Generation of 2D graph states of itinerant microwave photonic qubits with time- and frequency-domain multiplexing

Graph states are a class of multi-qubit entangled states which play a crucial role in various applications such as quantum metrology and one-way quantum computing. Recently, several protocols for generating graph states using superconducting qubits have been demonstrated [1-4]. In this work, we present a protocol to increase the dimensionality of the graph states using a system which only consists of a fixed-frequency transmon qubit and a resonator [5].

Our approach is realized by simultaneously driving two Raman processes: one between the second excited state and the ground state of the transmon, and the other between the third and first excited states. Each of these Raman processes emits an itinerant microwave photon whose frequency can be individually controlled. This generates a frequency-bin-encoded qubit when it is applied to a superposition state between the second and third excited states of the transmon.

In our experiment, we generate frequency-bin photonic qubits encoded in two co-propagating wave packets at different frequencies and characterize the fidelity of the encoding process. Using time- and frequency-domain multiplexing, we generate 2D graph states such as a multi-mode GHZ state. We also generate linear cluster states of the frequency-bin-encoded qubits, which allows the detection of photon loss during the state generation and transfer. We evaluate the entanglement among the photonic qubits by calculating the localizable entanglement. Our work provides an enabling step for generating graph states with higher dimensions in propagating microwave modes on a waveguide.

[1] J.-C. Besse et al., Nat. Commun. 11, 4877 (2020).

[2] J. O’Sullivan et al., arXiv:2409.06623 (2024).

[3] Y. Sunada et al., arXiv:2410.03345 (2024).

[4] V.-S. Ferreira et al., Nat. Phys. 20, 865(2024).

[5] T. Miyamura et al., Bulletin of the American Physical Society M53.00012 (2024).