Quantum Error correction must be applied at every step in a Quantum protocol.
Todd A. Brun - One of the best experts on this subject based on the ideXlab platform.
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catalytic Quantum Error correction
IEEE Transactions on Information Theory, 2014Co-Authors: Todd A. Brun, Igor Devetak, Minhsiu HsiehAbstract:We develop the theory of entanglement-assisted Quantum Error-correcting (EAQEC) codes, a generalization of the stabilizer formalism to the setting in which the sender and receiver have access to preshared entanglement. Conventional stabilizer codes are equivalent to self-orthogonal symplectic codes. In contrast, EAQEC codes do not require self-orthogonality, which greatly simplifies their construction. We show how any classical binary or quaternary block code can be made into an EAQEC code. We provide a table of best known EAQEC codes with code length up to 10. With the self-orthogonality constraint removed, we see that the distance of an EAQEC code can be better than any standard Quantum Error-correcting code with the same fixed net yield. In a Quantum computation setting, EAQEC codes give rise to catalytic Quantum codes, which assume a subset of the qubits are noiseless. We also give an alternative construction of EAQEC codes by making classical entanglement-assisted codes coherent.
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Quantum Error correction
Quantum Error Correction, 2013Co-Authors: Daniel A. Lidar, Todd A. BrunAbstract:Prologue Preface Part I. Background: 1. Introduction to decoherence and noise in open Quantum systems Daniel Lidar and Todd Brun 2. Introduction to Quantum Error correction Dave Bacon 3. Introduction to decoherence-free subspaces and noiseless subsystems Daniel Lidar 4. Introduction to Quantum dynamical decoupling Lorenza Viola 5. Introduction to Quantum fault tolerance Panos Aliferis Part II. Generalized Approaches to Quantum Error Correction: 6. Operator Quantum Error correction David Kribs and David Poulin 7. Entanglement-assisted Quantum Error-correcting codes Todd Brun and Min-Hsiu Hsieh 8. Continuous-time Quantum Error correction Ognyan Oreshkov Part III. Advanced Quantum Codes: 9. Quantum convolutional codes Mark Wilde 10. Non-additive Quantum codes Markus Grassl and Martin Rotteler 11. Iterative Quantum coding systems David Poulin 12. Algebraic Quantum coding theory Andreas Klappenecker 13. Optimization-based Quantum Error correction Andrew Fletcher Part IV. Advanced Dynamical Decoupling: 14. High order dynamical decoupling Zhen-Yu Wang and Ren-Bao Liu 15. Combinatorial approaches to dynamical decoupling Martin Rotteler and Pawel Wocjan Part V. Alternative Quantum Computation Approaches: 16. Holonomic Quantum computation Paolo Zanardi 17. Fault tolerance for holonomic Quantum computation Ognyan Oreshkov, Todd Brun and Daniel Lidar 18. Fault tolerant measurement-based Quantum computing Debbie Leung Part VI. Topological Methods: 19. Topological codes Hector Bombin 20. Fault tolerant topological cluster state Quantum computing Austin Fowler and Kovid Goyal Part VII. Applications and Implementations: 21. Experimental Quantum Error correction Dave Bacon 22. Experimental dynamical decoupling Lorenza Viola 23. Architectures Jacob Taylor 24. Error correction in Quantum communication Mark Wilde Part VIII. Critical Evaluation of Fault Tolerance: 25. Hamiltonian methods in QEC and fault tolerance Eduardo Novais, Eduardo Mucciolo and Harold Baranger 26. Critique of fault-tolerant Quantum information processing Robert Alicki References Index.
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Duality in Entanglement-Assisted Quantum Error Correction
IEEE Transactions on Information Theory, 2013Co-Authors: Todd A. Brun, Mark M. WildeAbstract:The dual of an entanglement-assisted Quantum Error-correcting (EAQEC) code is defined from the orthogonal group of a simplified stabilizer group. From the Poisson summation formula, this duality leads to the MacWilliams identities and linear programming bounds for EAQEC codes. We establish a table of upper and lower bounds on the minimum distance of any maximal-entanglement EAQEC code with length up to 15 channel qubits.
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catalytic Quantum Error correction
arXiv: Quantum Physics, 2006Co-Authors: Todd A. Brun, Igor Devetak, Minhsiu HsiehAbstract:We develop the theory of entanglement-assisted Quantum Error correcting (EAQEC) codes, a generalization of the stabilizer formalism to the setting in which the sender and receiver have access to pre-shared entanglement. Conventional stabilizer codes are equivalent to dual-containing symplectic codes. In contrast, EAQEC codes do not require the dual-containing condition, which greatly simplifies their construction. We show how any quaternary classical code can be made into a EAQEC code. In particular, efficient modern codes, like LDPC codes, which attain the Shannon capacity, can be made into EAQEC codes attaining the hashing bound. In a Quantum computation setting, EAQEC codes give rise to catalytic Quantum codes which maintain a region of inherited noiseless qubits. We also give an alternative construction of EAQEC codes by making classical entanglement assisted codes coherent.
