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Optics Express

On the photonic implementation of universal quantum gates, Bell states preparation circuit and quantum LDPC encoders and decoders based on directional couplers and HNLF

Ivan B. Djordjević

Published Apr 1, 2010• 5 citations
Publisher

Abstract

The Bell states preparation circuit is a basic circuit required in quantum teleportation. We describe how to implement it in all-fiber technology. The basic building blocks for its implementation are directional couplers and highly nonlinear optical fiber (HNLF). Because the quantum information processing is based on delicate superposition states, it is sensitive to quantum errors. In order to enable fault-tolerant quantum computing the use of quantum error correction is unavoidable. We show how to implement in all-fiber technology encoders and decoders for sparse-graph quantum codes, and provide an illustrative example to demonstrate this implementation. We also show that arbitrary set of universal quantum gates can be implemented based on directional couplers and HNLFs.

DOI
10.1364/oe.18.008115

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The Bell states preparation circuit is a basic circuit required in quantum teleportation. We describe how to implement it in all-fiber technology. The basic building blocks for its implementation are directional couplers and highly nonlinear optical fiber (HNLF). Because the quantum information processing is based on delicate superposition states, it is sensitive to quantum errors. In order to enable fault-tolerant quantum computing the use of quantum error correction is unavoidable. We show how to implement in all-fiber technology encoders and decoders for sparse-graph quantum codes, and provide an illustrative example to demonstrate this implementation. We also show that arbitrary set of universal quantum gates can be implemented based on directional couplers and HNLFs.
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.
We show that any family of deterministic universal quantum gates can be implemented in integrated optics. We further show how to implement Pauli gates, needed in quantum-error correction, using the same technology. Two basic circuits required in quantum teleportation systems are Bell states and quantum relay. We describe how to implement them in integrated optics. Finally, we study the implementation of sparse-graph (SG) quantum codes in integrated optics. We demonstrate that entanglement assisted SG codes significantly outperform corresponding dual-containing quantum codes.
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.
Quantum error correction is an essential tool for reliably performing tasks for processing quantum information on a large scale. However, integration into quantum circuits to achieve these tasks is problematic when one realizes that nontransverse operations, which are essential for universal quantum computation, lead to the spread of errors. Quantum gate teleportation has been proposed as an elegant solution for this. Here, one replaces these fragile, nontransverse inline gates with the generation of specific, highly entangled offline resource states that can be teleported into the circuit to implement the nontransverse gate. As the first important step, we create a maximally entangled state between a physical and an error-correctable logical qubit and use it as a teleportation resource. We then demonstrate the teleportation of quantum information encoded on the physical qubit into the error-corrected logical qubit with fidelities up to 0.786. Our scheme can be designed to be fully fault tolerant so that it can be used in future large-scale quantum technologies.
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.