A collaborative research group consisting of quantum information scientists from Quandela, the Center for Theoretical Physics of the Polish Academy of Sciences, and the University of Warsaw has experimentally demonstrated a scalable physical Quantum Machine Learning (QML) architecture. Supported by the European Union’s Horizon Europe QUONDENSATE Pathfinder project, the team utilized a programmable silicon photonic Quantum Processing Unit (QPU) excited by single-photon states to perform both classical machine learning classification and intrinsically quantum information processing tasks.
Crucially, the hardware deployment introduces a practical method to overcome exponential scaling bottlenecks in quantum state characterization by successfully executing complete quantum state tomography and multi-mode entanglement tracing using a single, fixed measurement basis.
[ Multimode Fock States ] ──► [ Programmable Silicon MZI Matrix (Belenos QPU) ]
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[ Software Linear Readout Layer ] ◄── [ Photon-Number-Resolving (PNR) Detectors ]
Quantum Reservoir Processing via Unitary Photonic Matrices
The experimental setup leverages the physical principles of Quantum Reservoir Computing (QRC)—specifically configured as a Quantum Reservoir Processing (QRP) network. In a physical QML framework, complex non-linear mathematical transformations are executed natively via hardware-level quantum dynamics rather than mapped as digital computing code. The non-trainable “reservoir” consists of a universal Bell-Walmsley interferometer mesh fabricated on a compact silicon chip, featuring a dense network of integrated optical waveguides, mode couplers, and thermo-optically controlled thermal phase shifters.
To process information, single-photon pulses generated on demand by a semiconductor quantum dot embedded in a micropillar cavity are routed through a 12-mode active demultiplexer and injected into Quandela’s 24-mode Belenos QPU chip as a non-classical multimode state. As photons propagate through the programmable Mach-Zehnder Interferometer (MZI) array, they undergo complex transformations driven by quantum interference. The output states are mapped by polarization-resolved Photon-Number-Resolving (PNR) detectors paired with an electronic correlator. This allows the system to construct a 15-element feature vector from multi-photon coincidence probability distributions, bypassing the binary limits (0 or 1 photon) of standard threshold detectors.
[ Tomography Scaling Topologies ]
Standard State Tomography ──► Exponential measurement arrays executed across varying bases.
Photonic QRP Protocol ──► Unitary cross-mode interference captured via a single, fixed basis.
Single-Basis Quantum Tomography and Feature Extraction Metrics
The QRP platform was benchmarked directly against a standard PNR setup to execute quantum state tomography on a multi-mode, two-photon mixed density matrix. In standard quantum tomography architectures, reconstructing a complex quantum state requires an exponential number of physical measurements performed across multiple distinct measurement bases. The QRP framework bypasses this scaling trap by utilizing a single, fixed random unitary transformation matrix to map multi-mode quantum correlations into traceable photon-counting signatures.
To generate the mixed target states, an initial two-photon state was processed through a state preparation unitary acting over specific modes. Mixedness was subsequently introduced by tracing out and discarding ancillary modes, forcing a block-diagonal reduced density matrix structure.
The empirical coincidence counts collected from the hardware were fed into a classical multi-output ridge regression software layer utilizing regularization to map the linear relationships. The model reconstructs the initial matrix, enforces Hermiticity, and projects the negative components of the resulting spectrum onto a probability simplex to guarantee semi-positivity.
[ Experimental Reconstruction Performance ]
Pure PNR Benchmark Baseline ──■■■■■■■■ Mean Fidelity = 0.747 (Fails to capture off-diagonal coherences)
Photonic QRP Hardware Core ──■■■■■■■■■■ Mean Fidelity = 0.820 (Recovers full phase and state structures)
The hardware-executed QRP architecture achieved a mean testing dataset fidelity of 0.820, distinctly outperforming the baseline PNR benchmark (0.747), which systematically failed to resolve off-diagonal phase coherences due to a lack of optical interference. From this reconstructed density matrix, the software extracted three fundamental quantum metrics with high precision: Purity, von Neumann Entropy, and Negativity (a rigorous measure of quantum entanglement).
Furthermore, the team mapped the circuit’s scaling properties, proving that the dimension of the required feature space scales quadratically with the target state’s mode count, establishing a sustainable blueprint for 3-mode (45 independent parameters) and larger multi-mode state characterization.
Hardware-Aware Regularization and Perturbation Mitigation Loops
To expand the platform’s utility to classical data processing, the researchers mapped a non-linear binary classification task—resolving intertwined dual-spiral data points—on Quandela’s legacy 12-mode Ascella processor. Real-world silicon hardware is inherently degraded by micro-scale fabrication variations, thermal drifts, and transpilation bugs, creating an operational divergence between idealized digital simulations and physical hardware execution.
[ Classical Coordinates (x,y) ] ──► [ Dual-Rail QPU Encoding ] ──► [ Unitary Perturbation Loop ]
To bridge this gap, the team engineered a hardware-aware in-silico training framework. During the classical optimization cycle of the software readout layer, the ideal simulation reservoir matrix was intentionally injected with a random, sample-specific unitary perturbation matrix containing localized fluctuations. This perturbation layer acts as a physical regularization code, training the software readout network to maintain functional elasticity when subjected to localized hardware variations.
By running the optimization loop at a perturbation amplitude directly matching the physical chip’s measured transpilation error, the physical hardware achieved an experimental classification accuracy of roughly 79.7%. This outpaced an identical, idealized classical simulation network processing coherent state inputs and mean intensity counts, demonstrating a clear path toward localized error mitigation in current optical networks.
The full peer-reviewed proofs, error mitigation logs, and Hilbert space scaling calculations can be analyzed in the complete Preprint Research Paper here, with high-level corporate research roadmaps and neuromorphic development goals tracked via the Quandela Science Blog here.
June 26, 2026
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