Monitoring the generation of photonic linear cluster states with partial measurements

TL;DR

The work reports a resource-efficient scheme for generating photonic linear cluster states via sequential entanglement in a fiber-loop memory, enabling up to 6-photon entanglement with improved rates and fidelities using a quantum-dot single-photon source. A CZ gate is effectively implemented through post-selection, with a scaling ratio of $r=46\pm5$, indicating favorable scaling compared with prior approaches. The authors introduce Partial Post-Selection (PPS) visibility measurements to monitor entanglement in real time, enabling live optimization and drift compensation during long MBQC-type experiments. Together, these advances bring photonic MBQC closer to practicality by combining high indistinguishability, manageable losses, and a diagnostic method that preserves measurement throughput. The approach remains compatible with future improvements in source efficiency and indistinguishability, potentially enabling larger cluster states beyond six photons.

Abstract

Quantum states of light with many entangled photons are key resources for photonic quantum computing and quantum communication. In this work, we exploit a highly resource-efficient generation scheme based on a linear optical circuit embedding a fibered delay loop acting as a quantum memory. The single photons are generated with a bright single-photon source based on a semiconductor quantum dot, allowing to perform the entangling scheme up to 6 photons. We demonstrate $2$, $3$, $4$ and $6$-photon entanglement generation at respective rates of $6$kHz, $120$Hz, $2.2$Hz, and $2$mHz, corresponding to an average scaling ratio of $46$. We introduce a method for real-time control of entanglement generation based on partially post-selected measurements. The visibility of such measurements carries faithful information to monitor the entanglement process, an important feature for the practical implementation of photonic measurement-based quantum computation.

Figures (8)

• Figure 1: a) The entangling scheme: input single photons are entering sequentially, being stored in the delay loop before being entangled with the next input photon on the PBS by a CZ gate realized by detection post-selection on one of its outputs. b) Experimental setup for the sequential entanglement of single photons from a quantum-dot source. A laser pulse picked by the EOM excites an InGaAs QD in a micropillar cavity, emitting single photons. The photons are entangled sequentially on a PBS connected in a fiber loop configuration. The loop system is mounted in a 19” rack-mountable 2U box, and the polarization of the propagating photons is controlled using four EPCs. The generated cluster state exits the box toward two SNSPDs. Inset: Energy level structure of the negative trion device - Red - Optical transitions of the QD - Blue - Laser drive with $H$ or $V$ polarization. Correlations between the modulated laser and the clock of the experiment, c) before and d) after the loop apparatus. The photons are distributed from the input time slot $T_0$ to several sequential time slots $T_N$ by the Hadamard gate in the loop, leading to exponential decay of the signal in d).
• Figure 2: Measured $N=2$ to $4$-photon observables, characterizing $N-$photon cluster state generation. The experimental data correspond to the symbols with smaller error bars than symbol size, and the line represents the expected behavior derived from $V_\mathrm{HOM} = 82.7\pm1.6\%$. The measured observable is in the inset for a) a $2$-photon cluster state, b) $3$-photon cluster state, c) $4$-photon cluster state for the visibility $V_4$, and d) $V_4'$.
• Figure 3: Measured $6$-photon observables with the experimental data corresponding to the symbols and the line representing the expected behavior derived from $V_{\mathrm{HOM}} = 82.7\pm1.6\%$. The observables are a) $X_{\varphi}IX_{\varphi}IX_{\varphi}Z$ corresponding to $V_6^\prime$ and b) $X_{\varphi}X_{\varphi}IX_{\varphi}X_{\varphi}Z$ corresponding to $V_6^{\prime\prime}$.
• Figure 4: Partially post-selected 2-photon observable measurement plots in a 6-photon experiment. The color corresponds to the position of the 2 photons measured within the 6-photon chain. The error bars are plotted but smaller than the marker size. The oscillations are fitted with the same function as for the 2-photon measurement ${V}_{2,\mathrm{PPS}}(\varphi) = V_{2,\mathrm{PPS}}\cos(\varphi+ \varphi_0)$. Inset: Visibility $V_{2,\mathrm{PPS}}$ of the oscillations plotted as a function of the position in the cluster state.
• Figure 5: Partially post-selected measurements of the observables a) $X_{\varphi}Z$, b) $X_{\varphi}X_{\varphi}Z$, c) $X_{\varphi}X_{\varphi}X_{\varphi}Z$, and d) $X_{\varphi}IX_{\varphi}Z$ in a 6-photon experiment. They follow the identical oscillatory behavior as $V_{2,\mathrm{PPS}}(\varphi)$, $V_{3,\mathrm{PPS}}(\varphi)$, $V_{4,\mathrm{PPS}}(\varphi)$, $V_{4,\mathrm{PPS}}^{'}(\varphi)$ with lower amplitudes than the observables shown in Fig.\ref{['fig:Visibilities']}. The dotted lines represent the fits. Inset: The black points represent the position of the photons measured in the $6$-photon cluster state.