A paradigm for universal quantum information processing with integrated acousto-optic frequency beamsplitters

TL;DR

The paper proposes a paradigm for universal quantum information processing in the frequency domain using acousto-optic Frequency-transverse-mOde Operations (FRODOs). By coupling two adjacent frequency bins via phase-matched intermodal Brillouin scattering between TE0 and TE1-like modes, each FRODO yields a $2\times 2$ beamsplitter, and cascading $P=N(N-1)/2$ such layers enables any $N\times N$ unitary through an analytic Clements-based decomposition. The authors derive the transfer matrix $\mathfrak{F}(\Delta k)$ from a forward Brillouin interaction, show unitary behavior even with nonzero phase mismatch, and define a ladder of interactions with phase-mismatch parameters $\\mathcal{K}$ to realize large-scale unitaries while discussing practical implementation in CMOS-compatible platforms. Numerical simulations for random unitaries and the discrete Fourier transform up to $N=10$ demonstrate high fidelities and uniformity achievable with realistic dispersion engineering and per-layer lengths, with potential for 100% bandwidth parallelization in certain regimes. The work outlines a scalable, low-power path toward on-chip quantum information processing in the frequency domain, aided by analytic gate synthesis, potential cm-to-meter scale devices, and avenues for further optimization and materials improvements.

Abstract

Frequency-bin encoding offers tremendous potential in quantum photonic information processing, in which a single waveguide can support hundreds of lightpaths in a naturally phase-stable fashion. This stability, however, comes at a cost: arbitrary unitary operations can be realized by cascaded electro-optic phase modulators and pulse shapers, but require nontrivial numerical optimization for design and have thus far been limited to discrete tabletop components. In this article, we propose, formalize, and computationally evaluate a new paradigm for universal frequency-bin quantum information processing using acousto-optic scattering processes between distinct transverse modes. We show that controllable phase matching in intermodal processes enables 2$\times$2 frequency beamsplitters and transverse-mode-dependent phase shifters, which together comprise cascadable FRequency-transverse-mODe Operations (FRODOs) that can synthesize any unitary via analytical decomposition procedures. Modeling the performance of both random gates and discrete Fourier transforms, we demonstrate the feasibility of high-fidelity quantum operations with existing integrated photonics technology, highlighting prospects of parallelizable operations achieving 100\% bandwidth utilization. Our approach is realizable with CMOS technology, opening the door to scalable on-chip quantum information processing in the frequency domain.

Figures (5)

• Figure 1: System concept for synthesizing arbitrary frequency-bin unitaries with acousto-optic FRequency-transverse mODe Operations (FRODOs). A microring filter with a free spectral range tuned to twice the bin spacing, followed by a mode multiplexer (MM), first maps even (odd) frequency bins to TE0 (TE1) transverse modes, whose distinct group velocities (bottom) enable selective mixing by an acousto-optic field with appropriate parameters (angle and power). By cascading $N(N-1)/2$ FRODO layers---each tuned to a specific pair of bins---and multiplexing both even and odd bins back into the same spatial mode, an arbitrary $N\times N$ frequency-bin unitary can be realized.
• Figure 2: Simulation of random unitaries for $N\in\{3,4,5\}$. Kernel-density maps show fidelity $\mathcal{F}$ and success probability $\mathcal{P}$ versus per-layer interaction length $L$; solid curves overlay the DFT gate. Dashed vertical lines indicate selected phase-mismatch levels $\mathcal{K}=\Delta k_{1}L$ (see main text for parameter choices and definitions).
• Figure 3: Simulation of DFT gates up to $N=10$. Fidelity $\mathcal{F}$ and uniformity $B_c$ versus per-layer interaction length $L$, using the (a-b) analytic Clements decomposition and (c-d) after local parameter optimization. Solid markers connected by curves indicate the interaction length thresholds required to reach $\{0.99, 0.999, 0.9999\}$ for the respective metrics. The threshold is defined as the minimum length $L$ such that the metric remains above the target value for all sampled lengths $\ge L$. Note that although not explicitly shown, the success probability satisfies $\mathcal{P}>0.99$ for all cases where $\mathcal{F}\ge0.99$.
• Figure 4: Simulation of parallel frequency-bin Hadamard (beamsplitter) operations across the ladder. See main texts for details.
• Figure 5: Simulated symmetric (top) and antisymmetric (bottom) transverse mode profiles of a suspended Si rib waveguide. The color map displays $E_x$, the electric field in $\hat{x}$, as it depends on position in the $xy$-plane, given that the waveguide is translationally invariant in $\hat{z}$.