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arXiv:2102.04071 · Physical Review Research

Loss-tolerant concatenated Bell-state measurement with encoded coherent-state qubits for long-range quantum communication

Seok-Hyung Lee, Seung-Woo Lee, Hyunseok Jeong

Published Dec 21, 2021• 2 citations
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Abstract

The coherent-state qubit is a promising candidate for optical quantum information processing due to its nearly deterministic nature of the Bell-state measurement (BSM). However, its nonorthogonality incurs difficulties such as the failure of the BSM. One may use a large amplitude $(\ensuremath{\alpha})$ for the coherent state to minimize the failure probability, but the qubit then becomes more vulnerable to dephasing by photon loss. We propose a hardware-efficient concatenated BSM (CBSM) scheme with modified parity encoding using coherent states with reasonably small amplitudes $(|\ensuremath{\alpha}|⪅2)$, which simultaneously suppresses both failures and dephasing in the BSM procedure. We numerically show that the CBSM scheme achieves a success probability arbitrarily close to unity for appropriate values of $\ensuremath{\alpha}$ and sufficiently low photon loss rates (e.g., $⪅5%$). Furthermore, we verify that the quantum repeater scheme exploiting the CBSM scheme for quantum error correction enables one to carry out efficient long-range quantum communication over 1000 km. We show that the performance is comparable to those of other up-to-date methods and even exceeds them in some cases. Finally, we present methods to prepare logical qubits under modified parity encoding, and we implement elementary logical operations, which consist of several physical-level ingredients such as generation of superpositions of coherent states (SCSs) and elementary gates under the coherent-state basis. We then estimate the effects of imperfect physical-level elements on the performance of the scheme. Our work demonstrates that the encoded coherent-state qubits in free-propagating fields provide an alternative route to fault-tolerant information processing, especially to long-range quantum communication.

DOI
10.1103/physrevresearch.3.043205

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The coherent-state qubit is a promising candidate for optical quantum information processing due to its nearly deterministic nature of the Bell-state measurement (BSM). However, its nonorthogonality incurs difficulties such as the failure of the BSM. One may use a large amplitude (\ensuremathα)(\ensuremath{\alpha})(\ensuremathα) for the coherent state to minimize the failure probability, but the qubit then becomes more vulnerable to dephasing by photon loss. We propose a hardware-efficient concatenated BSM (CBSM) scheme with modified parity encoding using coherent states with reasonably small amplitudes (∣\ensuremathα∣⪅2)(|\ensuremath{\alpha}|⪅2)(∣\ensuremathα∣⪅2), which simultaneously suppresses both failures and dephasing in the BSM procedure. We numerically show that the CBSM scheme achieves a success probability arbitrarily close to unity for appropriate values of \ensuremathα\ensuremath{\alpha}\ensuremathα and sufficiently low photon loss rates (e.g., ⪅5⪅5%⪅5). Furthermore, we verify that the quantum repeater scheme exploiting the CBSM scheme for quantum error correction enables one to carry out efficient long-range quantum communication over 1000 km. We show that the performance is comparable to those of other up-to-date methods and even exceeds them in some cases. Finally, we present methods to prepare logical qubits under modified parity encoding, and we implement elementary logical operations, which consist of several physical-level ingredients such as generation of superpositions of coherent states (SCSs) and elementary gates under the coherent-state basis. We then estimate the effects of imperfect physical-level elements on the performance of the scheme. Our work demonstrates that the encoded coherent-state qubits in free-propagating fields provide an alternative route to fault-tolerant information processing, especially to long-range quantum communication.
Quantum repeaters constitute a promising platform for enabling long-distance quantum communication and may ultimately serve as the backbone of a secure quantum internet, a scalable quantum network, or a distributed quantum computer. An efficient approach to encoding qubits within an error correcting code is provided by bosonic codes, in which even a single oscillator mode can function as a sufficiently large physical system. In this work, we initially investigate the bosonic Gottesman Kitaev Preskill (GKP) code as a promising platform for loss correcting quantum repeaters, compatible with room temperature implementation, and analyse how loss and other noise sources propagate through the circuit using Heisenberg evolution. We analyse three quantum repeater protocols in which transmission loss is suppressed at the cost of logical errors, identifying a relay-like teleamplifier as the optimal scheme. This enables long distance quantum communication via densely packed nodes without higher-level encoding, and we evaluate the resulting secure key rates exploiting analog syndrome information. Furthermore, we propose a concatenated Bell-state measurement (CBSM) scheme with a modified parity encoding based on GKP qubits, CV measurement with teleamplifier and a clipping method that corrects transmission loss without introducing logical errors. This significantly enhances the possible secure key distance. We find that GKP based repeaters can achieve performance comparable to approaches relying on photonic qubits, while requiring orders of magnitude fewer qubits. Our parity encoded GKP repeater protocol achieves a substantially higher secret key rate than existing GKP based repeater schemes while maintaining a comparable resource overhead.
Fault tolerance is essential for scalable quantum technologies and is enabled by quantum error-correction codes. Bell-state measurements (BSMs) are a fundamental building block for modern quantum technologies such as measurement-based quantum computation and fusion-based quantum computation, as well as quantum networks. Therefore, performing BSMs on error-corrected qubits is a necessary step for achieving fault tolerance in these applications. In this work, we realise a logical BSM using linear optics, based on a two-qubit repetition code, an instance of a quantum parity code that allows detection of bit-flip errors, and experimentally achieve a mean success probability of (70.8 +/- 0.4)%. While standard linear-optical BSMs are fundamentally limited to a maximum success probability of 50%, this increased success probability enables higher secure key rates in quantum communication and facilitates the generation of large graph states for quantum computation. Since fault-tolerant schemes require error-correction codes regardless, this improvement comes at no additional resource overhead. Our results demonstrate that error-correction codes can be used to surpass the linear-optics limit of BSMs, which is an important step towards practical, fault-tolerant, and scalable photonic quantum technologies.
To realize long-distance quantum communication, it is crucial to design quantum repeater architectures that can deal with transmission losses and operational errors. Code concatenation of photonic graph codes is a promising way to achieve this; however, existing concatenated codes that can correct both transmission losses and operational errors are extremely hardware-demanding. We propose a one-way quantum repeater architecture based on concatenated ring graph codes and linear optical Bell-state measurements. We construct a scheme to generate the concatenated ring graph codes using quantum emitters, where the number of matter qubits scales linearly with concatenation depth. Furthermore, we devise a measurement strategy at each repeater station with a simple experimental setup where photons are measured in the order that they are created and show that entanglement swapping is fault-tolerant to both transmission losses and operational errors. This allows for long-distance quantum communication (>104> 10^4>104 km) at a kHZ rate even in the presence of single qubit error rates ε>10−3ε> 10^{-3}ε>10−3.
Entanglement swapping (ES) plays a key role in long-distance quantum communication. However, photon loss is inevitable due to noise in quantum channels, which makes existing ES focusing on the physical qubit fail to work, thereby degrading the efficiency of quantum communication. To address this issue, we resort to quantum parity codes (QPCs) and quantum nondemolition detection (QND) to realize a loss-tolerant ES (LTES), where each qubit is encoded into a logical qubit consisting of three levels: logical level, block level, and physical level. The research findings illustrate that the LTES can be successfully performed as long as the logical Bell state completely contains at least one block and each block contains at least one pair of physical Bell states. In addition, we evaluate the influence of the imperfect QND on the LTES, indicating that if the error probability of QND is lower than 0.47, the entanglement achieves a fidelity of 0.99 after performing the LTES. As a consequence, this LTES has the potential to pave the way for long-distance quantum communication.
Quantum repeaters are a promising platform for realizing long-distance quantum communication and thus could form the backbone of a secure quantum internet, a scalable quantum network, or a distributed quantum computer. Repeater protocols that encode information in single- or multiphoton states are limited by transmission losses and the cost of implementing entangling gates or Bell measurements. In this work, we consider implementing a quantum repeater protocol using Gottesman-Kitaev-Preskill (GKP) qubits. These qubits are natural elements for quantum repeater protocols, because they allow for deterministic Gaussian entangling operations and Bell measurements, which can be implemented at room temperature. The GKP encoding is also capable of correcting small displacement errors. At the cost of additional Gaussian noise, photon loss can be converted into a random displacement error channel by applying a phase-insensitive amplifier. Here we show that a similar conversion can be achieved in two-way repeater protocols by using phase-sensitive amplification applied in the postprocessing of the measurement data, resulting in less overall Gaussian noise per (sufficiently short) repeater segment. We also investigate concatenating the GKP code with higher-level qubit codes while leveraging analog syndrome data, postselection, and path-selection techniques to boost the rate of communication. We compute the secure key rates and find that GKP repeaters can achieve a comparative performance relative to methods based on photonic qubits while using orders-of-magnitude fewer qubits.
We present an in-depth analysis regarding the error resistance and optimization of our all-optical Bell measurement and ultrafast long-distance quantum communication scheme proposed by Ewert, Bergmann, and van Loock [Phys. Rev. Lett. 117, 210501 (2016)]. In order to promote our previous proposal from loss to fault tolerance, we introduce a general and compact formalism that can also be applied to other related schemes {including non-all-optical ones such as that of Muralidharan et al. [Phys. Rev. Lett. 112, 250501 (2014)]}. With the help of this new representation we show that our communication protocol does not only counteract the inevitable photon loss during channel transmission, but is also able to resist common experimental errors such as Pauli-type errors (bit and phase flips) and detector inefficiencies (losses and dark counts). Furthermore, we demonstrate that on the physical level of photonic qubits the choice of the standard linear optical Bell measurement with its limited efficiency is optimal for our setting in the sense that, apart from their potential use in state preparation, more advanced Bell measurements yield only a small decrease in resource consumption. We devise two state generation schemes that provide the required ancillary encoded Bell states (quasi-)on-demand at every station. The schemes are either based on nonlinear optics or on linear optics with multiplexing and exhibit resource costs that scale linearly or less than quadratic with the number of photons per encoded qubit, respectively. Finally, we show that it is possible to operate our communication scheme with on-off detectors instead of employing photon-number-resolving detectors.