Recirculating Quantum Photonic Networks for Fast Deterministic Quantum Information Processing

TL;DR

This work proposes a recirculating quantum photonic network (RQPN) that minimizes the duration of deterministic photonic quantum information processing by enabling all-to-all coupling among nonlinear cavities with dynamic control. Using the SLH framework and gradient-based optimal-control, the authors demonstrate a direct, all-qubit implementation of a three-qubit Toffoli gate achieving T = 2.00/χ_3 (I < 0.30%), beating decompositions by factors up to ~2.3, and they show substantial time savings for a measurement-free one-way quantum repeater using both self-phase modulation and emitter-based nonlinearities, with durations as low as T = 8.90/χ_3 (SPM) and T = 18.31/g (TLE) while maintaining low infidelity. The reported repeater schemes significantly improve hardware efficiency compared with neural-network and prior cavity-based approaches, underscoring the practical advantage of a reprogrammable, all-to-all connected architecture. The results suggest a clear path toward experimental realization using fast, tunable nonlinear cavities and integrated photonics, with future work to incorporate realistic loss and decoherence into the optimization and to explore diverse material platforms to maximize cooperativity and scalability.

Abstract

A fundamental challenge in photonics-based deterministic quantum information processing is to realize key transformations on time scales shorter than those of detrimental decoherence and loss mechanisms. This challenge has been addressed through device-focused approaches that aim to increase nonlinear interactions relative to decoherence rates. In this work, we adopt a complementary architecture-focused approach by proposing a recirculating quantum photonic network (RQPN) that minimizes the duration of quantum information processing tasks, thereby reducing the requirements on nonlinear interaction rates. The RQPN consists of a network of all-to-all connected nonlinear cavities with dynamically controlled waveguide couplings, and it processes information by capturing a photonic input state, recirculating photons between the cavities, and releasing a photonic output state. We demonstrate the RQPN's architectural advantage through two examples: first, we show that processing all qubits simultaneously yields faster operations than single- and two-qubit decompositions of the three-qubit Toffoli gate. Second, we demonstrate implementations of a measurement-free correction for single-photon loss, achieving up to seven-fold speedups and significantly improved hardware efficiency relative to state-of-the-art architecture proposals. Our work shows that a single hardware-efficient recirculating architecture substantially reduces the temporal overhead of multi-qubit gates and quantum error correction, thereby lowering the barrier to experimental realizations of deterministic photonic quantum information processing.

Figures (13)

• Figure 1: (a) Sketch of the RQPN architecture. Dynamic nonlinear cavities are coupled to a linear mixing circuit composed of Mach-Zehnder interferometers, and the network is closed by mirrors on the right. The waveguide coupling of the nonlinear cavities is controllable. (b) To capture and release photonic quantum states from the cavities, they may be opened towards the input/output channel with a controllable coupling, $\kappa(t)$ (dashed outline of the mirror). (c) When a quantum state is trapped in the cavities, the RQPN is in its recirculating configuration, with the cavities closed towards the input/output channels (solid outline of the mirrors). In this configuration, photons interact in the cavities with a nonlinear interaction rate, $\Gamma_{\rm{NL}}$, and the controllable resonances, $\omega_m(t)$, and waveguide couplings, $\kappa_m(t)$, are optimized to implement a targeted QIP task. Note that (b) and (c) illustrate the top cavity ($m=1$). Practically, we envision the nonlinear cavities having only one mirror with a controllable coupling, and the configurations in (b) and (c) to be realized using fast routers Heuck2023.
• Figure 2: Direct implementation of the three-qubit Toffoli gate with dual-rail encoding. (a) RQPN architecture with SPM nonlinearities and six cavities to encode three qubits. (b) Optimized cavity-waveguide coupling and (c) detuning for cavity $m=6$. (d) Probability of three photons occupying the same cavity, for the initial state $\ket{\psi_{\rm in}} = \ket{0,0,0}_L$. The probability of $n$ photons occupying cavity $m$ is $P(n_m) = \abs{\bra{\psi(t)}\ket{n_m}}^2$. The result was achieved using $N_{\rm{bin}}=80$, a fixed duration $T=2.0/\chi_3$, and trainable cavity-waveguide coupling, detuning, and coupling matrix $\bm{C}$. Additional information for the optimization and result is in Supplemental Material SV grovn2026supplementary, Fig. 6.
• Figure 3: Implementation of a measurement-free one-way quantum repeater using a three-mode RQPN with SPM interactions. (a) Modes 1 and 2 are used for the input state, and mode 3 contains the ancillary state. (b) The single-photon loss correction task is divided into two steps: the first corrects for loss in mode 1, and the second for loss in mode 2. Before each step, the ancilla cavity receives a single photon and is initialized to state $\ket{1_3}$. (c) Selected plots of the dynamics in step 1. The top and center panels plot the optimized waveguide coupling and detuning of the ancilla cavity ($m=3$). The bottom panel plots the expectation value of the photon number operator for the three correctable input states for the example of $\abs{\alpha}^2=\abs{\beta}^2=0.5$. (d) Selected plots of the dynamics in step 2. In the bottom panel, only the input states $\ket{C}$ and $\ket{E2}$ are relevant. Additional information for the optimization and result is in Supplemental Material SVI grovn2026supplementary, Figs. 7 and 8.
• Figure 4: Implementation of the measurement-free one-way quantum repeater using a two-mode RQPN with TLE interactions. (a) The input states are captured by the cavities, and the TLEs are used as ancillary systems by initializing them to their excited states, $\ket{A0}=\ket{e_1}\ket{e_2}$. (b)-(d) Plots of the evolution of the excited state probability of the two TLEs for input states $\ket{C}$ (b), $\ket{E1}$ (c), and $\ket{E2}$ (d). As in Fig. \ref{['fig:Repeater SPM']}, we consider the example of $\abs{\alpha}^2=\abs{\beta}^2=0.5$ in the input state. Additional information for the optimization and result, including optimized controls, is in Supplemental Material SVI grovn2026supplementary, Fig. 9.
• Figure S1: (a) Schematic illustration of the RQPN divided into blocks used to derive the Hamiltonian. (b) Corresponding SLH block diagram. Following photons through the RQPN, they start in the nonlinear cavities (blue), travel left-to-right through the linear mixing circuit (red), are reflected by the mirrors (purple), and travel back through the mixing circuit (green). The fields after one round trip are then the inputs to the nonlinear cavities, as illustrated using the lines connecting the green and blue blocks.