Modular architectures to deterministically generate graph states

Hassan Shapourian1 and Alireza Shabani2

1Cisco Quantum Lab, San Jose, CA 95134, USA
2Cisco Quantum Lab, Los Angeles, CA 90049, USA

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Graph states are a family of stabilizer states which can be tailored towards various applications in photonic quantum computing and quantum communication. In this paper, we present a modular design based on quantum dot emitters coupled to a waveguide and optical fiber delay lines to deterministically generate N-dimensional cluster states and other useful graph states such as tree states and repeater states. Unlike previous proposals, our design requires no two-qubit gates on quantum dots and at most one optical switch, thereby, minimizing challenges usually posed by these requirements. Furthermore, we discuss the error model for our design and demonstrate a fault-tolerant quantum memory with an error threshold of 0.53% in the case of a 3d graph state on a Raussendorf-Harrington-Goyal (RHG) lattice. We also provide a fundamental upper bound on the correctable loss in the fault-tolerant RHG state based on the percolation theory, which is 1.24 dB or 0.24 dB depending on whether the state is directly generated or obtained from a simple cubic cluster state, respectively.

Photons, elementary quantum particles of light, are one of the promising candidates for qubits in quantum information processing. They can be harnessed for fast scalable quantum computers and are the medium of choice for quantum networks. Unlike matter-based qubits which are stationary and persistent, photonic qubits are flying (at the speed of light) and consumable (they get destroyed upon measurement via a photon detector). These fundamental differences have led to the development of distinct processing methods tailored for optical quantum computing and networking, where resource states of entangled photonic qubits are prepared and various tasks are achieved by measuring the qubits. Generating such resource states, however, is quite challenging. In this paper, we propose a minimal architecture with a few devices, a quantum emitter, and a scattering block (based on quantum dots or defects) along with a delay-line feedback loop, and analyze its performance in generating some of the most common resource states.
Our architecture is modular, i.e., stacking the scattering blocks leads to devices capable of generating more sophisticated states (e.g., higher-dimensional graph states).

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[2] Daoheng Niu, Yuxuan Zhang, Alireza Shabani, and Hassan Shapourian, "All-photonic one-way quantum repeaters with measurement-based error correction", npj Quantum Information 9 1, 106 (2023).

[3] Yuan Zhan, Paul Hilaire, Edwin Barnes, Sophia E. Economou, and Shuo Sun, "Performance analysis of quantum repeaters enabled by deterministically generated photonic graph states", Quantum 7, 924 (2023).

[4] Naphan Benchasattabuse, Michal Hajdušek, and Rodney Van Meter, "Architecture and protocols for all-photonic quantum repeaters", arXiv:2306.03748, (2023).

[5] Jintae Kim, Jung Hoon Han, and Isaac H. Kim, "Fault-tolerant Quantum Error Correction Using a Linear Array of Emitters", arXiv:2403.01376, (2024).

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