This study explores the feasibility of utilizing quantum error correction (QEC) to generate and store logical Bell states in heralded quantum entanglement protocols, crucial for quantum repeater networks. Two lattice surgery-based protocols (local and non-local) are introduced to establish logical Bell states between distant nodes using an intermediary node. We simulate the protocols using realistic experimental parameters, including ion trap memories, noisy optical channels, frequency conversion and non-destructive detection of photonic qubits. The study evaluates rotated and planar surface codes alongside Bacon-Shor codes for small code distances (d = 3, 5) under depolarizing and physical noise models. Pseudo-thresholds are identified, with physical error rates above perr∼ 10−3 offering no advantage over unencoded Bell states under depolarizing noise. Pseudo-thresholds are also reevaluated in terms of gate error rates ${p_{{{\operatorname{err} }_H}}},{p_{{{\operatorname{err} }_{CX}}}}{\text{ and }}{p_{{{\operatorname{err} }_M}}}$. For a distance of 1 km between the end node and the intermediary, an advantage over unencoded Bell-state heralded protocols requires reducing gate error rates by an order of magnitude $\left({0.1{p_{{{\operatorname{err} }_H}}},0.1{p_{{{\operatorname{err} }_{CX}}}},{\text{ and }}0.1{p_{{{\operatorname{err} }_M}}}}\right)$. These results highlight the need for significant hardware improvements to implement logical Bell state protocols with quantum memories. Additionally, the non-local protocol rate was analyzed achieving rates up to (32.53±1.53) Hz over distances of 1 to 80 km between the end node and the intermediary node.
This study explores the feasibility of utilizing quantum error correction (QEC) to generate and store logical Bell states in heralded quantum entanglement protocols, crucial for quantum repeater networks. Two lattice surgery-based protocols (local and non-local) are introduced to establish logical Bell states between distant nodes using an intermediary node. We simulate the protocols using realistic experimental parameters, including ion trap memories, noisy optical channels, frequency conversion and non-destructive detection of photonic qubits. The study evaluates rotated and planar surface codes alongside Bacon-Shor codes for small code distances (d = 3, 5) under depolarizing and physical noise models. Pseudo-thresholds are identified, with physical error rates above perr∼ 10−3 offering no advantage over unencoded Bell states under depolarizing noise. Pseudo-thresholds are also reevaluated in terms of gate error rates perrH,perrCX and perrM. For a distance of 1 km between the end node and the intermediary, an advantage over unencoded Bell-state heralded protocols requires reducing gate error rates by an order of magnitude (0.1perrH,0.1perrCX, and 0.1perrM). These results highlight the need for significant hardware improvements to implement logical Bell state protocols with quantum memories. Additionally, the non-local protocol rate was analyzed achieving rates up to (32.53±1.53) Hz over distances of 1 to 80 km between the end node and the intermediary node.
This study explores the feasibility of utilizing quantum error correction to generate and store logical Bell states in heralded quantum entanglement protocols, crucial for quantum repeater networks. Two lattice surgery-based protocols (local and nonlocal) are introduced to establish logical Bell states between distant nodes using an intermediary node. We simulate the protocols using realistic experimental parameters, including ion trap memories, noisy optical channels, frequency conversion, and nondestructive detection of photonic qubits. The study evaluates rotated and planar surface codes alongside Bacon-Shor codes for small code distances ( d = 3 , 5 ) under depolarizing and physical noise models. Pseudothresholds are identified, with physical error rates above p err ∼ 10 − 3 offering no advantage over unencoded Bell states under depolarizing noise. Pseudo-thresholds are also reevaluated in terms of gate error rates p err H , p err C X , and p err M . For a distance of 1 km between the end node and the intermediary, an advantage over unencoded Bell-state heralded protocols requires reducing gate error rates by an order of magnitude ( 0.1 p err H , 0.1 p err C X , and 0.1 p err M ). These results highlight the need for significant hardware improvements to implement logical Bell state protocols with quantum memories. Additionally, the nonlocal protocol rate was analyzed achieving rates up to ( 32.53 ± 1.53 ) Hz over distances of 1 to 80 km between the end node and the intermediary node.
The future of quantum repeater networking will require interoperability between various error-correcting codes. A few specific code conversions and even a generalized method are known, however, no detailed analysis of these techniques in the context of quantum networking has been performed. In this paper we analyze a generalized procedure to create Bell pairs encoded heterogeneously between two separate codes used often in error-corrected quantum repeater network designs. We begin with a physical Bell pair and then encode each qubit in a different error-correcting code, using entanglement purification to increase the fidelity. We investigate three separate protocols for preparing the purified encoded Bell pair. We calculate the error probability of those schemes between the Steane [[7,1,3]] code, a distance-3 surface code, and single physical qubits by Monte Carlo simulation under a standard Pauli error model and estimate the resource efficiency of the procedures. A local gate error rate of ${10}^{\ensuremath{-}3}$ allows us to create high-fidelity logical Bell pairs between any of our chosen codes. We find that a postselected model, where any detected parity flips in code stabilizers result in a restart of the protocol, performs the best.
Advances in single-photon creation, transmission, and detection suggest that sending quantum information over optical fibers may have losses low enough to be correctable using a quantum error correcting code (QECC). Such error-corrected communication is equivalent to a novel quantum repeater scheme, but crucial questions regarding implementation and system requirements remain open. Here we show that long-range entangled bit generation with rates approaching 10 8 entangled bits per second may be possible using a completely serialized protocol, in which photons are generated, entangled, and error corrected via sequential, one-way interactions with as few matter qubits as possible. Provided loss and error rates of the required elements are below the threshold for quantum error correction, this scheme demonstrates improved performance over transmission of single photons. We find improvement in entangled bit rates at large distances using this serial protocol and various QECCs. In particular, at a total distance of 500 km with fiber loss rates of 0.3 dB km −1 , logical gate failure probabilities of 10 −5 , photon creation and measurement error rates of 10 −5 , and a gate speed of 80 ps, we find the maximum single repeater chain entangled bit rates of 51 Hz at a 20 m node spacing and 190 000 Hz at a 43 m node spacing for the and QECCs respectively as compared to a bare success rate of 1 × 10 −140 Hz for single photon transmission.
Quantum repeaters are essential for scalable long-distance quantum networking. As quantum information processing moves toward fault-tolerant and error-corrected operations, it becomes increasingly important to study quantum repeaters that also move beyond raw physical entanglement and towards logical entanglement. In this paper, we implement and simulate the quantum repeater with encoding and classical error correction (QRE-CEC) protocol in SeQUeNCe, a discrete-event simulator of quantum networks. The protocol distributes logical Bell pairs, performs encoded entanglement swapping, and uses classical error correction for the decoding of entanglement swapping measurement outcomes to determine Pauli-frame corrections. For this study, we extend SeQUeNCe with a stabilizer-based backend, add support for CSS code-based encoded operations, and integrate gate, measurement, idle decoherence, and state-initialization noise models. Our simulation results show that QRE-CEC suppresses all modeled errors to the second order. Also, QRE-CEC can distribute logical Bell pairs with 0.91 fidelity over a distance of 2000 km under the parameter regimes we study. Beyond protocol-level performance evaluation, our implementation exposes practical simulator and control-plane challenges that are typically abstracted away in theoretical studies.
Modular architectures are a promising approach to scaling quantum computers to fault tolerance. Small, low-noise quantum processors connected through relatively noisy quantum links are capable of fault-tolerant operation as long as the noise can be confined to the interface. Finding protocols that implement the quantum links between modules as efficiently as possible is essential because inter-module entanglement is challenging to produce at a similar rate and fidelity as local entanglement. We introduce a protocol for lattice surgery on surface codes in which all non-local operations are Bell measurements. The protocol simultaneously confines the link noise and requires only half as many module-crossing gates as previously proposed protocols. To mitigate distance-reducing hook errors, we introduce a strategy of alternating the gate sequence between rounds of syndrome measurement, which prevents multiple hooks from simultaneously aligning with a logical operator in the code. We evaluate our protocol's performance when two logical qubits on separate modules are prepared in a logical Bell state. Circuit-level simulations under depolarizing noise show that the logical error suppression for a given entanglement rate between modules is consistently stronger compared to the best-performing alternative protocols for a wide range of link noise, with a typical 40% entanglement resource saving for a constant logical error rate. Our approach to protocol design is applicable to any quantum circuit that must be divided across processor modules and can therefore guide development of resource-efficient modular quantum computation beyond the surface code.
Quantum communication between two distant parties will serve as a cornerstone of the future quantum internet. However, generating enough entangled Bell pairs over long distances is a critical bottleneck. Although photons are ideal carriers of quantum information, overcoming photon loss and the exponential attenuation of signals remains a major challenge. We propose an all-photonic quantum repeater architecture that enables quantum communication over 1,000 km with an equidistant repeater spacing of 9 km. This repeater spacing is enabled by elementary entangled Bell pairs protected through the concatenation of continuous-variable and discrete-variable quantum error correction codes, namely, the bosonic Gottesman-Kitaev-Preskill (GKP) code and the [[7,1,3]] Steane code, whose combination yields a synergistic improvement in robustness against photon loss. This architecture incorporates a new ranking criterion and a multi-reflection mirror-based optical cavity as a free-space photonic memory module, which we model in terms of its length and mirror-reflection efficiency. Additionally, we propose two heuristic construction methods for the elementary entangled Bell pairs. One method introduces up to two-qubit correlated errors within each logical qubit but requires a large number of GKP qubits, while the other allows up to three-qubit correlated errors within each logical qubit but requires fewer GKP qubits. To more accurately capture realistic physical conditions during photonic resource preparation, we include switching-induced imperfections in our simulations, in addition to other standard optical imperfections. In the presence of these imperfections, our realization requires only a few thousand GKP qubits per repeater station per protocol run, a resource requirement significantly smaller than the corresponding resource requirements of prior third-generation all-photonic repeater proposals.