Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE photonics journal

Cavity Quantum Electrodynamics (CQED)-Based Quantum LDPC Encoders and Decoders

Ivan B. Djordjević

Published Jul 21, 2011• 9 citations
Publisher

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-Zgate 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-Zgates 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 BIBDs-Steiner 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.

DOI
10.1109/jphot.2011.2162315

Related papers

Cavity quantum electrodynamics based quantum low-density parity-check encoders and decoders

Ivan B. Djordjević

Quantum information processing (QIP) relies on delicate superposition states that are sensitive to interactions with environment. The quantum gates are imperfect and the use of quantum error correction coding (QECC) is essential to enable the fault-tolerant computing and to deal with quantum errors. The most critical gate, CNOT-gate, has been implemented as a probabilistic device by using integrated optics. CNOT-gates from linear optics provide only probabilistic outcomes and as such are not suitable for large-scale computation. In this paper, we show that arbitrary set of universal quantum gates and gates from Clifford group, needed in QECC, can be implemented based on cavity quantum electrodynamics (CQED). We further show that encoders/decoders for quantum LDPC codes can be implemented based on Hadamard and CNOT gates using CQED. Finally, we perform simulations and evaluate performance of several classes of quantum LDPC codes suitable for implementation in CQED technology.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Feb 10, 2011•5 citations

Photonic entanglement-assisted quantum low-density parity-check encoders and decoders

Ivan B. Djordjević

I propose encoder and decoder architectures for entanglement-assisted (EA) quantum low-density parity-check (LDPC) codes suitable for all-optical implementation. I show that two basic gates needed for EA quantum error correction, namely, controlled-NOT (CNOT) and Hadamard gates can be implemented based on Mach-Zehnder interferometer. In addition, I show that EA quantum LDPC codes from balanced incomplete block designs of unitary index require only one entanglement qubit to be shared between source and destination.

Optics Letters•Apr 28, 2010•34 citations

Photonic Quantum Dual-Containing LDPC Encoders and Decoders

Ivan B. Djordjević

We propose encoder and decoder architectures for quantum low-density parity-check (LDPC) codes suitable for all-optical implementation, based on controlled-not (CNOT) and Hadamard gates only. Given the fact that the CNOT gate can be implemented using directional couplers, and Hadamard gate by using pi-hybrid, the proposed encoders/decoders architectures are suitable for implementation in integrated optics. In addition, we propose several quantum LDPC codes based on balanced incomplete block designs.

IEEE Photonics Technology Letters•Apr 3, 2009•27 citations

On the Photonic Implementation of Universal Quantum Gates, Bell States Preparation Circuit, Quantum Relay and Quantum LDPC Encoders and Decoders

Ivan B. Djordjević

We show that any family of universal quantum gates can be implemented based on a single optical hybrid/Mach-Zehnder interferometer (MZI)/directional coupler (DC) and either a highly nonlinear optical fiber or a tap coupler with an avalanche photodiode. We further show how to implement Pauli gates, which are needed in quantum error correction, using the same technology. The use of Bell states in quantum teleportation is essential. We also show how to implement the Bell states preparation circuit. To extend the transmission distance of quantum teleportation systems, the use of quantum relays is necessary. We show how to implement the quantum relay in integrated optics as well. We further study the implementation of encoders/decoders for sparse-graph quantum codes and show that the encoder/decoder for arbitrary quantum sparse-graph code can be implemented in integrated optics as well. We also study the performance of sparse-graph codes and demonstrate that entanglement-assisted sparse-graph codes from balanced incomplete block designs significantly outperform the corresponding dual-containing quantum codes. Finally, we provide several theorems that can be used in the design of entanglement-assisted (EA) quantum codes that require only one qubit to be shared between the source and the destination.

IEEE photonics journal•Feb 1, 2010•15 citations

Fault-Tolerant Quantum LDPC Encoders

Abhi Kumar Sharma, Shayan Srinivasa Garani

We propose fault-tolerant encoders for quantum low-density parity check (LDPC) codes. By grouping qubits within a quantum code over contiguous blocks and applying preshared entanglement across these blocks, we show how transversal implementation can be realized. The proposed encoder reduces the error propagation while using multi-qubit gates and is applicable for both entanglement-unassisted and entanglement-assisted quantum LDPC codes.

arXiv:2405.07242•Jul 7, 2024•1 citation

Addressable fault-tolerant universal quantum gate operations for high-rate lift-connected surface codes

Josias Old, Juval Bechar, Markus Müller +1 more

Quantum low-density parity check (qLDPC) codes are among the leading candidates to realize error-corrected quantum memories with low qubit overhead. Potentially high encoding rates and large distance relative to their block size make them appealing for practical suppression of noise in near-term quantum computers. In addition to increased qubit-connectivity requirements compared to more conventional topological quantum error correcting codes, qLDPC codes remain notoriously hard to compute with. In this work, we introduce a construction to implement all Clifford quantum gate operations on the recently introduced lift-connected surface (LCS) codes (Old et al. 2024). These codes can be implemented in a 3D-local architecture and achieve asymptotic scaling $[[n, \mathcal{O}(n^{1/3}), \mathcal{O}(n^{1/3})]]$. In particular, LCS codes realize favorable instances with small numbers of qubits: For the $[[15,3,3]]$ LCS code, we provide deterministic fault-tolerant (FT) circuits of the logical gate set $\{\overline{H}_i, \overline{H}_i, \overline{C_i X_j}\}_{i,j \in (0,1,2)}$ based on flag qubits. By adding a procedure for FT magic state preparation, we show quantitatively how to realize an FT universal gate set in $d=3$ LCS codes. Numerical simulations indicate that our gate constructions can attain pseudothresholds in the range $p_{\mathrm{th}} \approx 4.8\cdot 10^{-3}-1.2\cdot 10^{-2}$ for circuit-level noise. The schemes use a moderate number of qubits and are therefore feasible for near-term experiments, facilitating progress for fault-tolerant error corrected logic in high-rate qLPDC codes.

quant-pharXiv:2511.10191•Nov 14, 2025•0 citations
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-Zgate 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-Zgates 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 BIBDs-Steiner 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.
Quantum information processing (QIP) relies on delicate superposition states that are sensitive to interactions with environment. The quantum gates are imperfect and the use of quantum error correction coding (QECC) is essential to enable the fault-tolerant computing and to deal with quantum errors. The most critical gate, CNOT-gate, has been implemented as a probabilistic device by using integrated optics. CNOT-gates from linear optics provide only probabilistic outcomes and as such are not suitable for large-scale computation. In this paper, we show that arbitrary set of universal quantum gates and gates from Clifford group, needed in QECC, can be implemented based on cavity quantum electrodynamics (CQED). We further show that encoders/decoders for quantum LDPC codes can be implemented based on Hadamard and CNOT gates using CQED. Finally, we perform simulations and evaluate performance of several classes of quantum LDPC codes suitable for implementation in CQED technology.
I propose encoder and decoder architectures for entanglement-assisted (EA) quantum low-density parity-check (LDPC) codes suitable for all-optical implementation. I show that two basic gates needed for EA quantum error correction, namely, controlled-NOT (CNOT) and Hadamard gates can be implemented based on Mach-Zehnder interferometer. In addition, I show that EA quantum LDPC codes from balanced incomplete block designs of unitary index require only one entanglement qubit to be shared between source and destination.
We propose encoder and decoder architectures for quantum low-density parity-check (LDPC) codes suitable for all-optical implementation, based on controlled-not (CNOT) and Hadamard gates only. Given the fact that the CNOT gate can be implemented using directional couplers, and Hadamard gate by using pi-hybrid, the proposed encoders/decoders architectures are suitable for implementation in integrated optics. In addition, we propose several quantum LDPC codes based on balanced incomplete block designs.
We show that any family of universal quantum gates can be implemented based on a single optical hybrid/Mach-Zehnder interferometer (MZI)/directional coupler (DC) and either a highly nonlinear optical fiber or a tap coupler with an avalanche photodiode. We further show how to implement Pauli gates, which are needed in quantum error correction, using the same technology. The use of Bell states in quantum teleportation is essential. We also show how to implement the Bell states preparation circuit. To extend the transmission distance of quantum teleportation systems, the use of quantum relays is necessary. We show how to implement the quantum relay in integrated optics as well. We further study the implementation of encoders/decoders for sparse-graph quantum codes and show that the encoder/decoder for arbitrary quantum sparse-graph code can be implemented in integrated optics as well. We also study the performance of sparse-graph codes and demonstrate that entanglement-assisted sparse-graph codes from balanced incomplete block designs significantly outperform the corresponding dual-containing quantum codes. Finally, we provide several theorems that can be used in the design of entanglement-assisted (EA) quantum codes that require only one qubit to be shared between the source and the destination.
Quantum low-density parity check (qLDPC) codes are among the leading candidates to realize error-corrected quantum memories with low qubit overhead. Potentially high encoding rates and large distance relative to their block size make them appealing for practical suppression of noise in near-term quantum computers. In addition to increased qubit-connectivity requirements compared to more conventional topological quantum error correcting codes, qLDPC codes remain notoriously hard to compute with. In this work, we introduce a construction to implement all Clifford quantum gate operations on the recently introduced lift-connected surface (LCS) codes (Old et al. 2024). These codes can be implemented in a 3D-local architecture and achieve asymptotic scaling [[n,O(n1/3),O(n1/3)]][[n, \mathcal{O}(n^{1/3}), \mathcal{O}(n^{1/3})]][[n,O(n1/3),O(n1/3)]]. In particular, LCS codes realize favorable instances with small numbers of qubits: For the [[15,3,3]][[15,3,3]][[15,3,3]] LCS code, we provide deterministic fault-tolerant (FT) circuits of the logical gate set {H‾i,H‾i,CiXj‾}i,j∈(0,1,2)\{\overline{H}_i, \overline{H}_i, \overline{C_i X_j}\}_{i,j \in (0,1,2)}{Hi​,Hi​,Ci​Xj​​}i,j∈(0,1,2)​ based on flag qubits. By adding a procedure for FT magic state preparation, we show quantitatively how to realize an FT universal gate set in d=3d=3d=3 LCS codes. Numerical simulations indicate that our gate constructions can attain pseudothresholds in the range pth≈4.8⋅10−3−1.2⋅10−2p_{\mathrm{th}} \approx 4.8\cdot 10^{-3}-1.2\cdot 10^{-2}pth​≈4.8⋅10−3−1.2⋅10−2 for circuit-level noise. The schemes use a moderate number of qubits and are therefore feasible for near-term experiments, facilitating progress for fault-tolerant error corrected logic in high-rate qLPDC codes.