Scalable Memory Sharing in Photonic Quantum Memristors for Reservoir Computing

Although photons are robust, room-temperature carriers well suited to quantum machine learning, the absence of photon-photon interactions hinder the realization of memory functionalities that are critical for capturing long-range context. Recently, measurement-based implementations of photonic quantum memristors (PQMRs) have enabled tunable non-Markovian responses. However, their memory remains confined to local elements, in contrast to biological or artificial networks where memory is shared across the system. Here, we propose a scalable PQMR network that enables measurement-based memory sharing. Each memristive node updates its internal state using the history of its own and neighbouring quantum states, thereby realizing distributed memory. By modelling each node as a photonic quantum memtransistor, we demonstrate pronounced enhancements in both classical and quantum hysteresis at the device level, as well as enhanced network-level quantum hysteresis. Implemented as a quantum reservoir, the architecture achieves improved Fashion-MNIST classification accuracy and confidence via increased data separability. Our approach paves the way toward high-capacity quantum machine learning using memristive devices compatible with linear-optical quantum computing.

💡 Research Summary

The paper addresses a fundamental limitation of photonic quantum memristors (PQMRs): their memory is confined to individual devices, preventing the long‑range context capture that is essential for many machine learning tasks. The authors propose a scalable architecture in which each memristive node updates its internal state not only from its own measurement history but also from the histories of neighboring nodes. This “memory‑sharing” is realized through a measurement‑based feedback loop that routes indirect measurement outcomes from adjacent ports into a gating function.

To formalize the concept, the authors introduce the photonic quantum mem‑transistor (PQMT) model. Starting from the original PQMR update rule (Eq. 1), they add a second input port E and a gate port F. The transmission of a PQMT is given by Eq. 2:
(T_{\text{PQMT}}(t)=T_{\text{PQMR}}(t)-f_{\text{mod}}(t),d,\tau_{\text{int}},\int_{t-\tau_{\text{int}}}^{t}!\langle n_E(\tau)\rangle d\tau),
where (f_{\text{mod}}) is a sigmoid‑shaped gating function parameterized by an inflection point p and a memory‑sharing strength d. When d = 0 the device reduces to a conventional PQMR; increasing d turns the gate on and couples the device’s transmission to the neighboring measurement record.

Device‑level simulations use a sinusoidally varying input state (Eq. 3) and evaluate hysteresis loops for both the classical observable ⟨n_C⟩ versus ⟨n_A⟩ and the quantum coherence γ_C versus γ_A. As d grows, the contrast and area of both loops increase dramatically. Notably, the quantum coherence loop retains its area even though overall transmission drops, indicating that memory sharing amplifies non‑linear quantum response without sacrificing coherence.

At the network level, N PQMTs are arranged in parallel with cyclic gate coupling: the D‑port of node q + 1 (or D₁ for the last node) feeds the gate of node q. This creates a shared history across the array. Multi‑mode inputs are constructed from superpositions of low‑photon‑number Fock states (≤ 2 photons). The authors plot the multimode coherence hysteresis γ_in‑γ_out for different d values, showing that larger d yields a larger hysteresis area S_γ. The dependence of S_γ on the memory‑window ratio τ_int/τ_osc is examined; while S_γ oscillates with τ_int/τ_osc due to the periodic drive, it is systematically higher for d > 0, especially when τ_int/τ_osc > 0.5. This demonstrates that the enhancement observed at the single‑device level survives in a full network.

The architecture is then embedded in a quantum reservoir computing (QRC) framework. A random Haar unitary circuit precedes and follows a layer of nine PQMTs (Fig. 4b). Fashion‑MNIST images are encoded column‑wise into time‑varying Fock‑state superpositions, injected sequentially into the reservoir. After the final column, the reservoir output (the set of transmittances T_i from each PQMT) is measured and fed to a linear classifier.

Two key performance metrics are reported: (1) data separability, quantified by the average L₂ distance ⟨L_T⟩ between transmittance vectors of different images; (2) a combined accuracy‑confidence score for a three‑class Fashion‑MNIST task. As the memory‑sharing strength d increases, ⟨L_T⟩ grows substantially, indicating that the shared‑memory reservoir explores a larger portion of Hilbert space and separates classes more effectively. Correspondingly, both classification accuracy and confidence more than double compared with the baseline d = 0 (the original PQMR).

The authors discuss extensions: more complex graph topologies (higher node degree, bidirectional links, random or small‑world networks), integration of modal‑mixing techniques (fractional Fourier transforms, synthetic‑dimensional matrices), and the possibility of leveraging light‑matter interactions to embed additional degrees of freedom in each port. These avenues could further increase memory capacity and task‑specific performance.

In summary, the paper presents a measurement‑based, globally shared memory scheme for photonic quantum memristors, formalizes it through the PQMT model, validates enhanced hysteresis at both device and network scales, and demonstrates a concrete advantage in quantum reservoir computing on a benchmark image‑classification task. The work establishes a practical pathway toward high‑capacity, non‑Markovian quantum machine learning using linear‑optical platforms.