Quantized Neurons

• Quantized neurons are neural units defined by discrete states, parameters, or responses, enabling efficient low-precision computation across various hardware substrates.
• They span multiple traditions—from fixed-point deep learning and spiking neuromorphic designs to optical phase modulators and quantum-mechanical constructs—with each approach addressing unique design challenges.
• Practical strategies like mixed-precision scheduling and repair techniques balance reduced memory footprint, hardware constraints, and regularization, improving performance in real-world applications.

Quantized neurons are neural units whose state, parameters, responses, or governing operators are constrained to discrete sets rather than unconstrained continuous values. In contemporary research, the term spans several non-equivalent traditions: low-bit electronic neurons in quantized neural networks, spiking and neuromorphic neurons implemented with fixed-point state updates or multi-level spikes, optical neurons with discretized phase or amplitude settings, and quantum-mechanical constructions in which neurons are represented by qubits, roots of unity, Hamiltonians, or quantum particles (Chu et al., 2019, Kariyawasam et al., 2023, He et al., 6 Jul 2026). The shared theme is discretization, but the substrate, training procedure, and meaning of “quantization” differ substantially across these literatures.

1. Terminology and conceptual scope

The literature uses “quantized neurons” in at least four distinct senses. In mainstream deep learning, quantization usually means that weights, biases, and sometimes activations are represented with finite bitwidth and processed with fixed-point or bitwise arithmetic. In optical computing, quantization refers to bounded and discrete physical settings of optical neurons, such as phase values in diffractive layers. In spiking and neuromorphic systems, quantization may refer to fixed-point membrane states, discretized spike phases, or multi-level burst outputs. In quantum machine learning and quantum neuromorphics, it may refer either to qubit-based neuron constructions or to canonical quantization of a neuron’s energy function into a Hamiltonian observable (Chu et al., 2019, Kariyawasam et al., 2023, Matinizadeh et al., 2024, AlMasri, 2023).

Usage	Quantized object	Representative papers
Electronic QNN	Weights, biases, activations	(Chu et al., 2019, Song et al., 2023)
Spiking / neuromorphic	Membrane states, spike phase, burst levels, fixed-point synapses	(Bezugam et al., 2024, Matinizadeh et al., 2024, Bai et al., 28 Apr 2026, Moyal et al., 2024, S et al., 2024)
Optical / photonic	Phase or amplitude settings of optical neurons	(Kariyawasam et al., 2023)
Quantum / quantum-inspired	Qubit states, roots of unity, Hamiltonians, quantum particles, memristive quantum circuits	(Cao et al., 2017, Barney et al., 19 Mar 2025, He et al., 23 May 2026, Brand et al., 26 Jun 2025)

A recurrent source of ambiguity is that “quantized” can denote low numerical precision or genuine quantum-mechanical quantization. One paper explicitly distinguishes standard machine-learning quantization from neurons that are “genuinely quantum-mechanical—quantized degrees of freedom with path-integral dynamics, tunneling, and thermal fluctuations” (Dorozhinsky et al., 2018). Another body of work instead treats quantization as canonical quantization: a classical neuron is written as an activation applied to an energy function, then the energy is replaced by a quantum Hamiltonian and the activation is applied by matrix functional calculus (He et al., 6 Jul 2026).

2. Low-precision electronic quantized neural networks

In the low-precision deep-learning literature, a quantized neuron is typically a neuron whose weights and/or activations are drawn from a finite set of levels, enabling reduced memory footprint and cheaper arithmetic. A canonical formulation represents binary weights through a learned scale,

$$x_b = B(x) = \frac{\lVert x \rVert_1}{n}\,\mathrm{sign}(x),$$

and handles the non-differentiability of binarization with a straight-through estimator,

$$\frac{\partial L}{\partial x} \approx \frac{\partial L}{\partial x_b}\cdot \mathbb{I}\{|x|<1\}.$$

For $k>1$, a uniform quantizer on $[0,1]$ is used,

$$Q_k(x)=\frac{1}{2^k-1}\left\lfloor (2^k-1)x \right\rceil,$$

again trained with straight-through backpropagation (Chu et al., 2019).

A central result is that quantization need not be homogeneous across depth. In "Mixed-Precision Quantized Neural Network with Progressively Decreasing Bitwidth For Image Classification and Object Detection" (Chu et al., 2019), the assigned weight precision decreases stage-by-stage with depth, motivated by the observation that posterior layers operate on progressively more separable features. Representative schedules include VGG-7 with weights $$8\rightarrow4\rightarrow2\rightarrow1\rightarrow1\rightarrow1$$, ResNet-20 with $4\rightarrow2\rightarrow1$ or $8\rightarrow4\rightarrow2$, and AlexNet or ResNet-18 with $8\rightarrow4\rightarrow2\rightarrow1$. The paper reports that such mixed-precision schedules can reduce parameter memory by more than 30\% relative to homogeneous counterparts while maintaining or improving accuracy, and further reports that higher-precision bottom layers appreciably improve 1-bit networks whereas lower-precision posterior layers can act as a regularizer in $k$-bit networks (Chu et al., 2019).

This depth-aware view yields a more specific notion of a quantized neuron: quantization level becomes part of the neuron’s allocated representational capacity. The paper’s weight-quantization pipeline also applies $$\frac{\partial L}{\partial x} \approx \frac{\partial L}{\partial x_b}\cdot \mathbb{I}\{|x|<1\}.$$0 and per-output-channel normalization before uniform quantization, and notes that per-channel scaling can be folded into batch normalization so inference remains integer-only. On CIFAR-10, mixed-precision VGG-7 with average 1.06-bit weights and 2-bit activations achieved 93.22\%, versus 92.33\% for homogeneous 1/2-bit DoReFa and 92.48\% full precision; on ImageNet, mixed ResNet-18 with average 1.42-bit weights and 2-bit activations reached 65.03\% Top-1, outperforming DoReFa 2/2 at 62.60\% and PACT 2/2 at 64.40\% (Chu et al., 2019).

A distinct but related problem is that quantization can create a small set of pathological neurons whose activation status differs from that of the full-precision model. "QNNRepair: Quantized Neural Network Repair" (Song et al., 2023) formalizes this failure mode. It models affine quantization as

$$\frac{\partial L}{\partial x} \approx \frac{\partial L}{\partial x_b}\cdot \mathbb{I}\{|x|<1\}.$$1

and identifies neurons whose ReLU activation state flips after quantization. Statistical fault localization metrics such as Tarantula, Ochiai, Jaccard, Euclid, and Wong3 are used to rank suspicious neurons, after which an LP/MILP adjusts incoming quantized weights so that failing tests recover the full-precision activation sign while perturbations remain bounded. The paper reports that repaired models achieve 24\% higher accuracy than SQuant’s on the independent validation set, especially for ImageNet, and gives MobileNetV2 results improving from 65.86\% to 70.77\% on ImageNet after repair (Song et al., 2023). This suggests that, in practical deployment, quantized neurons are not merely lower-precision surrogates of floating-point neurons; they can become distinct error loci that require post-quantization diagnostics and correction.

3. Quantized spiking and neuromorphic neurons

In spiking systems, quantization is often imposed on membrane states, synaptic weights, spike timing, or spike amplitude. A particularly hardware-oriented example is the quantized Context-Dependent LIF neuron, qCLIF, which retains a two-compartment structure—apical context and somatic stimulus—but replaces analog multiplications in the input path with digital spike-weighting through bitwise AND and integer addition (Bezugam et al., 2024). Its discrete-time update is

$$\frac{\partial L}{\partial x} \approx \frac{\partial L}{\partial x_b}\cdot \mathbb{I}\{|x|<1\}.$$2

$$\frac{\partial L}{\partial x} \approx \frac{\partial L}{\partial x_b}\cdot \mathbb{I}\{|x|<1\}.$$3

with a hard reset when threshold $$\frac{\partial L}{\partial x} \approx \frac{\partial L}{\partial x_b}\cdot \mathbb{I}\{|x|<1\}.$$4 is exceeded. Implemented in 45 nm, a single 8-bit qCLIF occupies approximately $$\frac{\partial L}{\partial x} \approx \frac{\partial L}{\partial x_b}\cdot \mathbb{I}\{|x|<1\}.$$5 and the paper reports 90\% accuracy on DVS Gesture despite 8 bit quantization, with scalability to 82k synapses in a $$\frac{\partial L}{\partial x} \approx \frac{\partial L}{\partial x_b}\cdot \mathbb{I}\{|x|<1\}.$$6 footprint (Bezugam et al., 2024).

A broader digital framework is QUANTISENC, which exposes neuron precision directly as a configurable hardware parameter. Here, LIF neurons with current-based synapses operate in signed fixed-point $$\frac{\partial L}{\partial x} \approx \frac{\partial L}{\partial x_b}\cdot \mathbb{I}\{|x|<1\}.$$7 format, and the membrane update is implemented as

$$\frac{\partial L}{\partial x} \approx \frac{\partial L}{\partial x_b}\cdot \mathbb{I}\{|x|<1\}.$$8

The architecture supports multiple reset modes, configurable refractory periods, all-to-all, one-to-one, and Gaussian connectivity, and uses distributed synaptic memory to sustain pipelined execution (Matinizadeh et al., 2024). In the reported configurations, Q5.3 offered the best area–power–accuracy trade-off on MNIST, reaching 96.5\% hardware accuracy with RMSE 0.43 mV relative to software, while Q9.7 achieved 97.1\% and Q3.1 dropped to 88.3\% (Matinizadeh et al., 2024). In this setting, a quantized neuron is literally a digital arithmetic datapath whose numerical format determines spike timing fidelity, saturation behavior, and power.

More recent work shifts from binary spikes to multi-level spike outputs. QB-LIF interprets burst spiking as saturated uniform quantization of membrane potential with a learnable per-layer scale,

$$\frac{\partial L}{\partial x} \approx \frac{\partial L}{\partial x_b}\cdot \mathbb{I}\{|x|<1\}.$$9

with emitted amplitude $k>1$0 (Bai et al., 28 Apr 2026). The learned scale is absorbed into downstream weights during inference so execution remains accumulate-only. The paper reports consistent gains over binary and fixed-burst SNNs under short horizons, including 95.40\%, 96.21\%, and 96.43\% on CIFAR-10 with ResNet-20 at $k>1$1, and 73.14\% on ImageNet with ResNet-34 at $k>1$2 (Bai et al., 28 Apr 2026). Here the quantized neuron is no longer defined by low precision alone, but by its controlled discrete information throughput per timestep.

Another line of work uses quantization to regularize activity rather than merely compress arithmetic. In a bio-inspired olfactory model, analog ET activations are first $k>1$3-normalized so that

$k>1$4

then mapped to duplicated spiking principal neurons with heterogeneous ET$k>1$5MC gains (Moyal et al., 2024). Each duplicated MC neuron spikes iff

$k>1$6

and spike phase is quantized into 50 bins per oscillation cycle. The paper shows that, with heterogeneous gains chosen to emulate uniformly spaced effective thresholds, the fraction of active MCs is approximately yoked to network constants,

$k>1$7

which regularizes layer utilization under open-set concentration and saturation variability (Moyal et al., 2024). This is a distinct meaning of a quantized neuron: the neuron becomes a discretized phase encoder with deliberately heterogeneous transfer characteristics.

A related application-specific architecture is MC-QDSNN, where the MCLeaky neuron introduces multi-compartment dendritic recurrence as an intrinsic memory mechanism. Its quantized form, QMCLeaky, fixes decay constants to 0.875 for hardware simplicity and quantizes thresholds, states, and synapses to 8 bits (S et al., 2024). The recurrent compartmental dynamics are

$k>1$8

$k>1$9

$[0,1]$0

$[0,1]$1

On stress detection from physiological signals, the full-precision MCLeaky model reached 98.8\% on EDA Combo, while the quantized QMCLeaky+QFC model reached 91.84\% and delivered reported energy savings of 25.12x to 39.20x and EDP gains of 52.37x to 81.9x over ANN baselines (S et al., 2024).

4. Optical neurons with discrete physical parameters

In optical processors, a quantized neuron is a physically realizable optical modulation element whose phase and/or amplitude can take only a finite number of values. QuATON studies diffractive deep neural networks in which each optical neuron applies a phase-only modulation,

$[0,1]$2

while free-space propagation between layers is modeled by Rayleigh–Sommerfeld diffraction (Kariyawasam et al., 2023). Hard quantization of a bounded parameter $[0,1]$3 with $[0,1]$4 levels uses

$[0,1]$5

and for phase discretization with $[0,1]$6 bits, $[0,1]$7 and $[0,1]$8 (Kariyawasam et al., 2023).

Because hard quantization is nondifferentiable, QuATON replaces it during training with a progressive sigmoid quantizer,

$[0,1]$9

and increases the temperature $$Q_k(x)=\frac{1}{2^k-1}\left\lfloor (2^k-1)x \right\rceil,$$0 so the soft quantizer approaches the deployable hard quantizer. Two schedules are studied: linearly increasing temperature and learnable temperature with regularization (Kariyawasam et al., 2023). The paper also emphasizes phase-specific constraints such as wrapping to $$Q_k(x)=\frac{1}{2^k-1}\left\lfloor (2^k-1)x \right\rceil,$$1 and using $$Q_k(x)=\frac{1}{2^k-1}\left\lfloor (2^k-1)x \right\rceil,$$2 during QAT to avoid the $$Q_k(x)=\frac{1}{2^k-1}\left\lfloor (2^k-1)x \right\rceil,$$3 degeneracy.

This framework is not merely a numerical convenience; it is dictated by fabrication and device physics. Spatial light modulators may support 8-bit phase-only control, digital micromirror devices provide 1-bit amplitude, and 3D-printed optics yield bounded phase values with limited precision. Quantization-aware design is therefore needed to avoid a train–deploy mismatch between ideal continuous parameters and realizable optical neurons (Kariyawasam et al., 2023).

The reported results show that quantized optical neurons can remain competitive when the quantization process is modeled during training. For all-optical classification, eight phase levels were sufficient to match full precision on MNIST and CIFAR10, while low-bit regimes benefited substantially from progressive soft quantization. On MNIST classification, Q4 yielded 87.73\% with PSQ-LI and 87.06\% with PSQ-LT, versus 86.89\% for post-quantization and 84.69\% for DSQ; on CIFAR10, Q2 gave 22.27\% with PSQ-LT versus 14.54\% for post-quantization and 11.97\% for STE (Kariyawasam et al., 2023). For quantitative phase imaging, the required precision was higher: Q16 approached full-precision SSIM, whereas Q4 remained substantially degraded. This difference clarifies that the relevant “quantized neuron” in optics is task- and substrate-constrained, not a generic low-bit approximation.

5. Quantum logic and gate-based quantum neurons

Several works define quantized neurons directly in terms of quantum states and quantum logic. In multi-valued quantum neurons, truth values are represented as roots of unity on the unit circle,

$$Q_k(x)=\frac{1}{2^k-1}\left\lfloor (2^k-1)x \right\rceil,$$4

and the neuron computes

$$Q_k(x)=\frac{1}{2^k-1}\left\lfloor (2^k-1)x \right\rceil,$$5

Training can be performed by a complex-valued error-correction rule,

$$Q_k(x)=\frac{1}{2^k-1}\left\lfloor (2^k-1)x \right\rceil,$$6

with $$Q_k(x)=\frac{1}{2^k-1}\left\lfloor (2^k-1)x \right\rceil,$$7 (AlMasri, 2023). In this construction, the neuron’s output is quantized in phase rather than amplitude, and the paper argues that the information per neuron is at least $$Q_k(x)=\frac{1}{2^k-1}\left\lfloor (2^k-1)x \right\rceil,$$8 bits and that movement along the unit circle yields fast convergence (AlMasri, 2023).

A gate-based threshold neuron is developed in "Quantum Neuron: an elementary building block for machine learning on quantum computers" (Cao et al., 2017). Here the weighted sum is encoded as a rotation angle, and a repeat-until-success circuit implements a nonlinear threshold map on that angle through the iterated transformation

$$Q_k(x)=\frac{1}{2^k-1}\left\lfloor (2^k-1)x \right\rceil,$$9

With sufficient iterations, $$8\rightarrow4\rightarrow2\rightarrow1\rightarrow1\rightarrow1$$0 is driven toward $$8\rightarrow4\rightarrow2\rightarrow1\rightarrow1\rightarrow1$$1 or $$8\rightarrow4\rightarrow2\rightarrow1\rightarrow1\rightarrow1$$2, approximating a binary threshold. The paper gives expected runtime bounds of

$$8\rightarrow4\rightarrow2\rightarrow1\rightarrow1\rightarrow1$$3

for a single neuron and extends the construction to feedforward and Hopfield-like networks (Cao et al., 2017). The resulting quantized neuron is a quantum circuit primitive whose nonlinearity is induced by measurement and repetition rather than by low-bit arithmetic.

A different qubit-based formulation appears in "Natural Quantization of Neural Networks" (Barney et al., 19 Mar 2025). There, each hidden-layer neuron becomes a qubit rotated by

$$8\rightarrow4\rightarrow2\rightarrow1\rightarrow1\rightarrow1$$4

with angle

$$8\rightarrow4\rightarrow2\rightarrow1\rightarrow1\rightarrow1$$5

where $$8\rightarrow4\rightarrow2\rightarrow1\rightarrow1\rightarrow1$$6 smoothly interpolates between classical sign behavior and a stochastic quantum regime. A second approach uses ancilla-mediated weak measurements with entanglement angle $$8\rightarrow4\rightarrow2\rightarrow1\rightarrow1\rightarrow1$$7, recovering the classical limit at $$8\rightarrow4\rightarrow2\rightarrow1\rightarrow1\rightarrow1$$8 (Barney et al., 19 Mar 2025). On a reduced MNIST benchmark, the paper reports a best validation error of 0.0472 at $$8\rightarrow4\rightarrow2\rightarrow1\rightarrow1\rightarrow1$$9 for the rotation-based approach, 0.0529 at $4\rightarrow2\rightarrow1$0 for the weak-measurement approach, and 0.0463 at $4\rightarrow2\rightarrow1$1 when both knobs are tuned jointly. It also reports a sharp loss of learnability below a critical point $4\rightarrow2\rightarrow1$2 (Barney et al., 19 Mar 2025). This suggests that some gate-based quantized neurons function as controlled stochastic regularizers rather than exact replacements for classical threshold units.

6. Canonical quantization and quantum neuromorphic circuits

A more systematic line of work treats the neuron itself as an object to be canonically quantized. In this framework, a classical neuron is written as an activation applied to an energy function,

$4\rightarrow2\rightarrow1$3

and quantization replaces the classical energy with a Hermitian operator,

$4\rightarrow2\rightarrow1$4

so that the neuron becomes an activation observable

$4\rightarrow2\rightarrow1$5

For an input state $4\rightarrow2\rightarrow1$6, the output is

$4\rightarrow2\rightarrow1$7

This construction reduces exactly to a classical neuron when the Hamiltonian terms commute and are jointly diagonalizable, but yields richer operator structure when they do not (He et al., 23 May 2026, He et al., 6 Jul 2026).

Within this paradigm, Fermi–Dirac neurons use

$4\rightarrow2\rightarrow1$8

and define activation observables such as $4\rightarrow2\rightarrow1$9 or $8\rightarrow4\rightarrow2$0. Gradient estimation is carried out with hybrid quantum-classical routines based on random sampling, Hamiltonian simulation, and the Hadamard test. One representative formula for the tanh activation gradient is

$8\rightarrow4\rightarrow2$1

where $8\rightarrow4\rightarrow2$2 and $8\rightarrow4\rightarrow2$3 (He et al., 23 May 2026). A companion formulation applies the same canonical-quantization principle to function approximation on labeled quantum data and develops measurement of activation observables using the power of one qumode and Schrödingerization (He et al., 6 Jul 2026). Both papers report enhanced expressive capability relative to corresponding classical neurons on representative tasks (He et al., 23 May 2026, He et al., 6 Jul 2026).

Quantum neuromorphic circuit models adopt a more physical route. A quantized memristive LIF neuron is obtained by replacing the dissipative leak element of a classical LIF circuit with a semi-infinite lossless transmission line whose characteristic impedance is slowly modulated as a memristance $8\rightarrow4\rightarrow2$4, then canonically quantizing the resulting cQED system (Brand et al., 26 Jun 2025). In the weak-coupling and adiabatic regime, the classical limit

$8\rightarrow4\rightarrow2$5

is recovered, while the quantum model evolves under a time-dependent GKSL master equation with decay rate

$8\rightarrow4\rightarrow2$6

Spiking is implemented by thresholding the voltage expectation $8\rightarrow4\rightarrow2$7 and resetting the oscillator state to the vacuum (Brand et al., 26 Jun 2025). This yields a quantized neuron that is not a qubit classifier but a quantum open-system analogue of a spiking cell.

The same quantum-memristive strategy has been applied to reduced and full Hodgkin–Huxley models. A single potassium-channel quantized Hodgkin–Huxley neuron identifies the channel conductance with a quantum memristor and reports purely quantum contributions in higher moments of the voltage arising from zero-point energy (Gonzalez-Raya et al., 2018). The later three-ion-channel formulation represents potassium and sodium channels as memristors, chloride as a resistor, and adds both a quantum source and an output waveguide, reporting that—unlike the single-channel case—the full three-channel model reproduces the voltage spike in an adiabatic regime (Gonzalez-Raya et al., 2019). These works use circuit quantization and input–output theory rather than abstract variational circuits.

Other quantum-inspired proposals broaden the semantic field further. "Artificial Quantum Neural Network: quantum neurons, logical elements and tests of convolutional nets" (Dorozhinsky et al., 2018) models a neuron as a quantum particle in a double-well potential,

$8\rightarrow4\rightarrow2$8

with spikes interpreted as instanton events. The paper demonstrates AND, OR, NOT, XOR, a simple convolutional detector, and a handwritten-symbol recognizer, and reports that a classical multinomial logistic regression reaches 91\% test accuracy while the transferred quantum network performs somewhat worse because of Monte Carlo randomness (Dorozhinsky et al., 2018). "Spike and Tyke, the Quantized Neuron Model" (El-Dosuky et al., 2012) instead quantizes resistance and potential by analogy with Planck’s law, deriving

$8\rightarrow4\rightarrow2$9

and reporting over 97\% point-wise match to a target spiking curve (El-Dosuky et al., 2012). These models are conceptually remote from low-bit QNNs, yet they also use the phrase “quantized neuron.”

7. Limitations, misconceptions, and research directions

The first limitation is terminological. In the surveyed literature, “quantized neuron” does not denote a single research object. It can mean low-bit integer arithmetic, a multi-level spike emitter, an optical phase modulator with discrete settings, a qubit-based stochastic threshold unit, or a canonically quantized Hamiltonian observable. A common misconception is to equate low-bit quantization with quantum-mechanical quantization; one paper explicitly states that these are different senses of the word (Dorozhinsky et al., 2018).

In electronic QNNs, the main technical limitations are the heuristic nature of many precision-allocation rules and the task dependence of aggressive compression. The progressively decreasing bitwidth strategy is rule-based rather than optimized, narrow networks can bottleneck under overly low posterior precision, and object detection localizes less accurately than classification under heavy quantization (Chu et al., 2019). Repair-based methods alleviate some errors, but they introduce expensive optimization stages and can require hours on large layers (Song et al., 2023).

In spiking and neuromorphic systems, quantization improves hardware feasibility but creates dynamic-range and stability trade-offs. qCLIF and QMCLeaky show that 8-bit designs can remain accurate, but 4-bit or 2-bit settings can substantially degrade performance (Bezugam et al., 2024, S et al., 2024). QB-LIF indicates that multi-level quantization can recover information throughput lost by binary spikes, but this requires learned scales, burst payloads, and careful surrogate-gradient design (Bai et al., 28 Apr 2026). Heterogeneous spike-phase quantization regularizes utilization effectively, yet data-aware calibration can reduce robustness under distribution shift; this is a plausible implication of the reported trade-off between regularization and information retention (Moyal et al., 2024).

In optical systems, the dominant issue is physical mismatch. Quantization-aware training is essential because post-quantization can fail badly at low precision, but the reported experiments still assume ideal propagation and do not fully include fabrication variability, misalignment, or broadband effects (Kariyawasam et al., 2023). This suggests that future optical quantized neurons will likely be co-designed with explicit tolerance models rather than merely discretized after the fact.

In quantum and quantum-neuromorphic proposals, the principal constraint is scale. Canonically quantized neurons, Fermi–Dirac machines, qumode-based measurement schemes, and quantum memristive spiking circuits are mathematically explicit and sometimes accompanied by complexity-theoretic or expressive-power arguments, but the reported demonstrations remain small-scale, numerical, or architecture-specific (He et al., 23 May 2026, He et al., 6 Jul 2026, Brand et al., 26 Jun 2025). Gate-based quantum neurons show favorable results on reduced MNIST, yet also exhibit critical regimes where training fails (Barney et al., 19 Mar 2025). Quantum-particle and memristive HH models remain valuable as constructive physical frameworks, but their transition from proof-of-concept to scalable learning systems is still unresolved (Dorozhinsky et al., 2018, Gonzalez-Raya et al., 2019).

Across all of these strands, the enduring idea is that discretization can be structural rather than merely compressive. In some settings it reduces storage and compute; in others it regularizes activity, matches physical fabrication limits, enables sparse event-driven execution, or defines an intrinsically quantum computational primitive. The literature therefore supports a broad but precise definition: quantized neurons are neurons whose admissible states or transformations are restricted to discrete sets, with the exact meaning determined by the computational substrate and the way discreteness enters the model.