Cavity quantum electrodynamics (CQED)-based quantum LDPC encoders and decoders

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Quantum information processing (QIP) relies on delicate superposition states that are sensitive to interactions with environment, resulting in errors. Moreover, the quantum gates are imperfect so that the use of quantum error correction coding (QECC) is essential to enable the fault-tolerant computing. The QECC is also important in quantum communication and teleportation applications. The most critical gate, i.e., the CNOT gate, has been implemented recently as a probabilistic device by using integrated optics. CNOT gates from linear optics provide only probabilistic outcomes and, as such, are not suitable for any meaningful quantum computation (on the order of thousand qubits and above). In this paper, we show that arbitrary set of universal quantum gates and gates from Clifford group, which are needed in QECC, can be implemented based on cavity quantum electrodynamics (CQED). Moreover, in CQED technology, the use of the controlled-$Z$ gate instead of the CNOT gate is more appropriate. We then show that encoders/decoders for quantum low-density parity-check (LDPC) codes can be implemented based on Hadamard and controlled-$Z$ gates only using CQED. We also discuss quantum dual-containing and entanglement-assisted codes and show that they can be related to combinatorial objects known as balanced incomplete block designs (BIBDs). In particular, a special class of BIBDsSteiner triple systems (STSs)yields to low-complexity quantum LDPC codes. Finally, we perform simulations and evaluate the performance of several classes of large-girth quantum LDPC codes suitable for implementation in CQED technology against that of lower girth entanglement-assisted codes and dual-containing quantum codes.

Original languageEnglish (US)
Article number5955062
Pages (from-to)727-738
Number of pages12
JournalIEEE Photonics Journal
Volume3
Issue number4
DOIs
StatePublished - 2011

Fingerprint

decoders
Electrodynamics
coders
quantum electrodynamics
parity
Error correction
cavities
Fault tolerant computer systems
Quantum communication
Quantum computers
Integrated optics
coding
Optics
quantum communication
integrated optics
quantum computation
optics

Keywords

  • cavity quantum electrodynamics (CQED)
  • Clifford group
  • quantum error correction coding (QECC)
  • Quantum information processing (QIP)
  • quantum low-density parity-check (LDPC) codes

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Atomic and Molecular Physics, and Optics

Cite this

Cavity quantum electrodynamics (CQED)-based quantum LDPC encoders and decoders. / Djordjevic, Ivan B.

In: IEEE Photonics Journal, Vol. 3, No. 4, 5955062, 2011, p. 727-738.

Research output: Contribution to journalArticle

@article{f15b869ecf4145bdb822025f8dd5b82f,
title = "Cavity quantum electrodynamics (CQED)-based quantum LDPC encoders and decoders",
abstract = "Quantum information processing (QIP) relies on delicate superposition states that are sensitive to interactions with environment, resulting in errors. Moreover, the quantum gates are imperfect so that the use of quantum error correction coding (QECC) is essential to enable the fault-tolerant computing. The QECC is also important in quantum communication and teleportation applications. The most critical gate, i.e., the CNOT gate, has been implemented recently as a probabilistic device by using integrated optics. CNOT gates from linear optics provide only probabilistic outcomes and, as such, are not suitable for any meaningful quantum computation (on the order of thousand qubits and above). In this paper, we show that arbitrary set of universal quantum gates and gates from Clifford group, which are needed in QECC, can be implemented based on cavity quantum electrodynamics (CQED). Moreover, in CQED technology, the use of the controlled-$Z$ gate instead of the CNOT gate is more appropriate. We then show that encoders/decoders for quantum low-density parity-check (LDPC) codes can be implemented based on Hadamard and controlled-$Z$ gates only using CQED. We also discuss quantum dual-containing and entanglement-assisted codes and show that they can be related to combinatorial objects known as balanced incomplete block designs (BIBDs). In particular, a special class of BIBDsSteiner triple systems (STSs)yields to low-complexity quantum LDPC codes. Finally, we perform simulations and evaluate the performance of several classes of large-girth quantum LDPC codes suitable for implementation in CQED technology against that of lower girth entanglement-assisted codes and dual-containing quantum codes.",
keywords = "cavity quantum electrodynamics (CQED), Clifford group, quantum error correction coding (QECC), Quantum information processing (QIP), quantum low-density parity-check (LDPC) codes",
author = "Djordjevic, {Ivan B}",
year = "2011",
doi = "10.1109/JPHOT.2011.2162315",
language = "English (US)",
volume = "3",
pages = "727--738",
journal = "IEEE Photonics Journal",
issn = "1943-0655",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "4",

}

TY - JOUR

T1 - Cavity quantum electrodynamics (CQED)-based quantum LDPC encoders and decoders

AU - Djordjevic, Ivan B

PY - 2011

Y1 - 2011

N2 - Quantum information processing (QIP) relies on delicate superposition states that are sensitive to interactions with environment, resulting in errors. Moreover, the quantum gates are imperfect so that the use of quantum error correction coding (QECC) is essential to enable the fault-tolerant computing. The QECC is also important in quantum communication and teleportation applications. The most critical gate, i.e., the CNOT gate, has been implemented recently as a probabilistic device by using integrated optics. CNOT gates from linear optics provide only probabilistic outcomes and, as such, are not suitable for any meaningful quantum computation (on the order of thousand qubits and above). In this paper, we show that arbitrary set of universal quantum gates and gates from Clifford group, which are needed in QECC, can be implemented based on cavity quantum electrodynamics (CQED). Moreover, in CQED technology, the use of the controlled-$Z$ gate instead of the CNOT gate is more appropriate. We then show that encoders/decoders for quantum low-density parity-check (LDPC) codes can be implemented based on Hadamard and controlled-$Z$ gates only using CQED. We also discuss quantum dual-containing and entanglement-assisted codes and show that they can be related to combinatorial objects known as balanced incomplete block designs (BIBDs). In particular, a special class of BIBDsSteiner triple systems (STSs)yields to low-complexity quantum LDPC codes. Finally, we perform simulations and evaluate the performance of several classes of large-girth quantum LDPC codes suitable for implementation in CQED technology against that of lower girth entanglement-assisted codes and dual-containing quantum codes.

AB - Quantum information processing (QIP) relies on delicate superposition states that are sensitive to interactions with environment, resulting in errors. Moreover, the quantum gates are imperfect so that the use of quantum error correction coding (QECC) is essential to enable the fault-tolerant computing. The QECC is also important in quantum communication and teleportation applications. The most critical gate, i.e., the CNOT gate, has been implemented recently as a probabilistic device by using integrated optics. CNOT gates from linear optics provide only probabilistic outcomes and, as such, are not suitable for any meaningful quantum computation (on the order of thousand qubits and above). In this paper, we show that arbitrary set of universal quantum gates and gates from Clifford group, which are needed in QECC, can be implemented based on cavity quantum electrodynamics (CQED). Moreover, in CQED technology, the use of the controlled-$Z$ gate instead of the CNOT gate is more appropriate. We then show that encoders/decoders for quantum low-density parity-check (LDPC) codes can be implemented based on Hadamard and controlled-$Z$ gates only using CQED. We also discuss quantum dual-containing and entanglement-assisted codes and show that they can be related to combinatorial objects known as balanced incomplete block designs (BIBDs). In particular, a special class of BIBDsSteiner triple systems (STSs)yields to low-complexity quantum LDPC codes. Finally, we perform simulations and evaluate the performance of several classes of large-girth quantum LDPC codes suitable for implementation in CQED technology against that of lower girth entanglement-assisted codes and dual-containing quantum codes.

KW - cavity quantum electrodynamics (CQED)

KW - Clifford group

KW - quantum error correction coding (QECC)

KW - Quantum information processing (QIP)

KW - quantum low-density parity-check (LDPC) codes

UR - http://www.scopus.com/inward/record.url?scp=80051683424&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80051683424&partnerID=8YFLogxK

U2 - 10.1109/JPHOT.2011.2162315

DO - 10.1109/JPHOT.2011.2162315

M3 - Article

VL - 3

SP - 727

EP - 738

JO - IEEE Photonics Journal

JF - IEEE Photonics Journal

SN - 1943-0655

IS - 4

M1 - 5955062

ER -