Quantum error correction against correlated noise

Clemens, James; Siddiqui, Shabnam; Gea‐Banacloche, Julio

doi:10.1103/physreva.69.062313

Cited by 51 publications

(55 citation statements)

References 17 publications

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“…Moreover, clarifying the role of spatial correlations in the performance of a large variety of quantum processes, such as e.g. quantum error correction [12][13][14][15][16][17], photosynthesis and excitation transfer [18][19][20][21][22][23][24][25][26][27][28], dissipative phase transitions [29][30][31][32][33] and quantum metrology [34] has been and still is an active area of research.…”

Section: Introductionmentioning

confidence: 99%

Erratum: Quantifying spatial correlations of general quantum dynamics (2015 New J. Phys. 17 062001)

Rivas

Müller

2015

New J. Phys.

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Section: Introductionmentioning

confidence: 99%

Erratum: Quantifying spatial correlations of general quantum dynamics (2015 New J. Phys. 17 062001)

Rivas

Müller

2015

New J. Phys.

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“…Even some of the foundational work on decoherence in quantum computation considered both fully correlated and uncorrelated environments [15][16][17][18]. Recently, the ramifications of correlated environments have been discussed in such diverse situations as scalable quantum error correction [2,[19][20][21][22][23][24], photosynthesis and biological chromophores [25][26][27][28][29] and multi-atom trapping experiments [30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Derivation of Markovian master equations for spatially correlated decoherence

Jeske

Cole

2013

Phys. Rev. A

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We introduce a general formalism to describe the effects of Markovian noise which is spatially correlated, typically decaying over some finite correlation length. For any system of interest, this formalism describes spatial correlations without the necessity to choose a particular microscopic model for the environment. We present a method of mapping the equations to Lindblad form and discuss functional forms for homogeneous spatial correlation functions. We also discuss two example microscopic models for the environment which exhibit non-trivial spatial-temporal correlation functions.

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“…This assumption ensures that multiple qudit errors may be characterized using tensor products of single qudit unitary operations. Relaxation of this assumption is an active area of research within the greater QECC community [63,64], but does not feature significantly in the QKD literature [65,66]. These single qudit unitary operations may be constructed from members of the generalized Pauli group  [57], defined as…”

Section: Serialized Qudit-based Error Correcting Teleportationmentioning

confidence: 99%

Serialized quantum error correction protocol for high-bandwidth quantum repeaters

2016

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Advances in single-photon creation, transmission, and detection suggest that sending quantum information over optical fibers may have losses low enough to be correctable using a quantum error correcting code (QECC). Such error-corrected communication is equivalent to a novel quantum repeater scheme, but crucial questions regarding implementation and system requirements remain open. Here we show that long-range entangled bit generation with rates approaching 10 8 entangled bits per second may be possible using a completely serialized protocol, in which photons are generated, entangled, and error corrected via sequential, one-way interactions with as few matter qubits as possible. Provided loss and error rates of the required elements are below the threshold for quantum error correction, this scheme demonstrates improved performance over transmission of single photons. We find improvement in entangled bit rates at large distances using this serial protocol and various QECCs. In particular, at a total distance of 500 km with fiber loss rates of 0.3 dB km −1 , logical gate failure probabilities of 10 −5 , photon creation and measurement error rates of 10 −5 , and a gate speed of 80 ps, we find the maximum single repeater chain entangled bit rates of 51 Hz at a 20 m node spacing and 190 000 Hz at a 43 m node spacing for the [[ ]] 3, 1, 2 3 and [[ ]] 7, 1, 3 QECCs respectively as compared to a bare success rate of 1×10 −140 Hz for single photon transmission. limits for quantum-error-corrected quantum repeaters when we simultaneously minimize the number of matter qubits required, make few assumptions about long-term matter qubit coherence, and require that each photon interacts sequentially, and singly, with each matter qubit. We call this design a serial quantum repeater, and show in this paper that with current or slightly improved device performance, one-way quantum communication at 1000 km ranges may approach the giga-entangled bit per second range using a stream of entangled photons in a narrow bandwidth over single fibers.The quantum repeater protocol laid out in [26] uses teleportation based error correction to correct photonic errors in a fault tolerant manner. Here, we work along similar lines, now focusing on the explicit serialization of components themselves so that different photons encoding a single logical state may be undergoing simultaneous but distinct operations. Furthermore, by providing some physical realizations for the underlying protocol, it is ensured that the photons need interact only once with any particular element, allowing uninterrupted operation of a repeater node limited only by the physical speed of its slowest operation. The number of matter qudits is then minimized to ensure as few resources are utilized as possible. The required operations for any QECC are detailed, with a focus on general Calderbank-Shor-Steane (CSS) codes due to their convenient adaptability to this protocol.The signal for our serial repeater is comprised of several photons encoded in a codeword of a QECC; we use...

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Quantum error correction against correlated noise

Cited by 51 publications

References 17 publications

Erratum: Quantifying spatial correlations of general quantum dynamics (2015 New J. Phys. 17 062001)

Erratum: Quantifying spatial correlations of general quantum dynamics (2015 New J. Phys. 17 062001)

Derivation of Markovian master equations for spatially correlated decoherence

Serialized quantum error correction protocol for high-bandwidth quantum repeaters

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