High fidelity CNOT gates in photonic integrated circuits using composite segmented directional couplers

Abstract

Integrated photonic circuits are a promising platform for scalable quantum information processing, but their performance is often constrained by component sensitivity to fabrication imperfections. Directional couplers, which are crucial building blocks for integrated quantum logic gates, are particularly prone to such limitations, with strong dependence on geometric and spectral parameters which reduces gate fidelity. Here, we demonstrate that composite segmented directional couplers (CSDC) offer a fabrication-tolerant alternative that enhances gate fidelity without active tuning. We design and fabricate a fully integrated photonic controlled-NOT (CNOT) gate using both uniform and composite coupler variants and compare their performance via simulation, classical characterization, and quantum two-photon interference. The composite design reduces the average error probability by nearly a factor of two and decreases variability fivefold. The residual error is primarily limited by photon indistinguishability. Classical matrix reconstruction confirms improved agreement with the ideal CNOT operation. These results establish CSDCs as compact, passive, and foundry-compatible building blocks for robust scalable quantum photonic circuits.

Figures (4)

• Figure 1: Design and robustness comparison of composite and uniform directional couplers in an integrated CNOT gate.a) Schematic layout of the post-selected linear optical CNOT gate, consisting of directional couplers with $1/3$ and $1/2$ splitting ratios. The architecture requires two $1/2$ and three $2/3$ directional couplers. b) Zoom-in of a schematic conventional uniform directional coupler with a fixed cross-section. The ingoing and outgoing S-bend areas are marked as areas 1 and 3 respectively. The yellow area marked as 2 is the uniform cross-section interaction region. c) Zoom-in of a schematic composite segment directional coupler, composed of multiple segments with varying waveguide widths to implement detuned coupling. The different segments are marked as 2 and 3, and have a 2 $\mu m$ linear taper between them. d) Simulated gate error probability distribution function for $1/2$ directional couplers. This Monte Carlo simulation compares uniform (blue) and composite (orange) designs with fabrication errors distributions that follow our previous characterization, discussed in the main text. e) Same as (d), for $1/3$ directional couplers. In both cases, the composite design exhibits significantly reduced sensitivity to fabrication-induced variations in waveguide width.
• Figure 2: Quantum validation of CNOT gates implemented with uniform and composite segment directional couplers. a) The mean error probability, over all input basis states, for CNOT gates implemented with uniform (blue) and composite (orange) directional couplers. The limit of best fidelity according to indistinguishably is shown in a dashed line (more information on that in the main text). b) Error probability measured for each of the four computational basis inputs: $C_0T_0$, $C_0T_1$, $C_1T_0$, and $C_1T_1$. Error bars represent one standard deviation from repeated measurements. c-d) The probability detection matrix ofr uniform (c) and composite (d). Each bar height represents the normalized probability of detecting a coincidence in an output state for a given input state. The composite implementation shows improved agreement with the expected ideal CNOT truth table. In total, 5 CNOTs of each kind were measured.
• Figure 3: Classical validation of CNOT gate fidelity using power-only characterization.a) Power of the experimentally reconstructed transformation matrix for a representative uniform CNOT gate, after applying the Sinkhorn-based decomposition to isolate the contribution of input/output couplers. b) Corresponding power transformation matrix for the ideal CNOT operation. c) Frobenius distance between reconstructed ($P$) and ideal CNOT ($P_{ideal}$) power matrices for two designs, uniform and CSDC. Each design had nine copies. CSDC design shows smaller distance from ideal matrix, indicating improved fidelity and robustness under identical fabrication conditions.
• Figure 4: The CNOT experimental setup. Photons from a commercial SPDC source are separated and coupled simultaneously to the input ports of an integrated CNOT gate. The four outputs ports of the CNOT gates are measured using 4 cryogenic photon counters, and coincidences are extracted using a time tagger.