Quantum convolutional coding with shared entanglement: general structure

Wilde, Mark M.; Brun, Todd A.

doi:10.1007/s11128-010-0179-9

Cited by 12 publications

(1 citation statement)

References 28 publications

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“…-It might also be interesting to explore bipartite convolutional codes as an extension of the work in Ref's. [55,49,51] and the work in this paper. -There might be a way to develop multiparty codes that exploit a common secret key between multiple parties because of the connection between quantum privacy and quantum coherence [14,19,18].…”

Section: Resultsmentioning

confidence: 98%

Nonlocal quantum information in bipartite quantum error correction

Wilde

Fattal

2010

Quantum Inf Process

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We show how to convert an arbitrary stabilizer code into a bipartite quantum code. A bipartite quantum code is one that involves two senders and one receiver. The two senders exploit both nonlocal and local quantum resources to encode quantum information with local encoding circuits. They transmit their encoded quantum data to a single receiver who then decodes the transmitted quantum information. The nonlocal resources in a bipartite code are ebits and nonlocal information qubits and the local resources are ancillas and local information qubits. The technique of bipartite quantum error correction is useful in both the quantum communication scenario described above and in fault-tolerant quantum computation. It has application in fault-tolerant quantum computation because we can prepare nonlocal resources offline and exploit local encoding circuits. In particular, we derive an encoding circuit for a bipartite version of the Steane code that is local and additionally requires only nearest-neighbor interactions. We have simulated this encoding in the CNOT extended rectangle with a publicly available fault-tolerant simulation software. The result is that there is an improvement in the "pseudothreshold" with respect to the baseline Steane code, under the assumption that quantum memory errors occur less frequently than quantum gate errors.Comment: 14 pages, 4 figure

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Section: Resultsmentioning

confidence: 98%

Nonlocal quantum information in bipartite quantum error correction

Wilde

Fattal

2010

Quantum Inf Process

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Minimal-memory realization of pearl-necklace encoders of general quantum convolutional codes

Houshmand

Hosseini-Khayat

2011

Phys. Rev. A

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Quantum convolutional codes, like their classical counterparts, promise to offer higher error correction performance than block codes of equivalent encoding complexity, and are expected to find important applications in reliable quantum communication where a continuous stream of qubits is transmitted. Grassl and Roetteler devised an algorithm to encode a quantum convolutional code with a "pearl-necklace" encoder. Despite their algorithm's theoretical significance as a neat way of representing quantum convolutional codes, it is not well suited to practical realization. In fact, there is no straightforward way to implement any given pearl-necklace structure. This paper closes the gap between theoretical representation and practical implementation. In our previous work, we presented an efficient algorithm to find a minimal-memory realization of a pearl-necklace encoder for Calderbank-Shor-Steane (CSS) convolutional codes. This work is an extension of our previous work and presents an algorithm for turning a pearl-necklace encoder for a general (non-CSS) quantum convolutional code into a realizable quantum convolutional encoder. We show that a minimal-memory realization depends on the commutativity relations between the gate strings in the pearl-necklace encoder. We find a realization by means of a weighted graph which details the noncommutative paths through the pearl necklace. The weight of the longest path in this graph is equal to the minimal amount of memory needed to implement the encoder. The algorithm has a polynomial-time complexity in the number of gate strings in the pearl-necklace encoder.

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Quantum Error Correction via Less Noisy Qubits

Fujiwara

2013

Phys. Rev. Lett.

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Known quantum error correction schemes are typically able to take advantage of only a limited class of classical error-correcting codes. Entanglement-assisted quantum error correction is a partial solution which made it possible to exploit any classical linear codes over the binary or quaternary finite field. However, the known entanglement-assisted scheme requires noiseless qubits that help correct quantum errors on noisy qubits, which can be too severe an assumption. We prove that a more relaxed and realistic assumption is sufficient by presenting encoding and decoding operations assisted by qubits on which quantum errors of one particular kind may occur. As in entanglement assistance, our scheme can import any binary or quaternary linear codes. If the auxiliary qubits are noiseless, our codes become entanglement-assisted codes, and saturate the quantum Singleton bound when the underlying classical codes are maximum distance separable.

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Quantum convolutional coding with shared entanglement: general structure

Cited by 12 publications

References 28 publications

Nonlocal quantum information in bipartite quantum error correction

Nonlocal quantum information in bipartite quantum error correction

Minimal-memory realization of pearl-necklace encoders of general quantum convolutional codes

Quantum Error Correction via Less Noisy Qubits

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