A universal fully reconfigurable 12-mode quantum photonic processor

The heart of our photonic processor is a reconfigurable photonic integrated circuit based on stoichiometric silicon nitride (Si₃N₄) waveguides with the TripleX technology [31]. Thanks to the chosen material platform, we achieve propagation losses as low as 0.1 dB cm⁻¹ with a minimum bending radius of 100 μm. The waveguide cross-section used in the photonic processor is an asymmetric double-stripe (ADS) [31] as shown in figure 1(a). The waveguides are designed for single-mode operation at a wavelength of 1550 nm. ADS waveguides enable low-loss coupling to standard telecom fibers using spot-size converters, where the upper silicon nitride stripe is removed by adiabatic tapering [31].

The reconfigurability of the photonic processor is achieved by exploiting the thermo-optic effect via resistive heating of 1 mm-long platinum phase shifters (PSs). Using these thermo-optic PSs, a π phase shift is achieved at V_π ≅ 10 V, corresponding to an electric power of ∼385 mW per element.

The functional design of our processor is presented in figure 1(b). An optical unit cell, composed of a tunable beam splitter (TBS) (blue line) and a PS (red line) on the bottom output mode, is repeated 66 times over a square topology of 12 input/output modes ³ and circuit depth of 12. The circuit depth is defined as the maximum number of unit cells that an input mode encounters in the propagation direction of light. Twenty-four additional PSs are distributed across the inputs and outputs for sub-wavelength delay compensation and external phase tuning. In total, the processor contains 156 PSs. The TBSs are implemented by Mach–Zehnder interferometers (MZI) consisting of two 50:50 directional couplers (black lines in figure 1(b)) and an internal PS, θ, followed by an external PS, ϕ, at the bottom output mode. Each unit cell represents a node of the large-scale interferometer where light can interfere [1, 25, 26, 37].

The photonic processor presented above is embedded in a control box that includes electronic and temperature control modules (figures 1(c) and (d)). The reconfigurable photonic integrated circuit is optically packaged with polarization-maintaining (PM) fiber arrays for the in- and out-coupling of light. For ease of access the input and output fibers are fixed to the front panel of the control box via PM mating sleeves. We measure an average loss for the 24 PM mating sleeves of about 0.18 dB/connector.

A printed circuit board (PCB) was fabricated and wire-bonded to the photonic processor. A total of 132 voltage drivers are connected to the PCB enabling the independent tuning of each thermo-optic PS, achieved via serial communication with a standard pc.

Temperature control and stability of the processor is achieved by active cooling. A thermo-electric Peltier element is placed beneath the sub-mount of the packaged processor, i.e., a metallic mount holding the processor, the fiber arrays and the PCB. The Peltier element favors the heat transfer in the vertical direction, from the on-chip PSs to the heat-sink. To further increase the cooling capacity of the system, water cooling can also be installed.

The optical amplitude transmission through our photonic processor is given by ${E}_{\text{out}}=\tilde {S}\enspace {E}_{\mathrm{i}\mathrm{n}}$. The matrix $\tilde {S}$ is given by the product of two-mode matrices S_m,n of each unit cell between mode m and n. Considering a unit cell as in figure 1(b) with pairs of ideal and symmetric 50:50 directional couplers (k = 0.5), we find that

$$\begin{equation*}{S}_{\mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t}{\_}\mathrm{c}\mathrm{e}\mathrm{l}\mathrm{l}}\left(\theta ,\phi \right)=\frac{1}{2}\left(\begin{matrix}\hfill 1-{\mathrm{e}}^{-\mathrm{i}\theta }\hfill & \hfill -\mathrm{i}({\mathrm{e}}^{-\mathrm{i}\theta }+1)\hfill \\ \hfill -\mathrm{i}({\mathrm{e}}^{-\mathrm{i}\theta }+1){\mathrm{e}}^{-\mathrm{i}\phi }\hfill & \hfill -(1-{\mathrm{e}}^{-\mathrm{i}\theta }){\mathrm{e}}^{-\mathrm{i}\phi }\hfill \end{matrix}\right).\end{equation*}$$

Rewriting the unit cell in terms of sine and cosine we find for the two-mode matrix of the full system

$$\begin{equation*}{S}_{m,n}\left(\theta ,\phi \right)=\left(\begin{matrix}\hfill 1\hfill & \hfill 0\hfill & \hfill \dots \hfill & \hfill \dots \hfill & \hfill \dots \hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill \ddots \hfill & \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill {\vdots}\hfill \\ \hfill {\vdots}\hfill & \hfill \hfill & \hfill {\mathrm{e}}^{-\mathrm{i}(\theta -\pi )/2}\enspace \mathrm{sin}\enspace \frac{\theta }{2}\hfill & \hfill -{\mathrm{e}}^{-\mathrm{i}(\theta -\pi )/2}\enspace \mathrm{cos}\enspace \frac{\theta }{2}\hfill & \hfill \hfill & \hfill {\vdots}\hfill \\ \hfill {\vdots}\hfill & \hfill \hfill & \hfill -{\mathrm{e}}^{-\mathrm{i}(\theta -\pi )/2}\enspace {\mathrm{e}}^{-\mathrm{i}\phi }\enspace \mathrm{cos}\enspace \frac{\theta }{2}\hfill & \hfill -{\mathrm{e}}^{-\mathrm{i}(\theta -\pi )/2}\enspace {\mathrm{e}}^{-\mathrm{i}\phi }\enspace \mathrm{sin}\enspace \frac{\theta }{2}\hfill & \hfill \hfill & \hfill {\vdots}\hfill \\ \hfill {\vdots}\hfill & \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill \ddots \hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill \dots \hfill & \hfill \dots \hfill & \hfill \dots \hfill & \hfill 0\hfill & \hfill 1\hfill \end{matrix}\right),\end{equation*}$$

where θ is the internal phase of the MZI and ϕ is the external phase. By varying θ and ϕ over 2π it is possible to perform any transformation in the special unitary group, SU(2). It is important to note that the action of the processor is always described by the same classical transmission matrix S independently of the nature of the input state, i.e., either classical electric field amplitudes, photon-number states or other quantum states of light. Therefore, to know the transmission matrix, it is sufficient to characterize the processor classically. In the case of quantum input light, the formalism becomes ${\hat{a}}_{\text{out}}=\tilde {S}{\hat{a}}_{\mathrm{i}\mathrm{n}}$ where now the transmission matrix relates the ladder operators instead of classical electric field amplitudes [32].

The combination of quadratically many S_m,n allows the implementation of any complex-valued unitary transformation U. We can decompose any arbitrary unitary transformation U into sets of (θ, ϕ)_m,n belonging to specific unit cells between mode m and n of our processor [25, 26]. Assigning these (θ, ϕ)_m,n to the corresponding transmission matrix S_m,n and multiplying them in the order of light propagation through the processor, the exact optical response corresponding to U will be reproduced.

For classical characterization of the processor we use a CW diode laser at 1550 nm (2 mW output power—Thorlabs LP1550 PAD2). A PM fiber switch can be used to facilitate the procedure of characterization switching the input light across all the 12 inputs. For intensity measurements we use a set of InGaAs photodiodes each mounted on an FC/PC bulkhead (Thorlabs FGA01FC) (figure 2(a)). The output signal of the QuiX hardware, impinging on the PD array, is acquired and read out via an NI BNC-2090A and USB-6211 card.

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For quantum characterization a 2 mm ppKTP crystal emitting collinear frequency-degenerate cross-polarized single-photon pairs is pumped with a Ti:sapphire (Tsunami, Spectra Physics) mode-locked laser with a center wavelength of 775 nm. Coupling between the light source and the QuiX hardware is done via polarization maintaining fibers. The photons at the output of the chip are detected with superconducting nanowire single-photon detectors (SNSPD).

The classical characterization of the processor comprises the calibration of all the tunable elements and the total transmission of the processor, as shown in figures 3(a)–(c). Specific measurement protocols are used to characterize the TBS and PSs.

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In figure 3(a) we show the calibration of one of the on-chip heaters as, for example, the one belonging to a TBS. Both outputs of the TBS are monitored while only the internal phase θ is varied (inset figure 1(b)). This is done by applying a varying voltage, V, to the thermo-optic PS. The same procedure is adopted for characterizing the PSs. By following a specific order, we characterize the entire processor and find that all the 132 thermo-optic PSs are tunable over more than 2π phase range with high extinction ratio. In this way, we achieve full control over the processor.

In figure 3(b), we report the insertion loss matrix of the processor. The insertion loss matrix includes both the fiber-to-chip-to-fiber coupling losses and the on-chip propagation loss. It excludes thus the aforementioned connector loss of 0.18 dB/connector. The reader can clearly see that there is one input channel that shows higher losses than the others. This is confirmed by inspection of one of the fibers, which turned out to be damaged. The optimal transmission for this input channel can be easily retrieved by exchanging the damaged fiber. On average, excluding the damaged channel, the processor shows an insertion loss of ∼5 dB where ∼0.8 dB comes from propagation loss and the remaining ∼4.2 dB are coupling losses.

Finally, to confirm the universality and control of the processor, we perform a large variety of 12 × 12 unitary transformations as summarized in figures 3(c)–(e). For each target transformation U_i , we measure the corresponding experimental output intensity distribution |U_exp|². We compare the experimental results, normalized to the input\output coupling efficiency, with the target intensity output distribution |U_i |² via the fidelity ${\mathcal{F}}_{i}=\frac{1}{D}\enspace \mathrm{Tr}(\vert {U}_{i}^{{\dagger}}\vert \cdot \vert {{U}_{\mathrm{exp}}\enspace }^{\mathrm{norm}}\enspace \vert )$, where D is the dimension of the unitary transformation and of our processor, i.e., D = 12. Note that the calculated fidelity is an amplitude fidelity therefore not taking into account the phases of the unitary transformation elements.

We perform unitary transformations spanning various applications such as permutation (P), Haar-random matrices, high-dimensional Pauli-X gates (X) and optical switching matrices (S). Furthermore, to ultimately illustrate our full control over our processor we implement the letters Q and X of our company name QuiX.

In figure 3(c), we report, as an example, the target (theory) P_th, X_th and S_th matrix (top row from left to right) and their corresponding experimental implementations (bottom row). Figure 3(d) shows the fidelity distribution of 1000 Haar random unitaries. We note that an increase in the complexity of the optical transformation is associated with a decrease in fidelity, as is natural to expect. Since, by definition, Haar matrices cover the space of unitary transformations in a uniform way, we expect the fidelity for this set to be representative for an arbitrary transformation. Finally, figure 3(e) reports the measurements of the first and last letter of the company name QuiX. The results are summarized in table 1.

Table 1. Summary of measured fidelities.

	#	${\mathcal{F}}_{\text{ave}}{\pm}\sigma$
Random perm	12	0.930 ± 0.013
Pauli-Xn=0,…,12	12	0.945 ± 0.007
Switching	12	0.985 ± 0.006
Haar random	1000	0.904 ± 0.024
Logo	2	0.926 ± 0.004

After having demonstrated full control of the processor via the classical response characterization, we attach the QuiX hardware to the quantum light source as shown in figure 2(b). Quantum interference experiments were performed across the whole photonic processor evaluating to what extent the processor preserves the indistinguishability of the input single photons. This measurement tests all sources of induced distinguishability on the single photons, such as path-dependent dispersion.

The single-photon source is characterized separately by running a Hong–Ou–Mandel (HOM) [33] interference experiment over a tunable fiber splitter that gives a visibility of 0.93. By choosing inputs pairwise, we run HOM interference experiments on every single TBS on the processor (figure 4). The average visibility of the on-chip HOM interference dips is calculate as ${\mathrm{v}\mathrm{i}\mathrm{s}}_{\text{ave}}=\sum _{n}\enspace \begin{matrix}\hfill \frac{{\left(1-\frac{{\mathrm{c}\mathrm{c}}_{\text{ind}}}{{\mathrm{c}\mathrm{c}}_{\mathrm{dist}}}\right)}_{n}}{{n}_{\text{tot}}}\hfill \end{matrix}$ where n_tot = 66, where cc_ind/dist is the coincidence count rate for indistinguishable or distinguishable photons (as indicated in figure 4). We obtain an average visibility of vis_ave = 0.923. We observe from figure 4(c) that the distribution of the HOM visibility is rather random across the UMI confirming the absence of any systematic error in the processor. Some TBSs, e.g., #136, 140 and 145, present a low visibility of the quantum interfere: this is due to an imperfectly optimized 50:50 splitting ratio setting of these TBSs, which reduces the HOM visibility.

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Comparing the reference HOM dip visibility measured outside the chip of ∼93% and the measured average on-chip visibility we can conclude that the processor does not affect the spectral-temporal indistinguishability of the signal and idler photons coming from the single-photon source. The on-chip visibility is ultimately limited by the source itself.