One excitation can branch.
A tree spreads one 1 through several branches at once. A chain reaches new qubits one by one, so more qubits wait.
W treesame target, shorter schedule
An interactive field guide · Team Popeyes · Duke Quantum Hackathon
A perfect state on an imperfect chip.
New to quantum computing? Start with a game of sharing 1s. Then explore Google's 105-qubit Willow map and see why our code chooses different circuits for different targets.
Interactive demos are educational. Error rates in the routing lab are illustrative, not live Willow calibration.
GOOGLE QUANTUM AI CHALLENGE · MAJOR LEAGUE HACKING (MLH)SCROLL TO EXPLORE ↓
01 / THE MISSION
Share the excitement equally.
A qubit is a quantum version of a bit. Here, an excitation simply means a 1. A Dicke state shares exactly n ones across N qubits in every possible position.
For four qubits and two 1s, there are six valid answers. We want all six to have equal quantum amplitude and the right relative phase.
PLAYGROUND A EXACT TARGET STATE
Build your own Dicke state
Change the number of qubits and excitations. Then take a sample measurement.
Press measure to draw one valid bitstring.
|D⁴₂⟩ = (|0011⟩ + |0101⟩ + ···) / √6
VALID STRINGS6
CHANCE EACH16.7%
AMPLITUDE1/√6
The equal-weight outcomes6 states
Lit dots are 1s. Each valid row has exactly two.
02 / THE HARDWARE
Find a way through Willow.
This is the real 105-qubit, 182-coupler willow_pink topology. Tap two qubits, mark one unavailable, and compare the fewest-hop route with a route that avoids noisy links.
105QUBITS
ON THIS MAP
ON THIS MAP
PLAYGROUND BTOPOLOGY: REAL / ERRORS: ILLUSTRATIVE
Loading topology…
start target fewest hops noise aware weak qubit unavailable
Which path would you take?
Try the weak qubit at (6, 7). It sits on the direct path. The illustrative risk slider changes how costly its links are.
FEWEST HOPS——
NOISE AWARE——
Choose two qubits to compare routes.
FEWEST-HOP PATH
—ALTERNATIVE PATH
—Toy cost: independent CZ failures, approximately three CZs per SWAP. It omits idle decoherence, readout, parallel scheduling, and the exact gate compilation. This is a teaching demo, not the submission router.
Why not simply choose the shortest path? A SWAP typically costs several entangling gates. One bad coupler can erase the gain from a shorter route. Our actual submission weighs calibrated gate error, readout error, idle time, and expected score when choosing a placement.
HOW THE ALTERNATIVE PATH IS FOUND
Turn the chip into a weighted map.
Each qubit is a node and each coupler is an edge. Marking a qubit unavailable removes it from both searches. The gray route minimizes hop count. The green route runs Dijkstra’s algorithm again, this time minimizing estimated gate error.
- Price each move. If a coupler has illustrative CZ error p, a preterminal SWAP costs
−3 ln(1−p); the final interaction costs−ln(1−p). - Choose the smallest total. Adding those costs is equivalent to maximizing
∏(1−p)m, where m is 3 for a SWAP or 1 for the final interaction. - Compare and explain. The path readout above lists the exact qubits, SWAP count, and estimated gate survival for both choices. A longer detour wins when its lower edge errors offset the extra moves.
ARDUINO UNO Q · BROWSER PREVIEW
The chip, in 104 lights.
The UNO Q’s built-in 8 × 13 LED matrix shows the central window of this Willow map. Use the route controls above to change its paths. The browser's bonus bars compare the previous site snapshot with the attached folder's current circuit depths. The physical board's bundled demo still uses its earlier two-candidate bonus display.
Loading matrix preview…
Board connected to your computer? Open its local controls ↗ This address works only on the computer connected to the UNO Q; it is not a public board stream.
UNO Q8 × 13 MATRIX
ERROR-AWARE ROUTE
route qubit marker
03 / THE TWO CHECKS
The same answers can hide a different state.
The challenge checks measurements in both Z and X bases. Z asks whether the excitation count and probabilities look right. X probes the phases that make it a coherent quantum superposition.
THE PHASE FLIP EXPERIMENT
Same probabilities. Different interference.
For two qubits, flip the relative phase between |01⟩ and |10⟩. Watch what changes.
01 / Z BASISPopulation
The Z outcomes stay 50/50 in both cases.
02 / X BASISCoherence
⟨X⊗X⟩+1
The + state has the target correlation.
04 / THE CURRENT FOLDER'S SOLUTION
Several recipes. One selector.
Choose a target to see the first recipe used by the attached folder's submission.ipynb. The real Python code also checks the day's available qubits and connections, estimates error, and falls back when needed. See how the program does that →
MAIN TASK · D⁹₄
▤
Calibrated portfolio branch
Build several connected shapes, estimate their errors, and keep a promising valid circuit.
Here k = min(n, N−n): the code works on the side with fewer 1s, then flips all qubits if needed. The attached folder's selector is newer than the previously shown FINAL_v2 selector. Its performance comparisons are local simulations, not a measured score for this exact notebook. Read the full decision story →
BONUS · LOCAL DEPTH COMPARISON
How long are the circuits?
A moment is one time layer. The upper bar is the earlier FINAL_v2 depth; the lower bar is the current folder's submission.ipynb depth. Its bonus function compares several exact recipes internally. Move the sliders to inspect a pair.
Loading checked depths…
Earlier FINAL_v2
—
Current folder
—
Current depth —moments
05 / WHY THESE CHOICES
Save gates. Save time. Keep the state exact.
These examples come from the attached folder's local circuit comparisons. A smaller circuit can reduce opportunities for error, but these gate counts are not measured Willow fidelity.
Optimize small circuits ahead of time.
For six qubits with three 1s, an exact saved pattern uses far fewer CZ interactions than an earlier routed construction.
80→15CZ gates, earlier → current
The angles are found offline; physical placement uses the supplied calibration.
Use connected shapes for larger states.
For ten qubits with five 1s, a two-arm candidate cut the number of CZ interactions in the local comparison.
185→85CZ gates, earlier → current
The portfolio also checks paths and ladders, then estimates error.
ATTACHED FOLDER · LOCAL EVIDENCE
What was actually checked?
The folder reports automated tests, robustness builds with changed calibrations, and a checked depth for each eligible bonus pair. These are local checks.
419automated tests reported in folder
969robustness builds reported in folder
44.47bonus Σ Nn/depth · local comparison
The current submission.ipynb is a newer implementation than the previously displayed FINAL_v2. The organizer's preliminary hardware email tested an earlier notebook, so its hardware score must not be assigned to this current file. The final judging pairs and device calibration may differ from local simulations. See exactly what each check means →
THE CHALLENGE & EVENT
The community behind this project.
Team Popeyes built this explainer for the Google Quantum AI challenge at DuQuantum, the quantum hackathon at Duke. DuQuantum is a Major League Hacking (MLH) member event.
DuQuantum · Duke Quantum HackathonOfficial event site ↗
Google Quantum AIOfficial site ↗
Major League Hacking (MLH)Official site ↗
Logos are sourced from the organizations’ official sites linked above. This is an independent Team Popeyes explainer.
TAKE IT FURTHER
Now you can see the tradeoff.
Willow is a map of possible interactions. Dicke states need equal quantum amplitudes and intact phases. Our code joins exact math, physical connections, and calibration-aware choices.
Read the beginner guide