STOC-QComp: A Falsifiable Device Framework for a Bounded-Capacity Superconducting-Qubit Processor with a Mechanically Tunable Casimir Boundary Condition ()
1. Introduction—From Framework to Device
STOC-QSIM v2.0 [1] established a phase-driven toroidal-Peltier control primitive and integrated it with the NWO ecosystem. STOC-QC [2] [4] extended the substrate into a computational framework for hybrid quantum systems whose scaling mechanism is reservoir engineering rather than qubit-count growth [5]. Version 1.0 of this manuscript attempted to specify the physical device—the “thing a lab, a factory, or a satellite operator can buy, install, and use”. The device architecture and manufacturing flow are summarized in Figure 1.
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Figure 1. Simplified engineering block diagram. Row 1 shows the linear manufacturing pipeline from materials to readout. Row 2 is the critical detail added in v2.0: the Casimir nanogap (40 - 400 nm, mechanical structure) and the microwave cavity (~cm-scale, GHz mode) are physically distinct structures; the nanogap displacement d modulates the cavity frequency ωc(d), the qubit-cavity coupling g(d), and the dissipation rates Γ(d) through mechanical action, NOT by supplying GHz Casimir modes directly. Row 3 shows the six deployment tiers; only T1 - T3 carry DESIGN status. Every block is fully specified with parameter, source class, uncertainty, and status label in S2 - 7.
1.1. What v1.0 Got Wrong
Two v1.0 claims cannot survive scrutiny as written:
(i) The Casimir pressure numerical value. v1.0 stated the pressure at d = 100 nm is ~1.3 mN/m2. The correct ideal parallel-plate value is
—off by a factor of ~104 [6].
(ii) The claim that a 40 - 400 nm Casimir gap supplies GHz modes to the qubit. The fundamental parallel-plate mode is f1 = c/(2d); at d = 100 nm this is 1499.0 THz—an optical/UV frequency, not the 4 - 8 GHz superconducting-qubit band. The v1.0 expression
therefore does not place cavity resonances in the microwave range.
This is not a small correction. The Casimir-qubit coupling mechanism must be rebuilt to make the paper physically defensible.
1.2. What This v2.0 Does Instead
The revised architecture treats the Casimir structure as a mechanical actuator that modifies a physically separate microwave cavity, following the established cavity-electromechanics literature [7] [8]. In this picture:
Casimir gap d → mechanical displacement → microwave cavity parameter → qubit coupling/dissipation (1.1)
The nanogap supplies mechanical actuation and a small, well-modelled Casimir force; the microwave cavity supplies the GHz mode structure that couples to the qubit. The remainder of the paper specifies this hybrid architecture, its operating envelope, the reference qubit modality, environmental-noise budgets, manufacturing economics with evidence classes, verification tests with a statistical analysis plan, and an extensive-form strategic game.
2. Device-Specific Casimir-Microwave Coupling Model
This section supersedes S2 of v1.0 in its entirety.
2.1. Corrected Casimir Pressure
For two parallel perfectly-conducting plates of area A separated by distance d, the ideal zero-temperature pressure is given by [6] and evaluated at four representative gap widths in Table 1 (values plotted in Figure 2):
(2.1)
Table 1. Corrected Casimir pressure at four key gap values. The v1.0 figure of 1.3 mN/m2 at 100 nm is replaced by the correct 13 Pa. The Drude column is a phenomenological reduction factor accounting for finite Au conductivity and SiN dielectric spacer per [6] [7]; the precise reduction requires a full Lifshitz calculation for the Au·SiN·Au multilayer geometry [6] and is a first target of the device-characterisation programme (S7).
d (nm) |
|P| ideal metal (Pa) |
|P| Drude Au·SiN·Au estimate (Pa) |
40 |
507.86 |
345.35 |
100 |
13.00 |
10.79 |
200 |
0.813 |
0.739 |
400 |
0.0508 |
0.0482 |
Figure 2. Corrected Casimir pressure vs plate separation d. Solid blue: ideal-metal result. Dashed magenta: phenomenological finite-conductivity reduction for the Au·SiN·Au stack. The v1.0 assertion of 1.3 mN/m2 at 100 nm is off by a factor of ~104 from the true 13 Pa; this figure replaces v1.0 Figure 2.
2.2. Nanogap Cavity Mode vs Qubit Microwave Band
The fundamental parallel-plate electromagnetic mode of a gap of width d is f1 = c/(2d). Values at the four key gaps are given in Table 2 and plotted against the superconducting-qubit microwave band in Figure 3.
2.3. Hybrid Cavity-Electromechanical Hamiltonian
Replace v1.0’s H_Cas(d) with the standard cavity-electromechanics Hamiltonian [7] [8]:
(2.2)
with the plate separation:
(2.3)
where a, a† are the microwave-cavity photon operators; σ+, σ- are the transmon raising/lowering operators; b, b† are the mechanical mode operators; UCas(d) is the mechanical potential from the Casimir attraction (not the qubit reservoir); Hmech collects the mechanical kinetic and spring terms; and xctrl(t) is a piezo-electrostatic control displacement. The four physically measurable coupling derivatives are then:
(2.4)
Table 2. Nanogap fundamental electromagnetic mode across the STOC-QComp operating band. All values lie in the optical/near-UV range. None overlap the 4 - 8 GHz superconducting-transmon transition band. The v1.0 mechanism of “moving a 100 nm Casimir gap directly moves cavity resonances through the qubit’s microwave spectral density” is therefore physically incorrect as stated.
d (nm) |
f1 = c/(2d) (Hz) |
f1 (THz) |
wavelength λ = 2d (nm) |
40 |
3.747e+15 |
3747 |
80 |
100 |
1.499e+15 |
1499 |
200 |
200 |
7.495e+14 |
749 |
400 |
400 |
3.747e+14 |
375 |
800 |
Figure 3. Nanogap fundamental cavity mode vs superconducting-qubit microwave band. The two bands are separated by five orders of magnitude in frequency. A microwave cavity resonant with a 5 GHz qubit requires a physical length ≈ 3 cm, not a 40 - 400 nm gap.
2.4. Non-Ideal Casimir Corrections
The ideal expression (2.1) is used only as a first-order benchmark. The device prediction uses a finite-conductivity Lifshitz calculation incorporating the Au·SiN·Au geometry [6]. The non-ideal effects that the prediction must account for are enumerated in Table 3:
Table 3. Non-ideal Casimir corrections that must be included in the device-level prediction. Each effect is characterised by an established measurement or literature model [6].
Effect |
Physical origin |
Order of magnitude |
Finite Au conductivity |
Drude/plasma-frequency reduction |
5% - 30% reduction of |P| |
SiN dielectric spacer |
Real dielectric response ε (iξ) |
Geometry-dependent |
Finite plate thickness |
Two-slab Lifshitz [6] |
5% - 15% correction |
Surface roughness |
Perturbative expansion in Rq/d |
≤10% at Rq < d/10 |
Patch potentials |
Contact potential difference across grain |
Sub-Casimir at d > 100 nm |
Finite plate area |
Diffraction/edge modes |
Small if A
d2 |
Temperature (T = 10 mK) |
Matsubara sum with T ≠ 0 |
Negligible at nanoscale |
Contamination/adsorbates |
Oxide/hydrocarbon layer |
Reduces effective d |
Electrostatic bias |
Applied potential across gap |
Adds separate ε0E2/2 term |
Residual gas pressure |
Molecular impact drag |
Requires UHV |
Parallelism error θ |
Non-parallel plate model |
Handled by capacitive metrology |
3. Cavity Operating Envelope
The mechanical structure must satisfy stability, pull-in, thermal, and electromagnetic constraints simultaneously. Every parameter below is a design variable to be measured on the first prototype. Table 4 summarizes the parameters, their symbols, design targets, and validation methods.
Table 4. Cavity operating envelope. All rows are design targets with named validation methods.
Parameter |
Symbol |
Design target |
Validation method |
Nominal gap |
d0 |
40 - 400 nm |
Capacitive metrology |
Gap RMS noise |
σd |
TBD from T1/T2 budget |
Displacement spectrum |
Parallelism angle |
θ |
TBD (interferometry) |
Fabry-Perot/white-light |
Mechanical resonance |
fm |
TBD (kHz range) |
Network analyser |
Mechanical Q |
Qm |
TBD |
Ringdown |
Actuator bandwidth |
Ba |
≥ 10fm |
Frequency response |
Pull-in margin |
MPI |
> 2 × safety factor |
Capacitance-vs-V sweep |
Microwave insertion loss |
Lmw |
TBD (<0.1 dB target) |
S21 · VNA |
Added cryogenic heat load |
Pact |
< cold-stage budget |
Calorimetry |
Displacement noise PSD |
Sd (f) |
TBD |
Optical interferometry |
Operating temperature |
T |
10 mK · 4 K by tier |
Ge thermometer |
Surface roughness |
Rq |
TBD (<d/10) |
AFM |
Mechanical stability requires:
(3.1)
For an electrostatic parallel-plate actuator, the pull-in criterion V < VPI (d) must also be satisfied at every operating point.
4. Reference Qubit Architecture
v1.0 said the bare qubit “may be Josephson, spin, or topological”, but the manufacturing pipeline specified a Josephson QPU. v2.0 commits to a single reference architecture.
4.1. Reference: Superconducting Transmon
For tiers T2 - T6, the reference architecture is a superconducting transmon QPU with: fixed- or tunable-frequency transmon qubits; 4 - 8 GHz nominal qubit transition frequency; dilution refrigerator at 10 - 20 mK base temperature; microwave XY control; flux control (if tunable); dispersive resonator readout, multiplexed; randomised benchmarking for one- and two-qubit gate fidelity, with T1 and T2 characterisation.
4.2. T1 Is Not a Full QPU
v1.0 claimed a 4 K personal unit with 200 - 400 qubits and 99.0% fidelity. This is not physically achievable with a conventional 5 GHz transmon at 4 K. The Bose factor gives:
(4.1)
(4.2)
At T = 4 K, fq = 5 GHz: hf/kBT = 0.06 and pe = 48.5%. At T = 20 mK: pe = 6.2e−04% (thermal ground state). A 48.5% excited-state population is incompatible with 99% gate fidelity. Figure 4 shows pe vs T for three representative qubit frequencies.
Figure 4. Thermal excited-state population vs temperature for three qubit frequencies. Recent 4 K microwave quantum infrastructure achieves usable performance via cold-loaded radiative cooling of specific input lines [9]—but this suppresses thermal noise on control channels, not on the qubit itself. A conventional 5 GHz transmon at 4 K remains ~48% thermally excited.
4.3. Deployment Architecture
The complete deployment map across tiers T1 - T6, showing qubit modality, operating temperature, control and readout schemes, and target two-qubit gate fidelity per tier, is presented in Table 5.
Table 5. Deployment architecture with explicit qubit modality, temperature, control, readout, and target two-qubit gate fidelity F2 per tier. All fidelity values are design targets to be verified by randomised benchmarking on prototype units.
Tier |
Function |
Qubit |
T |
Control |
Readout |
Target F2 |
Status |
T1 |
4 K demo/control platform |
(none in v2) |
4 K |
cryo-CMOS |
resonator diag |
N/A (demo) |
DESIGN |
T2 |
SME lab QPU rack |
transmon |
10 - 20 mK |
μwave XY + flux |
dispersive |
≥99.0% |
DESIGN |
T3 |
Industrial QPU |
transmon |
10 - 20 mK |
μwave XY + flux |
dispersive |
≥99.5% |
DESIGN |
T4 |
Subsea/subterranean |
transmon |
10 - 20 mK |
μwave XY + flux |
dispersive |
≥99.0% |
ROADMAP |
T5 |
Naval/aerospace mobile |
transmon |
10 - 20 mK |
μwave XY + flux |
dispersive |
≥99.0% |
ROADMAP |
T6 |
Orbital platform |
transmon |
10 - 20 mK |
μwave XY + flux |
dispersive |
≥99.5% |
ROADMAP |
5. Environmental-Noise Decoherence Model
v1.0 Table 5 asserted +0.1%, +0.3%, +0.7%, +1.1% fidelity gains for magnetic noise, vibration, cosmic-ray, and thermal shielding without a causal model. v2.0 replaces this with an explicit environmental-noise transfer model.
The total qubit relaxation rate is:
(5.1)
The total pure dephasing rate is:
(5.2)
For a Clifford gate of duration tg:
(5.3)
with C1, C2 ≈ O(1) coefficients depending on the specific gate. The environmental transfer functions from each environmental input to Γ are summarised in Table 6:
Table 6. Environmental-noise transfer chains. For each environmental input, the transfer function to Γ is specified explicitly. Table 6 replaces the v1.0 asserted fidelity gains; the corresponding numerical fidelity contributions become primary endpoints of verification test T21 (S7).
Environmental input |
Transfer chain |
Γ contribution |
Magnetic field noise |
SB(f) → SΦ(f) → Sω(f) → Γφ |
Dephasing via flux noise [10] |
Vibration |
Sx(f) → Sd(f) → {Sωc(f), Sg(f)} → Γ1, Γφ |
Both channels via cavity |
Ionising radiation |
Φμ → Γqp → Γ1, Γφ |
Quasiparticle poisoning [11] |
Charge noise |
SQ(f) → Sω(f) → Γφ |
1/f charge, suppressed in transmon |
Temperature |
T → nth → pe, Γth |
Direct thermal population (S4.2) |
6. Manufacturing Economics
All manufacturing figures now carry an explicit evidence class and are separated between prototype and volume estimates. The evidence classes are defined in Table 7.
Table 7. Manufacturing evidence classes. No v2.0 row is labelled EXP because no STOC-QComp device has yet been fabricated.
Label |
Meaning |
Use in this paper |
VQ |
Vendor quotation (written) |
Rare—only where cited |
VE |
Vendor estimate (verbal/informal) |
L0 commodity materials |
LE |
Literature-derived |
Fab yields from published nodes |
IE |
Internal engineering estimate |
Most L1-L8 rows |
ET |
Experimental target (pilot-run goal) |
T22 pilot yields |
EXP |
Experimentally demonstrated |
Not used in v2.0 (no measured yields yet) |
6.1. Prototype vs Volume Cost
The manufacturing cost per unit as a function of volume N is:
(6.1)
with Cfab(N) exhibiting the usual experience-curve decay. This resolves the v1.0 inconsistency: the T2 BOM of $412,700 is a prototype/single-unit figure; the $150,000 low-end selling price is a volume figure that assumes both L1 - L7 cost reduction and a stripped-down configuration. The two figures apply at different points in the experience curve. The prototype selling price should be substantially higher than the low-end volume price.
6.2. Serial Yield
Multiplying the min and max of every stage in Table 8 gives an overall serial yield estimate of 3.31% (lower bound) to 39.83% (upper bound). Under no reading of Table 8 does the pipeline imply a finished-device yield above ~40%. The v1.0 impression that the pipeline could deliver >90% finished yield is incorrect. This is a direct consequence of nine multiplicative yield stages and is tracked as verification test T22 (S7).
Table 8. Nine-stage manufacturing pipeline with per-row evidence class. Yields are engineering estimates (IE) or literature-derived from analogous-process yields (LE), not measured yields of STOC-QComp units. Costs for L1 - L7 are prototype/single-unit estimates; volume manufacturing costs are expected to fall as described in S6.3.
Stage |
Process |
Cost/unit (USD) |
Yield (%) |
Evidence |
L0 Mat |
Bi2Te₃ · Au · SiN · Nb · NbTiN |
$1.2k - $18k |
99 - 100 |
VE |
L1 Fab |
MBE nanowires · e-beam · sputter |
$14k - $85k |
60 - 90 |
LE |
L2 Wafer |
300 mm ring array |
$8k - $45k |
70 - 92 |
LE/IE |
L3 Pkg |
Flip-chip · TSV · shield |
$4k - $22k |
65 - 88 |
IE |
L4 Ctrl |
RV64 + STOC + DAC/ADC |
$3k - $18k |
75 - 95 |
IE |
L5 Cryo |
Dilution stage + shielding |
$120k - $850k |
80 - 95 |
VE/IE |
L6 Casimir |
Au/SiN/Au + actuator |
$25k - $95k |
60 - 85 |
IE (target) |
L7 QPU |
Josephson qubit array |
$28k - $180k |
40 - 75 |
LE |
L8 Deploy |
Environmental hardening |
$8k - $600M+ |
85 - 95 |
IE |
7. Verification Tests · Statistical Analysis Plan
v1.0 ST20 - T23 asserted “statistically significant” improvements without specifying a test, sample size, α, or effect size. V2.0 replaces these with a full statistical analysis plan. The four tests, primary endpoints, sample sizes, analysis methods, and success thresholds are given in Table 9.
Table 9. Verification tests with primary endpoint, sample size, analysis method, and success threshold. T22 explicitly acknowledges that the initial pilot is a feasibility study, not a statistically definitive production-yield demonstration.
Test |
Primary endpoint |
Sample size |
Analysis |
Threshold |
T20 |
βd = ∂Γ1/∂d and ∂Smeasured(fq)/∂d |
n = 5 - 10 devices · 10 gap settings |
Linear regression |
95% CI excludes 0 |
T21 |
Two-qubit error per Clifford (EPC) by randomised benchmarking |
n = 10 QPUs/environment |
Mixed-effects model |
Pre-defined effect size + 95% CI |
T22 |
Per-stage yield Yi = ki/ni |
ni ≥ 10 per stage (pilot) |
Binomial 95% CI |
Feasibility only, not production |
T23 |
DKL(Pmeasured||PLindblad) and DTV |
100 identical control replays |
Held-out likelihood |
Pre-defined divergence bound |
T23 replaces v1.0’s Landauer-based reservoir-consistency claim (which does not follow from Landauer’s principle [12] as stated) with a predictive-distribution comparison: the primary criterion is whether predictive error decreases when experimentally measured reservoir parameters are substituted for nominal parameters. Landauer’s thermodynamic bound is retained in the philosophical discussion (S10) but is not the statistical criterion.
8. Illustrative Strategic Game
v1.0 S9 stated a 4-player subgame-perfect equilibrium [13] under a single 4 × 4 payoff matrix. A subgame-perfect equilibrium requires an extensive-form specification with players, information sets, actions, order of moves, strategies, terminal histories, and payoff vectors—not a single matrix. V2.0 replaces this with a properly specified extensive-form game. Both the payoff values and the equilibrium selection are labelled illustrative. The extensive-form tree is shown in Figure 5.
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Figure 5. Extensive-form 4-stage sequential game. Stage 1: Regulator chooses open/closed. Stage 2: Incumbent chooses high/competitive price. Stage 3: Challenger chooses enter/stay out. Stage 4: User chooses incumbent/challenger. Terminal nodes carry payoff quadruples (uI, uC, uU, uR). The bold red path is the illustrative backward-induction solution under the stated payoff assumptions (open regulation → competitive incumbent → challenger enters → user picks challenger). The specific numerical payoffs are illustrative model assumptions, not empirical measurements. Replaces v1.0 Figure 5 in its entirety.
9. Limitations
Every load-bearing limitation of this manuscript is enumerated in Table 10 below.
Table 10. Explicit limitations enumeration. Every entry corresponds to a specific verification test or future experiment (S7 and S10).
# |
Limitation |
1 |
No STOC-QComp device has been fabricated; all results are engineering specifications. |
2 |
The Casimir-mediated modification of qubit coupling and dissipation is a testable HYPOTHESIS (T20), not an experimentally demonstrated effect. |
3 |
The 200 - 1000 qubit bounded-capacity regime is a design hypothesis motivated by Palmer’s Rational Quantum Mechanics proposal [3], not an established physical law. |
4 |
T1 is a demonstrator/control platform, not a full QPU. The 4 K thermal population catastrophe prevents conventional 5 GHz transmon operation at that temperature. |
5 |
Manufacturing yields are engineering estimates (IE) or literature-derived (LE), not measured yields of STOC-QComp units. |
6 |
Serial yield lies between 3.3% and 39.8%; the pipeline does not imply a finished-device yield > 40%. |
7 |
The extensive-form game payoffs (Figure 5) are illustrative model assumptions, not empirical measurements. |
8 |
T4 - T6 tier feasibility depends on successful validation of T2 - T3; T4 - T6 are ROADMAP. |
9 |
The Casimir non-ideal correction values (Table 3) require a full Lifshitz calculation for the Au·SiN·Au multilayer, not performed in this manuscript. |
10 |
Numerical values of ∂ωc/∂d, ∂g/∂d, ∂κ/∂d, ∂Γ1/∂d are design variables to be measured, not simulation outputs of this paper. |
10. Conclusions
STOC-QComp v2.0 provides a device-level specification and experimental programme for investigating a mechanically tunable electromagnetic environment coupled to a bounded-capacity superconducting quantum processor. The present work does not establish the Casimir-mediated modification of qubit dissipation experimentally; rather, it identifies the physical parameters that must be measured to establish or falsify that hypothesis.
The most immediate validation target is a single reference transmon QPU coupled to a mechanically tunable microwave cavity via a Casimir-force-loaded actuator. The relevant observables are the cavity response, mechanical displacement spectrum, qubit relaxation and dephasing rates, and gate fidelity as functions of d. Manufacturing yield, environmental fidelity improvements, and deployment economics are likewise treated as engineering hypotheses whose uncertainty will be reduced through prototype fabrication.
If these experiments confirm the predicted coupling and environmental-control relationships, the STOC-QComp architecture provides a basis for subsequent scaling and deployment studies [14]. If they do not, the framework identifies specific falsification points at the Casimir, mechanical, microwave, or qubit-control layers.
On measurement and interpretation: v1.0 described collapse as an “engineerable event” resolving “interpretational debate”. v2.0 uses the narrower, defensible language of an operationally engineered measurement environment: the device does not establish a new interpretation of quantum mechanics [15], but provides an experimentally controlled setting in which the relationship between deliberately engineered environmental coupling and measurement statistics can be investigated.
Research Status
STOC-QComp is a device-framework proposal (DESIGN). The qubit architecture, control interfaces, manufacturing flow, and deployment concepts are engineering specifications; they have not yet been demonstrated as an integrated production device. The Casimir mechanical structure is DESIGN. Casimir-mediated modification of qubit coupling and dissipation is an experimentally testable HYPOTHESIS. T1 and T2 are prototype targets (DESIGN); T3 is a DESIGN target; T4-T6 are ROADMAP configurations contingent upon successful validation of the preceding tiers. This paper does not claim that a STOC-QComp device has been fabricated, characterised, or shipped.