Projected Hybrid Readout

• Projected hybrid readout is a class of strategies that maps system information into an easier-to-detect measurement space by combining distinct sensing, amplification, and transmission methods.
• It improves measurement fidelity and scalability by selectively preserving key signal features while overcoming bandwidth and noise bottlenecks inherent in conventional systems.
• Applications span quantum subspace learning, semiconductor qubit detection, NV-center imaging, and gaseous detector systems, driving advancements in efficiency, accuracy, and speed.

Projected hybrid readout denotes a family of readout strategies in which system information is deliberately mapped, projected, or transduced into a measurement space that is easier to detect, while the overall architecture remains hybrid in the sense of combining unlike sensing, amplification, encoding, or transmission paths. Across the cited literature, the phrase is not standardized: in active quantum subspace learning it denotes a projected quantum feature map appended to classical features (Bang et al., 30 May 2026); in semiconductor qubits it denotes projective or latched spin-to-charge conversion (Corrigan et al., 2022, Jang et al., 2021); in nitrogen-vacancy registers it denotes decomposition of a fluorescence time trace onto calibrated hybrid-spin basis traces (He et al., 2024); and in detector instrumentation it denotes simultaneous optical/charge, pad/pixel, slow/fast, or front-end/optical-link combinations (Deisting, 2022, Einhaus et al., 2018, Benac et al., 28 Aug 2025). This suggests a common architectural theme: the readout stage is treated as a bottleneck to be reshaped rather than merely observed.

1. Terminological scope and documentary status

The literature represented here does not supply a single canonical definition of projected hybrid readout. Instead, it presents several domain-specific uses of the same conceptual motif: projection onto a restricted observable set, projection of a quantum state onto charge configurations, projection of a track onto an image plane, or projection of locally processed detector data onto high-bandwidth transmission channels.

One arXiv entry that might have been expected to anchor the term, "Demonstration of ThGEM-Multiwire Hybrid Charge Readout for Directional Dark Matter Searches" (Ezeribe et al., 2019), is described in the supplied record as “essentially a blank LaTeX template with empty title, abstract, sections, and bibliography,” with “no usable physics information.” As a result, it does not provide extractable technical content about a ThGEM-Multiwire hybrid charge readout, its detector geometry, or its reported performance (Ezeribe et al., 2019).

Because the terminology is nonuniform, the most accurate encyclopedic treatment is comparative. In some papers, “projected” refers to an explicit mathematical projection onto a finite observable family; in others, it refers to a projective measurement, to a 2D geometrical projection, or to a projected/off-detector transmission architecture. In all of these cases, the readout is not a passive endpoint but a designed interface that determines statistical efficiency, signal persistence, bandwidth, and scalability.

2. Quantum-learning formulations

In active quantum subspace data-encoding, projected hybrid readout is defined formally. The input is split as

$$x=(x_C,x_Q)\in \mathcal X_{C,n}\times \mathcal X_{Q,n},$$

where only $x_Q$ is lifted into a quantum representation. The encoded state is

$$\hat{\rho}_x := \hat{E}_n(x)\,|0^{\kappa(n)}\rangle\langle 0^{\kappa(n)}|\,\hat{E}_n(x)^\dagger,$$

and readout is performed through a finite list of Hermitian observables $\hat O_1,\dots,\hat O_M$, producing

$\Phi_Q(x)=\big(\Tr[\hat O_1\hat\rho_x],\ldots,\Tr[\hat O_M\hat\rho_x]\big)\in \mathbb R^M.$

The hybrid feature map is

$$\Phi_H(x)=\Phi_C(x)\oplus \sqrt{\lambda}\,\Phi_Q(x),\qquad \lambda\ge 0,$$

with projected hybrid kernel

$$K_H(x,x') = K_C(x,x') + \lambda K_Q^{\mathrm{proj}}(x,x').$$

The projected quantum kernel has the factorization $K_Q^{\mathrm{proj}}=F_QF_Q^\top$, so it is PSD, and the paper proves

$\rank(K_H)\le \rank(K_C)+M,$

together with

$d_{\mathrm{reg}}^{(\mu)}(K_H)\le \rank(K_C)+M.$

The stated purpose is to avoid “the dimension blow-up of naive global kernels,” because the effective sample dimension grows with the number of projected observables rather than with the ambient Hilbert space (Bang et al., 30 May 2026).

The same work gives a necessary and sufficient condition for improvement over a purely classical predictor in squared loss. If $x_Q$0 is the classical residual, then strict improvement occurs iff there exists $x_Q$1 such that

$x_Q$2

is nonzero and

$x_Q$3

Equivalently,

$x_Q$4

In a realizable noisy-oracle setting, the sample-complexity bound scales as $x_Q$5, and for projected hybrid models with $x_Q$6, polynomial feature dimension plus inverse-polynomial oracle reliability implies PAC-learnability with polynomial sample complexity. The paper’s 64-qubit construction uses one projected quantum feature,

$x_Q$7

to represent a degree-8 interaction while the hybrid projected model uses 71 features, compared with 469, 3003, and 12,910 features for the listed classical baselines (Bang et al., 30 May 2026).

A related but distinct formulation appears in residual hybrid quantum-classical learning. There the bottleneck is the narrow quantum-to-classical interface: a parameterized quantum circuit exposes only $x_Q$8 with $x_Q$9. The proposed readout-side bypass concatenates the raw input and the measured quantum output,

$$\hat{\rho}_x := \hat{E}_n(x)\,|0^{\kappa(n)}\rangle\langle 0^{\kappa(n)}|\,\hat{E}_n(x)^\dagger,$$0

then applies a learned linear map before a two-layer MLP. The paper reports that this residual hybrid “outperforms pure quantum and prior hybrid models in both centralized and federated settings,” achieving “up to +55% accuracy improvement over quantum baselines,” with classical FL updates at about 2.0–2.5 MB and residual 6-qubit hybrid updates at about 1.7–2.1 MB. It also reports MIA AUC values clustered around $$\hat{\rho}_x := \hat{E}_n(x)\,|0^{\kappa(n)}\rangle\langle 0^{\kappa(n)}|\,\hat{E}_n(x)^\dagger,$$1–$$\hat{\rho}_x := \hat{E}_n(x)\,|0^{\kappa(n)}\rangle\langle 0^{\kappa(n)}|\,\hat{E}_n(x)^\dagger,$$2, and emphasizes that the method “does not fundamentally eliminate the measurement bottleneck inside the quantum circuit; it bypasses its downstream consequences by reintroducing the raw input at readout” (Zhang et al., 25 Nov 2025).

3. Projective and latched readout in semiconductor hybrid qubits

In semiconductor hybrid qubits, projected hybrid readout is implemented as state-dependent mapping into charge configurations that a nearby sensor can detect. In a GaAs double quantum dot hybrid qubit, single-shot projective readout is realized by adiabatically moving the qubit from the operation point $$\hat{\rho}_x := \hat{E}_n(x)\,|0^{\kappa(n)}\rangle\langle 0^{\kappa(n)}|\,\hat{E}_n(x)^\dagger,$$3 to an initialization/measurement point $$\hat{\rho}_x := \hat{E}_n(x)\,|0^{\kappa(n)}\rangle\langle 0^{\kappa(n)}|\,\hat{E}_n(x)^\dagger,$$4, where the reservoir chemical potential lies between the energies corresponding to $$\hat{\rho}_x := \hat{E}_n(x)\,|0^{\kappa(n)}\rangle\langle 0^{\kappa(n)}|\,\hat{E}_n(x)^\dagger,$$5 and $$\hat{\rho}_x := \hat{E}_n(x)\,|0^{\kappa(n)}\rangle\langle 0^{\kappa(n)}|\,\hat{E}_n(x)^\dagger,$$6. The mechanism is Elzerman-type energy-selective tunneling: $$\hat{\rho}_x := \hat{E}_n(x)\,|0^{\kappa(n)}\rangle\langle 0^{\kappa(n)}|\,\hat{E}_n(x)^\dagger,$$7 produces a tunnel-out event and a charge-state change, whereas $$\hat{\rho}_x := \hat{E}_n(x)\,|0^{\kappa(n)}\rangle\langle 0^{\kappa(n)}|\,\hat{E}_n(x)^\dagger,$$8 remains trapped. The reported operating ratios are $$\hat{\rho}_x := \hat{E}_n(x)\,|0^{\kappa(n)}\rangle\langle 0^{\kappa(n)}|\,\hat{E}_n(x)^\dagger,$$9 and $\hat O_1,\dots,\hat O_M$0, with $\hat O_1,\dots,\hat O_M$1, $\hat O_1,\dots,\hat O_M$2, $\hat O_1,\dots,\hat O_M$3, readout window $\hat O_1,\dots,\hat O_M$4, measurement fidelity $\hat O_1,\dots,\hat O_M$5, readout visibility $\hat O_1,\dots,\hat O_M$6, and state-resolved fidelities $\hat O_1,\dots,\hat O_M$7 and $\hat O_1,\dots,\hat O_M$8 (Jang et al., 2021).

Latched readout for the quantum dot hybrid qubit modifies the same logic by inserting a metastable storage step. In the reported $\hat O_1,\dots,\hat O_M$9 charge configuration,

$\Phi_Q(x)=\big(\Tr[\hat O_1\hat\rho_x],\ldots,\Tr[\hat O_M\hat\rho_x]\big)\in \mathbb R^M.$0

If the system is in $\Phi_Q(x)=\big(\Tr[\hat O_1\hat\rho_x],\ldots,\Tr[\hat O_M\hat\rho_x]\big)\in \mathbb R^M.$1, it can quickly tunnel to a metastable state $\Phi_Q(x)=\big(\Tr[\hat O_1\hat\rho_x],\ldots,\Tr[\hat O_M\hat\rho_x]\big)\in \mathbb R^M.$2 before relaxing back to $\Phi_Q(x)=\big(\Tr[\hat O_1\hat\rho_x],\ldots,\Tr[\hat O_M\hat\rho_x]\big)\in \mathbb R^M.$3. The rate condition is

$\Phi_Q(x)=\big(\Tr[\hat O_1\hat\rho_x],\ldots,\Tr[\hat O_M\hat\rho_x]\big)\in \mathbb R^M.$4

and the latching lifetime is set by

$\Phi_Q(x)=\big(\Tr[\hat O_1\hat\rho_x],\ldots,\Tr[\hat O_M\hat\rho_x]\big)\in \mathbb R^M.$5

Experimentally, $\Phi_Q(x)=\big(\Tr[\hat O_1\hat\rho_x],\ldots,\Tr[\hat O_M\hat\rho_x]\big)\in \mathbb R^M.$6 was measured to be 9.8 MHz, $\Phi_Q(x)=\big(\Tr[\hat O_1\hat\rho_x],\ldots,\Tr[\hat O_M\hat\rho_x]\big)\in \mathbb R^M.$7, $\Phi_Q(x)=\big(\Tr[\hat O_1\hat\rho_x],\ldots,\Tr[\hat O_M\hat\rho_x]\big)\in \mathbb R^M.$8, and the latched state persisted for as long as 2.5 ms. The paper further reports that the $\Phi_Q(x)=\big(\Tr[\hat O_1\hat\rho_x],\ldots,\Tr[\hat O_M\hat\rho_x]\big)\in \mathbb R^M.$9 regime is advantageous because the readout window is determined by a multi-electron orbital splitting $$\Phi_H(x)=\Phi_C(x)\oplus \sqrt{\lambda}\,\Phi_Q(x),\qquad \lambda\ge 0,$$0 rather than by a 2-electron valley splitting of $$\Phi_H(x)=\Phi_C(x)\oplus \sqrt{\lambda}\,\Phi_Q(x),\qquad \lambda\ge 0,$$1, making the window “larger and more tunable.” Rabi and Ramsey oscillations were measured with this latched readout, so the method functions in coherent-control experiments rather than only in static discrimination (Corrigan et al., 2022).

A common misconception is that projective readout in hybrid qubits is exhausted by a one-step charge projection. The latched variant shows that the decisive improvement may come from converting the projected state into a long-lived metastable occupation change, thereby increasing both persistence and sensor contrast.

4. Hybrid-spin optical readout and transduced spin sensing

In nitrogen-vacancy hybrid-spin registers, direct projected readout is performed by projecting a measured fluorescence time trace onto a basis of calibrated traces. The system is a negatively charged NV center in diamond, with an electron-spin subspace $$\Phi_H(x)=\Phi_C(x)\oplus \sqrt{\lambda}\,\Phi_Q(x),\qquad \lambda\ge 0,$$2 and a $$\Phi_H(x)=\Phi_C(x)\oplus \sqrt{\lambda}\,\Phi_Q(x),\qquad \lambda\ge 0,$$3 nuclear-spin qubit $$\Phi_H(x)=\Phi_C(x)\oplus \sqrt{\lambda}\,\Phi_Q(x),\qquad \lambda\ge 0,$$4, giving four hybrid basis states: $$\Phi_H(x)=\Phi_C(x)\oplus \sqrt{\lambda}\,\Phi_Q(x),\qquad \lambda\ge 0,$$5 At the excited-state level anti-crossing near $$\Phi_H(x)=\Phi_C(x)\oplus \sqrt{\lambda}\,\Phi_Q(x),\qquad \lambda\ge 0,$$6, photon emission becomes state dependent in time as well as in total counts. With 2 ns timing resolution, the time-binned vector

$$\Phi_H(x)=\Phi_C(x)\oplus \sqrt{\lambda}\,\Phi_Q(x),\qquad \lambda\ge 0,$$7

is modeled by

$$\Phi_H(x)=\Phi_C(x)\oplus \sqrt{\lambda}\,\Phi_Q(x),\qquad \lambda\ge 0,$$8

and the population vector is extracted by minimizing $$\Phi_H(x)=\Phi_C(x)\oplus \sqrt{\lambda}\,\Phi_Q(x),\qquad \lambda\ge 0,$$9. The paper states that this gives “the same outcome as traditional quantum state diagonal tomography” while reducing experimental time from $$K_H(x,x') = K_C(x,x') + \lambda K_Q^{\mathrm{proj}}(x,x').$$0 to $$K_H(x,x') = K_C(x,x') + \lambda K_Q^{\mathrm{proj}}(x,x').$$1, about a 32× speedup. Reported population-readout fidelities for the four basis states are $$K_H(x,x') = K_C(x,x') + \lambda K_Q^{\mathrm{proj}}(x,x').$$2, $$K_H(x,x') = K_C(x,x') + \lambda K_Q^{\mathrm{proj}}(x,x').$$3, $$K_H(x,x') = K_C(x,x') + \lambda K_Q^{\mathrm{proj}}(x,x').$$4, and $$K_H(x,x') = K_C(x,x') + \lambda K_Q^{\mathrm{proj}}(x,x').$$5, with superposition-state fidelities above 0.988 and mostly above 0.99 (He et al., 2024).

A second hybrid-spin usage appears in axion sensing, where the hybridization is between the sensing spin and the readout spin. The proposal uses a nuclear spin as the axion-sensitive element and an electron spin as the measurement channel. The total Hamiltonian is

$$K_H(x,x') = K_C(x,x') + \lambda K_Q^{\mathrm{proj}}(x,x').$$6

with axion drive

$$K_H(x,x') = K_C(x,x') + \lambda K_Q^{\mathrm{proj}}(x,x').$$7

In the secular regime, the effective Hamiltonian becomes

$$K_H(x,x') = K_C(x,x') + \lambda K_Q^{\mathrm{proj}}(x,x').$$8

so the axion-driven nuclear dynamics appear as an electron frequency modulation,

$$K_H(x,x') = K_C(x,x') + \lambda K_Q^{\mathrm{proj}}(x,x').$$9

The paper defines a hybrid gain

$K_Q^{\mathrm{proj}}=F_QF_Q^\top$0

and expresses the relative SNR as

$K_Q^{\mathrm{proj}}=F_QF_Q^\top$1

The reported implication is that hybrid nuclear–electronic readout “outperform[s] direct nuclear detection by more than an order of magnitude” over $K_Q^{\mathrm{proj}}=F_QF_Q^\top$2 to $K_Q^{\mathrm{proj}}=F_QF_Q^\top$3, while preserving sidereal and annual modulation signatures. With collective enhancement, the design is projected to reach a $K_Q^{\mathrm{proj}}=F_QF_Q^\top$4 sensitivity to DFSZ axion-nucleon couplings within one year (Tan et al., 11 Jan 2026).

Taken together, these works illustrate two different senses of projection. In the NV case, a hybrid state is projected onto a calibrated photon-time basis. In the axion proposal, a weak nuclear signal is projected into an electron-spin observable through hyperfine-mediated transduction.

5. Gaseous-detector and TPC implementations

In gaseous detectors, hybrid readout usually denotes the simultaneous use of distinct sensing modalities or the combination of unlike anode and electronics technologies. One line of work is a hybrid Time Projection Chamber with simultaneous optical and charge readout. There the optical system provides “2D images of particle tracks in the active volume,” while the charge readout “provides additional information on the particle position perpendicular to the image plane.” The commissioning setup uses a $K_Q^{\mathrm{proj}}=F_QF_Q^\top$5 readout plane, 128 rectangular segments, and a double GEM stack. The optical pixel size can be as small as $K_Q^{\mathrm{proj}}=F_QF_Q^\top$6, so the camera supplies a fine track projection, while the segmented charge readout supplies depth through drift timing and event association in multi-track events (Deisting, 2022).

A more electronic form of hybridization is ROPPERI, “Readout Of a Pad Plane with ElectRonics designed for pIxels.” Here the chain is primary ionisation $K_Q^{\mathrm{proj}}=F_QF_Q^\top$7 drift $K_Q^{\mathrm{proj}}=F_QF_Q^\top$8 GEM amplification $K_Q^{\mathrm{proj}}=F_QF_Q^\top$9 charge clouds on pads $\rank(K_H)\le \rank(K_C)+M,$0 Timepix-based digitisation and readout via SRS/FEC electronics. The design combines a triple GEM stack, a PCB pad plane, and a Timepix ASIC with $\rank(K_H)\le \rank(K_C)+M,$1 pixels. It is “hybrid” because it sits between conventional pad-based TPCs and pure pixel detectors: it seeks pad-plane flexibility and large coverage while borrowing fine-grained readout from pixel electronics. The stated scientific motivation is cluster counting for $\rank(K_H)\le \rank(K_C)+M,$2, since the number of generated electrons is given by a Landau distribution, whereas the number of ionising interactions is given by a Poissonian distribution with a significantly smaller width. The target pad scale is around $\rank(K_H)\le \rank(K_C)+M,$3, and the coverage can exceed 90%, compared with about 50% or 63% in the listed pixel-anode arrangements (Einhaus et al., 2017, Einhaus et al., 2018).

The simulation chain for ROPPERI was implemented in MarlinTPC and used Source Extractor for charge-cloud finding. Because “cluster counting efficiency” is ambiguous in the presence of splitting and merging, the paper introduced “exact cluster-to-hit-identification efficiency” or “double uniques.” For an envisaged ILD TPC track length of 1.2 m and a pad size of $\rank(K_H)\le \rank(K_C)+M,$4, the extrapolated pion/kaon separation power is 3.6, matching the 20% cluster counting efficiency curve. The hardware development, however, exposed substantial practical limits: standard FR-4 imposed a current minimum pad pitch of about $\rank(K_H)\le \rank(K_C)+M,$5, Timepix expects input capacitances below 100 fF, while routing in ROPPERI contributes about $\rank(K_H)\le \rank(K_C)+M,$6, and the first bonding attempts suffered from thermal-expansion mismatch between silicon at 2.5 ppm/K and FR-4 at about 15 ppm/K (Einhaus et al., 2018).

In this detector class, “projected” often has a literal geometrical meaning: tracks are first seen as 2D projections or charge clouds on an anode plane, and hybridization is used to recover depth, improve cluster identification, or enlarge coverage without fully pixelating the anode.

6. Instrumentation-scale hybrid architectures

At the instrumentation level, hybrid readout frequently means combining incompatible timing, bandwidth, or transport regimes within one chain. In SCALES, the H2RG detectors are “slow-mode-only” in the sense of JWST-style 4-channel operation at about 100 kHz per output, yielding a minimum full-frame readout time of about 10.5 s. The hybrid fast-slow solution keeps the slow-mode detector architecture but reads through the SIDECAR ASIC’s fast-mode ADC path, enabled by a custom buffered flexible cable, extra resistors in the cable, and custom MACIE firmware. In testing, the system operated up to 1.8 MHz pixel clock with minimum frame time 0.58 s, and the paper explicitly states that this enables readout up to 18× faster than slow mode alone. The purpose is to prevent saturation from the bright infrared sky background in the $\rank(K_H)\le \rank(K_C)+M,$7 band while retaining low-noise operation (Benac et al., 28 Aug 2025).

A broader HEP survey uses “hybrid” in the sense of front-end processing followed by projected/off-detector transmission. The practical chain is front-end ASICs near the sensor, electrical serialization or formatting, and high-speed optical or other long-haul transfer. The cited technologies include Versatile Link / Versatile Link+, lpGBT, LOCx2, silicon photonics-based links, VCSEL-based transmitters, and a PAM4 transmitter ASIC GBS20 at up to 20.48 Gbps with power consumption below 238 mW, reduced to 164 mW in low-power mode. In that survey, “projected” readout is best understood as moving the output of detector electronics off the detector through a planned high-bandwidth link architecture rather than performing all processing locally (Begel et al., 2022).

Mixed-signal ASICs provide another variant. The GRAPH ASIC introduces the Hybrid Universal sampLing Architecture, a double-buffer memory that permits concurrent waveform recording and selected event digitized data extraction. Each channel stores 2048 samples with 12-bit digital headroom, the sampling frequency is adjustable from a few kHz up to 125 MHz, one bank samples while the other is digitized or read out, and the power consumption is around 47 mW per channel. The architecture is explicitly intended to reduce operational dead time by reading only the region around the event pulse peak rather than draining full waveforms (Seljak et al., 2024).

In hybrid-pixel X-ray detection, HEPS-BPIX uses a BP40 ASIC, Front-End Electronics, an Input-Output Board, and a $\rank(K_H)\le \rank(K_C)+M,$8FCP in a two-tier FPGA-based readout system. A major architectural shift is from 72 low-speed buses to one high-speed LVDS serial interface per BP40. The detector target is a 6-million-pixel system partitioned into 40 independently readable subunits, with per-module data rate about 4.7 Gb/s at 1 kHz frame rate and full-system peak data rate about 192 Gb/s. The backend aggregation bandwidth is stated as 200 Gb/s, and the firmware redesign includes Wishbone-based configuration, calibration mode reducing configuration time by a factor of 12, and DDR3 used as an 8 GB FIFO to absorb TCP/IP fluctuations (Li et al., 2024).

These examples show that, at system scale, hybrid readout is often a negotiated compromise between detector-native operation and the bandwidth or latency demanded by the external environment.

7. Recurring principles, advantages, and limitations

A recurring principle is selective exposure of information. In the projected hybrid kernel, only $\rank(K_H)\le \rank(K_C)+M,$9 observables are exposed; in readout-side bypass, the classifier sees $d_{\mathrm{reg}}^{(\mu)}(K_H)\le \rank(K_C)+M.$0 and $d_{\mathrm{reg}}^{(\mu)}(K_H)\le \rank(K_C)+M.$1 rather than only the bottlenecked quantum output; in hybrid qubits, the logical basis is mapped onto charge states or a metastable latch; in NV centers, the fluorescence histogram is decomposed in a four-state basis; in TPCs, a 2D optical or pad-plane projection is augmented by charge timing; and in detector electronics, only selected events or serialized summaries are transmitted. This suggests that projected hybrid readout is less a single mechanism than a design rule: preserve the degrees of freedom that matter, and transduce or compress the rest into a channel with favorable SNR, bandwidth, or scalability.

The main advertised advantages are correspondingly diverse but structurally similar. The quantum-dot latch provides a metastable state persisting as long as 2.5 ms and a larger sensor signal; the AQSE formulation avoids kernel blow-up; the residual readout-side bypass improves accuracy and communication efficiency while maintaining privacy robustness; ROPPERI aims at charge-cloud and possibly cluster identification with more than 90% anode coverage; SCALES shortens minimum frame time from about 10.5 s to 0.58 s; and projected/off-detector architectures seek high bandwidth, low latency, radiation tolerance, low power, and cost-effective scaling (Corrigan et al., 2022, Bang et al., 30 May 2026, Zhang et al., 25 Nov 2025, Einhaus et al., 2018, Benac et al., 28 Aug 2025, Begel et al., 2022).

The limitations are equally consistent. Hybridization does not automatically remove the underlying bottleneck. The residual QML architecture explicitly “does not fundamentally eliminate the measurement bottleneck inside the quantum circuit”; it bypasses the downstream loss of information. ROPPERI’s first prototype revealed severe challenges in bonding, thermal expansion, flatness, and capacitance/noise. In SCALES, master clocks at $d_{\mathrm{reg}}^{(\mu)}(K_H)\le \rank(K_C)+M.$2 MHz caused degraded performance and additional frame structures that could not be tuned away. In GRAPH, a nominal 12-bit design achieved practical ENOB around 7 bits, and cell-to-cell mismatch required calibration. Optical readout alone in a TPC remains inherently a projection that loses the perpendicular coordinate until charge timing is added (Zhang et al., 25 Nov 2025, Einhaus et al., 2018, Benac et al., 28 Aug 2025, Seljak et al., 2024, Deisting, 2022).

A final misconception is terminological. Projected hybrid readout is not a universally fixed term, and it should not be interpreted as referring only to projective quantum measurement, only to 2D detector imaging, or only to mixed-signal electronics. The surveyed literature instead supports a broader reading: it is a class of readout strategies in which projection, transduction, or selective observation is combined with architectural hybridity to make otherwise unfavorable measurement tasks experimentally or statistically tractable.