From an engineering use case to a quantum solve · QUICK-PDE / H-DES
Mockup
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The challengeWhat keeps engineers up at night
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Why quantum?Classical vs quantum — the maze
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The QUICK platformOur approach & use cases
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Engineering problemWhat the simulation engineer needs
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Governing equationsThe physics as differential equations
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Quantum solveH-DES on quantum hardware
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The secret sauceWhy H-DES wins on PDEs
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Beyond the wallWhat quantum unlocks — and when
iHow to use this demo — a guided tour from an engineering problem to a quantum solution
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Follow the journeyMove left → right through the numbered tabs above. Click any tab to jump straight to that stage.
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Pick a use caseOn the platform and journey steps, choose an industry vertical from the list on the left to follow it end‑to‑end.
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Use Back / NextEvery panel has buttons at the bottom to walk through the story one stage at a time.
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Try the solverOn Quantum solve, adjust qubits & circuit depth, choose a backend, then press Run to watch it solve live.
Before we start · the big idea
Why a quantum computer is different
Finding the exit of a maze
A classical computer explores a maze the only way it can — one corridor at a time, walking each branch, hitting dead ends and backtracking. A quantum computer can hold many paths at once and let them interfere, so the route to the exit stands out. That same difference is what lets it attack simulations that overwhelm classical machines.
Classicalone path at a time
exploring…
Quantummany paths at once
superposition…
Three ideas do the work: superposition — hold many possibilities at the same time · interference — reinforce the right answer and cancel the wrong ones · measurement — read out the exit. Real quantum advantage applies to specific, structured problems — like the differential equations behind engineering simulation, which is exactly what QUICK targets.
Our solution · QUICK
The scalable, multi-hardware quantum software platform
QUICK turns a real engineering problem into a quantum solve. One platform brings together our patent-pending solver, a write-once programming layer, and the world's quantum hardware — so a simulation engineer can target today's quantum computers without rebuilding for each machine.
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Unique intellectual property
Universal Multiphysics Solver
H-DESpatent pending · EP24306601
Quantum algorithm development for today's quantum computers — a hybrid differential-equation solver that handles the physics behind real simulations.
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Productivity tool
MPQP — Multi-Platform Quantum Programming
Implement onceDeploy everywhere
A single programming layer that compiles the same algorithm to every supported backend, removing per-vendor rewrites and lock-in.
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Hardware partners
Quantum algorithm execution
IBMAWSIonQQuobly…
Run on real superconducting, trapped-ion and emerging hardware through one interface, and move as the hardware improves.
Develop with the solver → program once with MPQP → execute on any quantum partner
Applications · for the simulation engineer
Each QUICK application packages one family of physics. Pick a use case to follow it from the engineering problem to the governing equations to a quantum solve.
★ Quantum for GoodThe same platform turned on climate, disaster response and Earth observation — use cases spanning flood and tsunami forecasting, air quality and atmospheric modelling. Pick one to follow its journey.
Step 1 · the engineering problem
Objective
Why it's hard classically
What quantum could change
Step 2 · from physics to differential equations
Boundary / initial conditions
Variables
How H-DES takes over
Step 3 · quantum solve with H-DES
H-DES solve
Hybrid-loop convergence iteration 0
loss (log scale)
Solution vs. classical
classical / analyticalH-DES attempt
✓
Validated result
The challenge · across every simulation domain
What keeps simulation engineers up at night
Fluids · structures · combustion · electromagnetics · climate · risk — the same wall
From aerospace to energy to finance, high‑fidelity numerical simulation runs into the same barrier: the most realistic, highest‑value problems are the ones classical computers struggle to solve in time, at cost, or at all. Here is the wall every domain hits — and why quantum computing is a candidate to break through it.
Computational fluid dynamics
Structural / FEA
Combustion
Electromagnetics
Climate & weather
Finance & risk
☾
“Did I mesh it finely enough — or did I miss the thing that breaks?”
3 a.m. · CFD engineer
The resolution wall
Every step up in fidelity multiplies the work. Degrees of freedom grow as Nᵈ — the curse of dimensionality — so memory and runtime explode faster than hardware improves.
↳You coarsen the model and hope the missing detail didn’t matter.
Non‑linearity & coupling
Turbulence, combustion chemistry, contact, fluid–structure interaction — the realistic physics is non‑linear and tightly coupled. Classical solvers get slow, fragile, or simply don’t converge.
↳The highest‑value cases are the hardest to trust.
Time, cost & energy
High‑fidelity runs take hours to days on expensive, power‑hungry HPC clusters, and every design iteration waits in the queue.
↳Innovation moves at the speed of the cluster.
Why quantum computing is seen as a way through
A quantum computer holds an exponentially large state space in a compact way and operates on all of it at once. That is a natural fit for the linear‑algebra and differential‑equation cores at the heart of simulation — the very places classical methods hit the wall. The promise: push the fidelity wall back, explore far more of the design space, and attack non‑linear problems head‑on, at lower compute and energy cost.
Honest framing: quantum hardware is still early, and advantage applies to specific, structured problems — not everything. But PDE‑based simulation is exactly the kind of structured problem where it is most credible. That is the opening ColibriTD targets.
Step 4 · the secret sauce
Why H‑DES ultimately wins on PDEs
Encode the function, not the mesh · non‑linearity for free · NISQ‑ready today
Every route to a differential equation runs into the same two walls: dimensionality (the problem gets too big to store) and non‑linearity (the hardest physics breaks the method). Classical solvers hit the first wall; most quantum solvers hit both. H‑DES is built to clear both at once — here is how.
Classical mesh solvers
FEM / FDM / CFD
✗Degrees of freedom grow as Nᵈ — the curse of dimensionality.
✗Non‑linear & stiff systems demand fine meshes and many iterations.
✗Memory‑ and compute‑bound; each design loop costs hours–days of HPC.
Hits a wall on resolution & dimension
Other quantum methods
Linear‑systems / HHL
✗Built for linear systems — non‑linear PDEs don't fit the framework.
✗Need deep circuits and fault‑tolerant hardware that doesn't exist yet.
✗Reading the full solution back out erases the theoretical speed‑up.
Powerful in theory, blocked in practice
ColibriTD
H‑DES
✓Encodes the function, not a mesh — grid‑free, evaluate anywhere.
✓Non‑linear terms cost the same as linear ones.
✓Shallow & variational — runs on today's NISQ hardware.
Validated on real hardware, today
How it actually works · the H‑DES variational loop
The four ideas that make it better
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Encode the function, not the mesh
uᵢ(x) = Σᵢ cᵢ(θ) · φᵢ(x)spectral coefficients carried by the quantum state
A classical solver stores one value per mesh point, so cost explodes with resolution and dimension. H‑DES represents the entire solution as a short spectral series (Chebyshev / Legendre / Fourier). A smooth field needs only a few coefficients — and you can evaluate it anywhere in the domain, mesh‑free.
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Turn the PDE into an optimization
L(θ) = ∫ | R[ uᵢ ](x) |² dx → minthe equation's residual becomes the cost function
Instead of inverting a giant linear system, H‑DES measures how well the trial function satisfies the equation — its residual — and lets a classical optimizer tune the circuit parameters θ until that residual vanishes. Boundary conditions enter the same cost.
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Non‑linearity for free
R[u] = ∂ₜu + u ∂ₓu − ν ∂ₓₓuthe non‑linear term is just one more term in the cost
This is the differentiator. For linear‑systems quantum solvers, a term like u·∂u/∂x breaks the method outright. In H‑DES it is simply another term added to the residual — handled at no extra algorithmic cost versus a linear one. The hardest physics (Navier–Stokes, combustion) stops being a special case.
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One circuit per unknown — on today's hardware
read out { cᵢ }, not 2ⁿ amplitudesshallow, NISQ‑ready, no readout bottleneck
Each unknown function gets its own parametrized circuit, and the circuits stay shallow — so the loop runs on current noisy hardware rather than waiting for fault tolerance. Because the answer is a few coefficients, there is no exponential readout wall. Validated on IBM Heron (50 qubits, 10 000 shots) for inviscid Burgers.
Why it scales where the others stall
Classical mesh
DoF ~ Nᵈ
grid points per dimension — the curse of dimensionality.
Quantum linear‑systems
needs fault tolerance
deep circuits + full state readout undo the speed‑up.
H‑DES
qubits ~ log(basis)
scales with spectral resolution, not grid size — shallow & NISQ‑ready.
✓
Patented method (EP24306601) — one variational engine that handles linear and non‑linear PDEs alike, hardware‑agnostic through the QUICK write‑once layer, and demonstrated on real quantum processors.
The payoff · beyond the wall
We break through the wall — and not all at once
Quantum computing + the ColibriTD H‑DES approach push past the barrier from slide one
Remember the wall from the start: the most realistic, highest‑value simulations sit just out of classical reach. H‑DES on quantum hardware holds the cost under the feasible budget and carries it into that zone — the cases that were out of reach become solvable. But it arrives in waves: some use cases are validated on real hardware today, others land as the programmes and the machines mature.
Classical cost — explodes, stalls at the wallH‑DES (quantum + ColibriTD) — stays feasible, goes throughfeasible budget · deadline
What quantum unlocks — and when
TodayAs hardware scales
Wave 1 · validated today
Proven on real quantum hardware
Run and benchmarked now
Computational fluid dynamics
Inviscid Burgers on IBM Heron — 50 qubits, 10 000 shots
Material deformation / structures
Non‑linear FEA on Eviden QLM + IBM Heron (18 qubits)
Wave 2 · active programmes
Running in funded programmes
Climate · disaster response · Earth observation
Radiative transfer
Integral extension of H‑DES built for Earth-observation modelling
Shallow water — floods & tsunamis
Disaster response · climate modelling
Convection–diffusion — air quality
Air quality — pollutant & heat transport
Wave 3 · on the roadmap
Next, as hardware scales
Representative models ready to scale up
Combustion
Stiff, strongly non‑linear reaction–diffusion
Heat transfer
Process heat & thermal management
Electromagnetics (Maxwell)
Radar, antennas, semiconductors
Option pricing — finance
Derivatives & risk (Merton / Black–Scholes)
The bottom line
One patented engine (EP24306601), one write‑once QUICK layer, and a clear sequence: start where quantum already delivers on real hardware, expand through active climate and Earth‑observation programmes, then scale into the rest as the machines grow. The wall doesn’t move — we go through it, use case by use case.
Same chart as slide one — only now the green H‑DES curve stays under the feasible budget and crosses into the zone that used to be out of reach.
