Deterministic generation of two-dimensional multi-photon cluster states
James O’Sullivan, Kevin Reuer, Aleksandr Grigorev, Xi Dai, Alonso Hernández-Antón, Manuel H. Muñoz-Arias, Christoph Hellings, Alexander Flasby, Dante Colao Zanuz, Jean-Claude Besse, Alexandre Blais, Daniel Malz, Christopher Eichler, Andreas J. Wallraff
Multidimensional cluster states are a key resource for robust quantum communication, measurement-based quantum computing and quantum metrology. Here, we present a device capable of emitting large-scale entangled microwave photonic states in a two dimensional ladder structure. The device consists of a pair of coupled superconducting transmon qubits which are each tuneably coupled to a common output waveguide. This architecture permits entanglement between each transmon and a deterministically emitted photonic qubit. By interleaving two-qubit gates with controlled photon emission, we generate 2 × n grids of time- and frequency-multiplexed cluster states of itinerant microwave photons. We generate states with fidelities above 0.50 for up to eight qubits and, in addition, observe nonzero localizable entanglement for states of up to 16 qubits. We expect the device architecture to be capable of generating a wide range of other tensor network states such as tree graph states, repeater states or the ground state of the toric code, and to be readily scalable to generate larger and higher dimensional states. Cluster states are a key resource in quantum technologies, but generation of large-scale 2D cluster states faces several difficulties. Here, the authors show how to generate a 2 × n ladder-like cluster state via sequential emission of time- and frequency multiplexed photonic qubits from a transmon-based device.
Multidimensional cluster states are a key resource for robust quantum communication, measurement-based quantum computing and quantum metrology. Here, we present a device capable of emitting large-scale entangled microwave photonic states in a two dimensional ladder structure. The device consists of a pair of coupled superconducting transmon qubits which are each tuneably coupled to a common output waveguide. This architecture permits entanglement between each transmon and a deterministically emitted photonic qubit. By interleaving two-qubit gates with controlled photon emission, we generate 2 × n grids of time- and frequency-multiplexed cluster states of itinerant microwave photons. We generate states with fidelities above 0.50 for up to eight qubits and, in addition, observe nonzero localizable entanglement for states of up to 16 qubits. We expect the device architecture to be capable of generating a wide range of other tensor network states such as tree graph states, repeater states or the ground state of the toric code, and to be readily scalable to generate larger and higher dimensional states. Cluster states are a key resource in quantum technologies, but generation of large-scale 2D cluster states faces several difficulties. Here, the authors show how to generate a 2 × n ladder-like cluster state via sequential emission of time- and frequency multiplexed photonic qubits from a transmon-based device.
Cluster states are a class of multiqubit entangled states with broad applications such as quantum metrology and one-way quantum computing. Here, we present a protocol to generate frequency-bin-encoded dual-rail cluster states using a superconducting circuit consisting of a fixed-frequency transmon qubit, a resonator, and a Purcell filter. We implement time-frequency multiplexing by sequentially emitting copropagating microwave photons, where each time bin contains a dual-rail qubit encoded in two distinct frequency modes, and adjacent time bins are entangled to form the cluster state. The frequency-bin dual-rail encoding enables erasure detection based on photon occupancy. We characterize the state fidelity using quantum tomography and quantify the multipartite entanglement using localizable entanglement. Our implementation achieves a state fidelity exceeding 50 % for a cluster state consisting of up to four logical qubits. The localizable entanglement remains across chains of up to seven logical qubits. After discarding the erasure errors, the fidelity exceeds 50 % for states with up to eight logical qubits, and the entanglement persists across chains of up to 11 qubits. These results highlight the improved robustness of frequency-bin dual-rail encoding against photon loss compared to conventional single-rail schemes. This work provides a scalable pathway toward high-dimensional entangled state generation and photonic quantum information processing in the microwave domain.
Realizing a fully connected network of quantum processors requires the ability to distribute quantum entanglement. For distant processing nodes, this can be achieved by generating, routing, and capturing spatially entangled itinerant photons. In this work, we demonstrate the deterministic generation of such photons using superconducting transmon qubits that are directly coupled to a waveguide. In particular, we generate two-photon N00N states and show that the state and spatial entanglement of the emitted photons are tunable via the qubit frequencies. Using quadrature amplitude detection, we reconstruct the moments and correlations of the photonic modes and demonstrate state preparation fidelities of 84%. Our results provide a path toward realizing quantum communication and teleportation protocols using itinerant photons generated by quantum interference within a waveguide quantum electrodynamics architecture.
Cluster states are useful in many quantum information processing applications. In particular, universal measurement-based quantum computation (MBQC) utilizes two-dimensional cluster states [R. Raussendorf and H. J. Briegel, Phys. Rev. Lett. 86, 5188 (2001)] and topologically fault-tolerant MBQC requires cluster states of dimension 3 or higher [R. Raussendorf et al., New J. Phys. 9, 199 (2007)]. This work proposes a protocol to deterministically generate multidimensional photonic cluster states using a single atom-cavity system and time-delay feedback. The dimensionality of the cluster state increases linearly with the number of time-delay feedbacks. We first give a diagrammatic derivation of the tensor network states, which is valuable in simulating matrix product states and projected entangled pair states generated from sequential photons. Our method also provides a simple way to bridge and analyze the experimental imperfections and the logical errors of the generated states. In this method, we analyze the generated cluster states under realistic experimental conditions and address both one-qubit and two-qubit errors. Through numerical simulation, we observe an optimal atom-cavity cooperativity for the fidelity of the generated states, which is surprising given the prevailing assumption that higher-cooperativity systems are inherently better for photonic applications.
Abstract The central technological appeal of quantum science resides in exploiting quantum effects, such as entanglement, for a variety of applications, including computing, communication and sensing 1 . The overarching challenge in these fields is to address, control and protect systems of many qubits against decoherence 2 . Against this backdrop, optical photons, naturally robust and easy to manipulate, represent ideal qubit carriers. However, the most successful technique so far for creating photonic entanglement 3 is inherently probabilistic and, therefore, subject to severe scalability limitations. Here we report the implementation of a deterministic protocol 4–6 for the creation of photonic entanglement with a single memory atom in a cavity 7 . We interleave controlled single-photon emissions with tailored atomic qubit rotations to efficiently grow Greenberger–Horne–Zeilinger (GHZ) states 8 of up to 14 photons and linear cluster states 9 of up to 12 photons with a fidelity lower bounded by 76(6)% and 56(4)%, respectively. Thanks to a source-to-detection efficiency of 43.18(7)% per photon, we measure these large states about once every minute, which is orders of magnitude faster than in any previous experiment 3,10–13 . In the future, this rate could be increased even further, the scheme could be extended to two atoms in a cavity 14,15 or several sources could be quantum mechanically coupled 16 , to generate higher-dimensional cluster states 17 . Overcoming the limitations encountered by probabilistic schemes for photonic entanglement generation, our results may offer a way towards scalable measurement-based quantum computation 18,19 and communication 20,21 .
Microwave photonic graph states provide a promising approach for robust quantum communication between remote superconducting chips using microwave photons. Recently, Besse et al. [Nat. Commun. 11, 4887 (2020)] demonstrated that 1D graph states can be generated using two transmon qubits. In this paper, we propose to use transmon qubits combined with other microwave devices to construct more complex graph states. Specifically, we consider 2D lattice and tree-like graph states. We compare the performance using fixed- versus tunable-frequency transmon qubits and also for different photonic qubit encodings. In each case, we estimate the fidelity of the resulting microwave graph state assuming current experimental parameters and identify the main factors that limit performance.