QJosephson — Intelligent Simulation for Superconducting QPUs · QAIREON
Superconducting QPU simulation intelligence
QJosephson  ·  by QAIREON

QJosephson
Geometry in. T1 out.

Named after Brian Josephson — Nobel 1973 — who predicted the Josephson junction theoretically before it was ever fabricated. QJosephson does the same for your QPU: predict before you build.

1/T1  =  i  pi  ·  ω  ·  tan δi (1)
100×
Faster iteration
5
Loss interfaces modelled
2
Solvers · Palace + Elmer
T₁
Predicted before tapeout
BO
Bayesian design optimisation

§ 01   Solver Architecture

Two solvers.
One complete picture.

Palace is the gold standard for full 3D chip simulation. But not every simulation problem is 3D. Cross-sectional analysis — transmission line geometry, CPW field profiles, inductance per unit length — requires a different solver. QJosephson uses both, automatically selecting the right tool for each task.

Palace
AWS Center for Quantum Computing · awslabs/palace
3D FEM · Core
Production-grade open-source 3D finite element solver built specifically for superconducting quantum devices. Built on MFEM. Validated at parity with ANSYS HFSS and COMSOL. Scales from a laptop to 1.4B degrees of freedom on AWS EC2. Apache 2.0 licence — no licensing cost.
QJosephson uses Palace for
Full 3D chip eigenmode analysis — qubit frequencies, coupling strengths
Energy Participation Ratio (EPR) extraction across all 5 loss interfaces
Full chip T₁ prediction from assembled 3D geometry
Multi-qubit device simulation with complex 3D substrate stacks
Driven simulation for resonator quality factor extraction
Limitation

Palace operates exclusively in 3D. Cross-sectional problems require either an unnecessarily expensive 3D approximation or a dedicated 2D solver. This is where Elmer complements Palace.

Elmer FEM
CSC – IT Center for Science, Finland · ElmerCSC/elmerfem
2D/3D · Cross-section
Open-source, multi-physics FEM solver maintained by CSC Finland. Elmer handles 2D and 3D geometries across electrostatics, magnetostatics, and full electromagnetics. For superconducting circuit design, its strength is 2D cross-sectional analysis. GPL licence.
QJosephson uses Elmer for
CPW cross-section — characteristic impedance Z₀, capacitance and inductance per unit length (C′, L′)
Junction cross-section analysis — oxide barrier field distribution
Substrate-air interface participation at the 2D cross-section
Multi-layer substrate stacks — silicon, sapphire, SiO₂ permittivity effects
Fast design screening — 2D Elmer runs in seconds vs. hours for Palace
Limitation

Elmer's 2D cross-sectional results are approximations for a full 3D chip. Final T₁ validation always requires a full Palace 3D run.

QJosephson strategy
Elmer first, Palace to validate. A parametric sweep of 200 geometry variants runs in minutes via 2D Elmer cross-sections. The top 10 candidates proceed to full 3D Palace simulation. This two-stage architecture reduces total compute time by 20–50× while maintaining physical accuracy at the final prediction stage.

§ 02   Pipeline

Five steps, fully automated.
From geometry to fabrication decision.

01
GeomIQ
KQCircuits · GDS · NL

Geometry ingestion — KQCircuits, GDS, or natural language

Accepts KQCircuits Python designs, GDS II files, or plain-text chip descriptions. Parses the full layer stack, identifies junctions, pads, resonators, airbridges, and ground planes. Reconstructs a clean 3D geometry with correct material assignments for both Palace and Elmer meshing.

→ KQCircuits / GDS / text← 3D geometry + 2D cross-sections + layer stack
02
SimCore
Palace (3D) + Elmer (2D)

Dual-solver simulation — automatic routing between Palace and Elmer

QJosephson automatically decomposes the simulation task. Cross-sectional problems are dispatched to Elmer. Full chip eigenmode analysis goes to Palace. Both solvers are configured automatically — mesh density, boundary conditions, convergence targets — tuned for superconducting qubit geometries.

→ 3D geometry + 2D cross-sections← E-field distributions + eigenfrequencies + C′, L′ per unit length
03
EPREngine
All 5 interfaces

EPR extraction — complete interface loss budget

Computes the energy participation ratio for all five critical dielectric interfaces: metal-air top (MA-top), metal-air sidewall (MA-side), metal-air bottom (MA-bottom), substrate-air (SA), and metal-substrate (MS). The output is a complete interface loss budget showing which surface dominates T₁ limitation for this specific geometry.

→ E-field + geometry← p_MA · p_SA · p_MS · interface loss map
04
LossDB
Process-calibrated

Loss model — fabrication-process-calibrated tan δ database

Applies process-specific loss tangent values (tan δ) to convert EPR participation ratios into a predicted T₁. LossDB stores tan δ values organized by fabrication process — Nb on high-resistivity Si, Nb on sapphire, Al on Si, NbTiN on Si — each calibrated against real chip measurements.

→ EPR values + fabrication process← T₁ per channel + total T₁ + uncertainty bounds
05
VerifIQ
AI verification

Verification + confidence scoring

Compares the predicted T₁ against the historical distribution of measured T₁ values from chips simulated with the same process parameters. Generates a verification confidence score and flags predictions that disagree beyond expected variance before the design proceeds to optimisation.

→ T₁ prediction + historical LossDB← confidence score + anomaly flag + fabrication go/no-go

§ 03   Design Optimisation

The AI that designs
the qubit for you.

Semiconductor EDA tools have had multi-objective geometry optimisation for decades. QJosephson brings the same intelligence to superconducting QPU design.

Core engine

Bayesian Optimisation over geometry space

The design optimisation engine treats QPU geometry as a high-dimensional parameter space and uses Bayesian Optimisation (BO) to find the geometry that maximises T₁ subject to fabrication constraints. BO is sample-efficient, works well in 10–50 dimensional spaces, and provides uncertainty estimates alongside each recommendation.

After 50–200 evaluations, BO converges on a Pareto-optimal design that the engineer could not have found manually in weeks of iteration.

Optimisation parameters
Junction area→ EJ target
Pad dimensions (W × L)→ EC target
CPW gap width→ Z₀ = 50 Ω
Ground plane clearance→ min crosstalk
Coupling resonator length→ g target
Substrate thickness→ max T₁
Pareto front · T₁ vs anharmonicity
Optimised designs (BO output)
Manual design space (historical)
Selected candidate → Palace 3D validation
Speed layer

Gaussian Process surrogate model

QJosephson trains a Gaussian Process (GP) surrogate on completed simulation results — enabling 100× faster T₁ estimates. The GP provides uncertainty estimates: regions with high uncertainty are prioritised for true Palace simulations, minimising total compute time.

Multi-objective

Pareto-optimal QPU design

Maximising T₁ trades against anharmonicity, coupling strength, frequency targeting, and fabrication yield. QJosephson returns the full Pareto front — a set of designs where no objective can be improved without degrading another.

Domain AI

Superconducting QPU foundation model

A domain-specific neural network trained on superconducting qubit design data: thousands of simulated and measured transmon, fluxonium, and cat qubit geometries with their corresponding eigenfrequencies, anharmonicities, and T₁ values.

Constraints

Fabrication-aware design space

QJosephson integrates process design rules — minimum feature size, junction aspect ratio limits, proximity rules, etching bias — as hard constraints. Every candidate reaching Palace validation is tapeout-ready without manual DRC review.

Insight

T₁ sensitivity map

For each geometric parameter, how much does T₁ change per unit variation? The sensitivity map tells the engineer which dimensions matter most for coherence — and therefore which fabrication tolerances to tighten.


§ 04   Technology Comparison

QJosephson vs HFSS, COMSOL, Palace standalone, pyEPR

FeatureQJosephsonANSYS HFSSCOMSOL RFPalace standalonepyEPR
Purpose-built for superconducting QPUYesNoNoPartialYes
KQCircuits geometry importYesManualNoNoNo
3D FEM solver (Palace)YesYesYesYesNo
2D cross-section solver (Elmer)YesNoManualNoNo
Automatic solver routing (2D/3D)YesNoNoNoNo
Auto EPR extraction (all 5 interfaces)YesNoNoPartialPartial
T₁ prediction from geometryYesNoNoNoNo
Fabrication-calibrated loss databaseYesNoNoNoNo
Bayesian geometry optimisationYesNoNoNoNo
GP surrogate model (100× faster sweeps)YesNoNoNoNo
Trained QPU foundation modelYesNoNoNoNo
Verification confidence scoreYesNoNoNoNo
T₁ sensitivity mapYesManualManualNoNo
Natural language geometry inputYesNoNoNoNo
Requires FEM expertise to operateNoYesYesYesPartial
Licence cost€15–40K/yr€20–50K/yr€10–30K/yrFreeFree
Improves with chip measurement dataYesNoNoNoNo
Note on solver choice: Palace vs HFSSANSYS HFSS remains the commercial industry standard. QJosephson supports HFSS as an optional simulation backend. Palace is the default because it is free, open-source, and validated at HFSS parity for superconducting qubit simulation geometries. Teams choosing Palace save €20–50K/year per seat.
Note on FDTD methodsFDTD solvers (Lumerical, Tidy3D, MEEP) are time-domain methods designed for photonic devices at optical frequencies. Superconducting qubits are narrowband microwave resonators at 4–8 GHz — eigenmode FEM is the correct method, used universally across the field (Google, IBM, IQM, Alice & Bob).

§ 05   Defensibility

Why this cannot be replicated
by an AI agent next week.

Fabrication-calibrated LossDB
tan δ values per process backed by real chip measurements. The physics is open. This data is not — it accumulates with every chip measured.
Very strong · compounds over time
Trained QPU foundation model
A model trained on thousands of simulated and measured QPU geometries cannot be reproduced from public literature alone.
Strong · data-gated
Bayesian optimisation over fabrication-constrained space
The combination of BO + GP surrogate + process design rules + LossDB calibration is not a library integration — it is domain expertise encoded into a working system.
Strong · integration depth
Network effect — chip data flywheel
After 10 companies contribute chip measurements, QJosephson predictions outperform any single company's internal tool. After 50, it becomes the definitive reference.
Strong · accelerates with scale
KQCircuits native integration
IQM's design tool has 178+ stars and is the entry point for IQM's ecosystem. First-mover integration owns the workflow.
Strong · ecosystem position
The FEM solver layer (Palace + Elmer)
Commoditised. QJosephson competes on the verified intelligence layer above them.
None — by design

§ 06   Roadmap

From prototype to the
standard QPU design tool.

Now → Aug 2025
v0.1 — KQCircuits → Palace → T₁ prototype
First working end-to-end pipeline: KQCircuits geometry → Gmsh mesh → Palace eigenmode → EPR extraction → T₁ prediction. Validated on real superconducting chip geometries. First version of LossDB with Nb-on-Si process data.
KQCircuits importPalace backendEPR engine v1LossDB v1T₁ prediction
Sep 2025 → Feb 2026
v0.2 — Elmer integration + 2D/3D automatic routing
Elmer FEM integrated for 2D cross-sectional analysis. Automatic solver routing. Parametric sweep capability using Elmer for fast screening.
Elmer 2Dauto solver routingCPW cross-sectionjunction analysisparametric sweep
Mar 2026 → Sep 2026
v0.3 — AI geometry layer + natural language input
Natural language → KQCircuits geometry via fine-tuned LLM. First conference presentation (GDR IQFA). First preprint submitted to arXiv. First external user.
NL geometryDRC checkingarXiv preprintGDR IQFAexternal user
Oct 2026 → Jun 2027
v0.5 — Bayesian optimisation + GP surrogate
BO engine over geometry parameter space. GP surrogate for 100× faster evaluations. Multi-objective Pareto optimisation. First QPU design optimised entirely by QJosephson and submitted for fabrication.
Bayesian optimisationGP surrogatePareto frontverification scorefabrication candidate
Jul 2027 → Dec 2027
v0.8 — QPU foundation model + multi-process LossDB
Domain-specific neural network. LossDB extended to 4+ fabrication processes. 3+ publications. APS March Meeting contributed talk. Two paying companies.
QPU foundation modelmulti-process LossDB3 publicationsAPS talk2 customers
2028 → 2029
v1.0 — Production platform · QAIREON QJosephson
Clean Python API and web interface. 5+ paying customers. Enterprise contracts with 2+ quantum hardware companies. Seed round target €1–2M. Company incorporated under QAIREON.
v1.05 customersseed fundedQAIREON companyweb interface

Brian D. Josephson
Named after
Brian D.
Josephson
b. 1940  ·  Cambridge

Josephson predicted the quantum tunnelling of Cooper pairs through a thin insulating barrier — theoretically, before a single junction had been fabricated. The effect was verified experimentally two years later and now underpins every superconducting qubit in existence.

Nobel Prize in Physics  ·  1973

Early access

The QPU design tool
is being built.

QJosephson is in active development. If you are a quantum hardware company, a university lab designing superconducting circuits, or an investor interested in quantum EDA, we want to hear from you.