Coupled integrated photonic quantum memristors using a single photon source made of a colour center

TL;DR

We demonstrate a scalable network of two coupled photonic quantum memristors implemented on a silicon-nitride PIC, driven by a room-temperature SiV-color-center single-photon source. Each memristor is realized as a Mach-Zehnder interferometer whose phase-dependent reflectivity $R(t)$ is updated through measurement-based feedback, enabling non-Markovian input–output dynamics and enhanced memristive behavior. The experiments reveal non-pinched, large-area hysteresis and self-intersecting loops in inter-memristor relations, with memory depth and input phase ($T$ and $\Phi$) controlling the observed dynamics, and form factors reaching up to $F\approx 0.95$. These results establish coupled PQMs as compact nonlinear building blocks suitable for quantum neuromorphic and reservoir computing architectures on integrated photonic platforms.

Abstract

Photonic quantum memristors provide a measurement-induced route to nonlinear and history-dependent quantum dynamics. Experimental demonstrations have so far focused on isolated devices or simple cascaded devices configurations. Here, we experimentally realize and characterize a network of two coupled photonic quantum memristors with crossed feedback, implemented on a silicon nitride photonic integrated circuit and fed by a room-temperature single-photon source based on a silicon-vacancy color center SiV$^-$ in a nanodiamond. Each memristor consists of an integrated Mach-Zehnder interferometer whose transfer function is adaptively updated by photon detection events on another memristor, thus generating novel non-Markovian input-output dynamics with an enhanced memristive behaviour compared to single devices. In particular, we report inter-memristor input-output hysteresis curves exhibiting larger form factors and displaying self-intersecting loops, respectively revealing marked bistability and topologically non-trivial memory dynamics. Furthermore, numerical simulations show how these features emerge from the interplay between memory depth and relative input phase, for both intra- and inter-memristor input-output relations. Our results establish coupled integrated photonic quantum memristors as scalable nonlinear building blocks and highlight their potential for implementing compact quantum neuromorphic and reservoir computing architectures.

Figures (9)

• Figure 1: (a) The photoluminescence spectrum of the SiV$^-$ showing a sharp ZPL peak at 734 nm. In the inset, the time decay of the photoluminescence (points) and its single exponential fit (line). The fit yields a lifetime of the SiV of 1.89 ns. (b) Second order correlation data (points) of the emitted photons as a function of the time delay between the two arms of the HBT interferometer. Data are fitted by a two levels model (line) which evidences a clear photon antibunching behaviour.
• Figure 2: (a) Dual-rail scheme of the photonic quantum memristor, where the input state $\rho_{in}$ is encoded as a single photon in a superposition of the upper path modes A-B. The component in mode B is transformed by the Mach–Zehnder interferometer, implementing the photonic quantum memristor, while the component in mode A propagates freely to the output state $\rho_{out}$. The Mach-Zehnder interferometer is composed of two beam splitters (black rectangles), and a phase shifter (red rectangle). The output on mode C is used as a feedback for the phase setting of the memristor. (b) Schematic layout of the circuit implementing a single (MZI-M1) and two coupled integrated photonic quantum memristors (MZI-M1 and MZI-M2)). The red arrow on the left indicates the input waveguide, while the arrows on the right are placed to highlight the output waveguides, fiber-coupled to single-photon SPAD detectors. MZI-0, MZI-1, MZI-2 are used to prepare the suitable input state for the PQM. The input and output waveguides that are not used in the experiments are pointed out by a black oblique line.
• Figure 3: Experimental and simulation results of a single photonic quantum memristor with different ratios between the two time scales: oscillation period of the modulated input flux, $T_{\rm osc}$, and time length of the memristor's buffer, $T$. On the left, a schematic diagram of the device is shown.
• Figure 4: (a) Schematic representation of the coupled photonic memristors with crossed feedbacks whose relations are described in integral form. Eq. \ref{['eq:nest_feed_law']} shows the corresponding discrete version. (b-d) Experimental and simulation results of coupled photonic quantum memristors for different ratios $T/T_{\rm osc}$ and input phase difference $\Phi$. Both single photonic quantum memristors receive a sinusoidal input with the same period $T_{\rm osc}$ and they have the same buffer length $T$. In particular, (b) $T=0.2\,T_{\rm osc}$ and $\Phi=0.7$rad. (c) $T=0.3\,T_{\rm osc}$ and $\Phi=0.5$rad. (d) $T=0.4\,T_{\rm osc}$ and $\Phi=0.7$rad. The four panels refer to the intra (diagonal cells) and inter (off-diagonal cells) memristor relations.
• Figure 5: Simulations of the form factor $F$ of the intra- and inter-memristor hysteresis curves of two coupled photonic quantum memristors with crossed feedbacks as a function of the relative phase $\Phi$ between their inputs and the ratio $T/T_{\rm osc}$ between the buffer length of the memristors, $T$, and the period of the sinusoidal input modulation, $T_{\rm osc}$. The form factor $F$ is $4\pi$ times the ratio between the area and the squared perimeter of the hysteresis curve. The intra-relations, $(\langle N_{in}^{(1)} \rangle,\langle N_{out}^{(1)} \rangle)$ and $(\langle N_{in}^{(2)} \rangle,\langle N_{out}^{(2)} \rangle)$, are on the diagonal of the table, and the inter-relations, $(\langle N_{in}^{(2)} \rangle,\langle N_{out}^{(1)} \rangle)$ and $(\langle N_{in}^{(1)} \rangle,\langle N_{out}^{(2)} \rangle)$, are on the off-diagonal. The red symbols in the surface plots indicate the choice of parameters used in the experiments of the two coupled memristors with crossed feedback reported in Fig. \ref{['fig:coupled_mems']}: in particular, the triangle-square-circle represents the choice associated with the hysteresis curves in Fig. \ref{['fig:coupled_mems']}(b-c-d), respectively.