Deterministic and Universal Frequency-Bin Gate for High-Dimensional Quantum Technologies

TL;DR

The paper tackles the challenge of scalable, deterministic high-dimensional quantum gates by introducing a cavity-assisted sum-frequency generation (CSFG) architecture that implements an $M\times N$ frequency-bin transformation (full unitary when $M=N$) on a single fiber mode. It develops a detailed theoretical model for both the $1\times N$ and $M\times N$ gates, deriving fidelity and conversion-efficiency metrics that approach unity in the appropriate asymptotic limits and accounting for internal losses. The authors outline practical scaling estimates, showing that current technology can reach $M\times N\sim10^4$ (with $N$ up to about $10^3$) and discuss architectures that integrate SPDC sources, measurement, and fast feed-forward for applications in Gaussian boson sampling, CV quantum computation, and high-dimensional quantum communication. The proposed fiber-compatible, low-loss platform offers a realistic route to high-dimensional quantum processing across computation, communication, and sensing, with near-term experimental realizations feasible using multiple pulse shapers to extend dimensionality. $

Abstract

High-dimensional photonic systems access large Hilbert spaces for quantum information processing. They offer proven advantages in quantum computation, communication, and sensing. However, implementing scalable, low-loss unitary gates across many modes remains a central challenge. Here we propose a deterministic, universal, and fully programmable high-dimensional quantum gate based on a cavity-assisted sum-frequency-generation process, achieving near-unity fidelity. The device implements an M-by-N truncated unitary transformation (with 1 <= M < N), or a full unitary when M = N, on frequency-bin modes. With current technology, the attainable dimensionality reaches M-by-N on the order of ten to the power of four, with N up to about one thousand, and can be further increased using multiple pulse shapers. Combined with compatible SPDC sources, high-efficiency detection, and fast feed-forward, this approach provides a scalable, fiber-compatible platform for high-dimensional frequency-bin quantum processing.

Figures (8)

• Figure 1: Schematic illustration of the $1\times N$ gate. PS: pulse shaper.
• Figure 2: Amplitude of the transfer function $\tilde{g}_{\mathrm{s}}(\omega_{n},\omega_{m})$ for the $1\times N$ gate. For numerical tractability, the calculation is performed using 101 discrete frequency-bin modes. Panels (a) and (b) correspond to $\gamma/\Delta\omega=\eta^{2}/2\pi=0.01$, while panels (c) and (d) correspond to $\gamma/\Delta\omega=\eta^{2}/2\pi=0.5$. In panels (a) and (c), the pump field is encoded in a second-order Hermite–Gaussian mode, whereas in panels (b) and (d) it is encoded in the single-frequency-bin mode [$\beta(t)=1/\sqrt{T}$].
• Figure 3: FM fidelity and CE of the effective $1\times N$ gate versus $\gamma/\Delta\omega$, evaluated under the condition $\eta=\sqrt{\gamma T}$, for a second-order HG pump and an SF pump. The pink curve shows the peak achievable CE as a function of $\iota/\gamma$ in the limit $\eta=\sqrt{(\gamma+\iota)T}\to 0$.
• Figure 4: FM fidelity and CE, for a $101\times101$ gate versus $\gamma/\Delta\omega$, evaluated with respect to the ideal identity transformation under $\eta=\sqrt{\gamma T}$, using the pump $\beta(t)=-(1/\sqrt{T})\sum_{m} e^{-i(\omega_{\mathrm{p},\mathrm{c},m}-m\Delta\omega)t}$.
• Figure 5: Representative schemes for high-dimensional quantum processing using the programmable frequency-bin gate.