Guard the circuit. Spend your ancillas wisely. Mind the magic.
Place spacetime Pauli checks on a noisy circuit, decide where the T gates go, and run it. Your score is the fidelity rate R = Fps·keepβ of the post-selected output, computed with qiskit-paulice and Qiskit Aer. No number on this page is hand-set.
1 · Mission
2 · Sentinels
Click a qubit label on the board to post a sentinel (one ancilla, one check) on it.
3 · Magic placement
Spacetime board
Trade-off map for this level
Every dot is a legal move in this level, evaluated in Qiskit Aer. Curves are lines of equal fidelity rate for the current shot price. Your move is the ring; the optimum is the star (revealed after you play).
4 · Run
β=0 values purity only, β=1 values raw yield. β=½ is signal-to-noise per shot.
Result
| Ancilla qubits | - |
| Extra two-qubit gates | - |
| Two-qubit depth | - |
| Z-safe T sites left | - |
| Checks broken by T | - |
Your best scores
How the game maps onto the physics
Spacetime Sentinels is built around one technique: low-overhead error detection with spacetime codes
(Martiel and Javadi-Abhari, 2025), implemented by the qiskit-paulice add-on. The board is the spacetime diagram of a
six-qubit brickwork Clifford circuit. Rows are qubits, columns are layers of CZ gates.
Error detection
Ancilla checks flag the errors they can see and those shots are thrown away. Errors the checks cannot see pass through. Nothing is repaired. You pay in discarded shots.
Error mitigation
The noisy hardware is left alone. The estimate of an observable is corrected afterwards (ZNE, PEC, twirling, readout correction) at the cost of extra circuits and shots.
Error correction
One logical qubit lives in many physical qubits. Stabilizers are measured again and again and a decoder infers and undoes errors while the computation runs.
Rule to physics
| Game rule | Physics it stands for | Where it is computed |
|---|---|---|
| Post a sentinel on a qubit row (max 4) | One ancilla qubit coupled to one target data qubit. The check is a sequence of controlled-Pauli (X, Y or Z) gates from the ancilla onto that target at several times. | qiskit_paulice.add_pauli_checks (cost gamma, method windowed) |
| Teal dots on a row | The time steps at which that check touches its target. A spacetime check is spread in time instead of measuring one heavy operator at one instant. | Read from the checked circuit |
| Ancilla budget | Qubit overhead. Every extra check adds entangling gates and therefore its own noise. | Cost columns in every record |
| Green and red sites | Green: every check acts as I or Z there, so a Z error is invisible and a T gate commutes with all checks. Red: some check acts as X or Y there. | CheckedCircuit.uncovered_paulis |
| Magic quota (T gates) | Non-Clifford resource. add_pauli_checks only takes Clifford circuits, so T gates are injected after the checks are found. | T inserted into the checked circuit |
| Safe-zone placement | T only on green sites. Every check stays valid (verified: it never fires on the ideal circuit). | Noiseless statevector of the checked circuit |
| Blind placement | T on fixed random sites. A T on a red site turns a check into a random coin: it fires on perfect shots. | Same |
| Retire broken checks | Stop post-selecting on a broken check. Its gates stay, so it still disturbs the state. | Same |
| Run | Payload, checks, ancilla readout, post-selection, under the announced noise model. | Qiskit Aer density-matrix simulation, exact |
| Score | Fidelity rate R = Fps·keepβ with the ideal state as reference. Post-selected fidelity is never shown without its kept fraction. | sentinels.scoring |
How a score is computed
- Payload. A brickwork Clifford circuit on 6 qubits with 6, 12 or 18 CZ layers (same family as the IBM tutorial), optionally doped with 1 to 16 T gates.
- Reference. Stabilizer simulation for the Clifford payload, statevector simulation for T-doped payloads.
- Checks. qiskit-paulice finds one check per chosen target qubit.
- Noise. Two-qubit depolarizing noise after every CZ (payload and checks) and a readout bit flip on every qubit, the same model used to pick the checks. T gates are noiseless, as virtual RZ gates are on IBM hardware.
- Readout and post-selection. Each syndrome bit is the parity of the ancilla and some output bits. Shots with any non-zero syndrome are discarded.
- Numbers. Fps is the fidelity between the ideal state and the post-selected state; keep is the probability that a shot survives. Both are exact (density matrix), and were cross-checked against 50,000-shot runs of the Aer
SamplerV2primitive.
What the game is trying to teach
- Checks are not free. On shallow circuits the noise added by the checks costs about as much as they catch: most moves score below posting no sentinel at all, and the best one beats it by only a couple of percent.
- T gates are free on the hardware but not for the code. They add no noise, yet each one placed on an X/Y-covered wire breaks a check. A broken check is worse than no check: it throws away good shots, and even when ignored it still disturbs the state.
- Protection and magic compete for the same spacetime. Every check you add removes Z-safe sites. With too many checks there is nowhere left to put the T gates.
A very short history
Honest limitations
- Six data qubits and at most four checks, so that every move can be simulated exactly. Trends were checked over five random payloads, but larger circuits may behave differently.
- The noise is uniform and Pauli, and idling noise is ignored, as in the current qiskit-paulice check picker.
- The web page plays back results that were computed in advance with Qiskit for every legal move. The same moves can be computed live with
sentinels play. - Fidelity here is a state fidelity of the post-selected data register. The XOR of output bits into each syndrome is done coherently in simulation; it is classical post-processing in an experiment and gives identical measurement statistics.
Lab results
All plots are produced by the scripts in experiments/ of the repository, averaged over five random payloads unless stated. Full numbers are in results/data.
About
Spacetime Sentinels was built for the Advanced track of the Qiskit Fall Fest 2026 hackathon at IIT Jodhpur, on the prompt Gamifying Error Detection, Mitigation and Correction (error-detection track) written by Wenyu Sun and provided by IBM Quantum.
Team. Sumit Tapas Chongder and Aditya Kumar (equal contribution), Department of Computer Science & Engineering and Department of Physics, Indian Institute of Technology Jodhpur.
Links. Source code · Report (PDF) · Video walkthrough
Built on. Qiskit, Qiskit Aer, qiskit-paulice and qiskit-ibm-runtime (fake backends only). Method: S. Martiel and A. Javadi-Abhari, Low-overhead error detection with spacetime codes, arXiv:2504.15725, and S. Martiel et al., Sampling hard circuits with verifiably high fidelity, arXiv:2607.25941. Game idea inspired by D. Litinski, A Game of Surface Codes, Quantum 3, 128 (2019).
AI use. AI assistants were used while writing code and text, as disclosed in the report. All physics choices and results were checked by the authors.
Licence: Apache 2.0.