References

Work the bounds on this leaderboard are measured against.

Participate

Run it yourself, or point a coding agent at it.

git clone https://github.com/unitaryfoundation/stabrank
cd stabrank
# describe your decomposition in bounds/mybound.json
make fit BOUND=bounds/mybound.json ARGS=--write
make verify BOUND=bounds/mybound.json

fit solves for the exact coefficients, or tells you no exact combination of your terms reproduces the target. verify rebuilds the identity in exact arithmetic. If it passes, open a pull request adding the file and the leaderboard picks it up on the next build.

A bound the pipeline cannot check is recorded as cited and never takes a record.

  1. Campbell, Earl T., Anwar, Hussain, Browne, Dan E.. Magic-State Distillation in All Prime Dimensions Using Quantum Reed-Muller Codes. Physical Review X, vol. 2, p. 041021, 2012 · arXiv:1205.3104
    Distills the Howard-Vala eigenstates in every prime dimension; motivation for the p = 5 and p = 7 candidate orbits.
  2. Howard, Mark, Vala, Jiri. Qudit versions of the qubit pi/8 gate. Physical Review A, vol. 86, p. 022316, 2012 · arXiv:1206.1598
    The qudit pi/8 gates and their eigenstates for every prime p; the p = 3 eigenstate is the T3 orbit.
  3. Bravyi, Sergey, Gosset, David. Improved Classical Simulation of Quantum Circuits Dominated by Clifford Gates. Physical Review Letters, vol. 116, p. 250501, 2016 · arXiv:1601.07601 · DOI
    Approximate stabilizer rank and stabilizer extent only; carries no exact-rank value.
  4. Bravyi, Sergey, Smith, Graeme, Smolin, John A.. Trading Classical and Quantum Computational Resources. Physical Review X, vol. 6, p. 021043, 2016 · arXiv:1506.01396 · DOI
    Introduces stabilizer rank and the six-copy decomposition of the qubit H-type state.
  5. Bravyi, Sergey, Browne, Dan, Calpin, Padraic, Campbell, Earl, Gosset, David, Howard, Mark. Simulation of quantum circuits by low-rank stabilizer decompositions. Quantum, vol. 3, p. 181, 2019 · arXiv:1808.00128 · DOI
    Source of the seven-copy value chi(H^7) <= 12 recorded in the Qassim, Pashayan, and Gosset table; superseded by the 9 that the partial decomposition of kissinger2022partial gives.
  6. Huang, Yifei, Love, Peter. Approximate stabilizer rank and improved weak simulation of Clifford-dominated circuits for qudits. Physical Review A, vol. 99, p. 052307, 2019 · arXiv:1808.02406
    Approximate-rank exponents 2^{0.23 t}, 3^{0.32 t}, 5^{0.41 t}, 7^{0.40 t} for the qudit magic state at d = 2, 3, 5, 7; the d-term Clifford-orbit decomposition.
  7. Jain, Akalank, Prakash, Shiroman. Qutrit and Ququint Magic States. 2020 · arXiv:2003.07164
    Complete list of single-qutrit and single-ququint Clifford eigenstates; no strange-state analogue for any prime p > 3. Source list for p = 5 candidate orbits.
  8. Kocia, Lucas. Improved Strong Simulation of Universal Quantum Circuits. 2020 · arXiv:2012.11739
    Twelve-copy decomposition of the qubit H-type state into 47 stabilizer states, exponent log_2(47)/12 = 0.463.
  9. Prakash, Shiroman. Magic state distillation with the ternary {Golay} code. Proceedings of the Royal Society A, vol. 476, p. 20200187, 2020 · arXiv:2003.02717
    Golay-code distillation of the strange and Norrell states; no rank content.
  10. Heimendahl, Arne, Montealegre-Mora, Felipe, Vallentin, Frank, Gross, David. Stabilizer extent is not multiplicative. Quantum, vol. 5, p. 400, 2021 · arXiv:2007.04363 · DOI
    Extent is strictly sub-multiplicative for generic high-dimensional states; carries no exact-rank value.
  11. Kocia, Lucas, Sarovar, Mohan. Improved Simulation of Quantum Circuits by Fewer Gaussian Eliminations. Physical Review A, vol. 103, p. 022603, 2021 · arXiv:2003.01130
    Qutrit stabilizer-rank numerics; records chi(T3^3) as 8? and flags the search as possibly unconverged.
  12. Qassim, Hammam, Pashayan, Hakop, Gosset, David. Improved upper bounds on the stabilizer rank of magic states. Quantum, vol. 5, p. 606, 2021 · arXiv:2106.07740 · DOI
    Contracted cat states; source of the log2(3)/4 exponent.
  13. Seddon, James R., Regula, Bartosz, Pashayan, Hakop, Ouyang, Yingkai, Campbell, Earl T.. Quantifying quantum speedups: improved classical simulation from tighter magic monotones. PRX Quantum, vol. 2, p. 010345, 2021 · arXiv:2002.06181
    Dyadic negativity, mixed-state extent and generalized robustness; no exact-rank value.
  14. Kissinger, Aleks, van de Wetering, John. Simulating quantum circuits with {ZX}-calculus reduced stabiliser decompositions. Quantum Science and Technology, vol. 7, p. 044001, 2022 · arXiv:2109.01076
    Consumes the BBCCGH and QPG decompositions inside ZX simplification; no new rank value.
  15. Kissinger, Aleks, van de Wetering, John, Vilmart, Renaud. Classical Simulation of Quantum Circuits with Partial and Graphical Stabiliser Decompositions. vol. 232, p. 5:1--5:13, 2022 · arXiv:2202.09202
    chi(cat_4) = 2 used as a 2^{0.25 t} decomposition when the cat_4 pattern appears; a partial decomposition of T^5 into three terms each keeping one T, so chi(T^t) <= 3 chi(T^(t-4)): chi(H^7) <= 9 and chi(H^8) <= 12 on the board, and the glued cat_10 gives chi(H^10) <= 18.
  16. Kocia, Lucas, Tulloch, Genele. More Optimal Simulation of Universal Quantum Computers. 2022 · arXiv:2202.01233
    Weak-simulation prefactor via correlated sampling; quotes chi(T^4) = 4, chi(T^8) <= 12, chi(T^16) <= 108 from the cat-state construction.
  17. Labib, Farrokh. Stabilizer rank and higher-order Fourier analysis. Quantum, vol. 6, p. 645, 2022 · arXiv:2107.10551 · DOI
    Omega(n) exact-rank lower bound at every prime p; the p=3 magic state is the T3 orbit.
  18. Lovitz, Benjamin, Steffan, Vincent. New Techniques for Bounding Stabilizer Rank. Quantum, vol. 6, p. 692, 2022 · arXiv:2110.07781 · DOI
    Prop. 3.7 bounds exact rank from the field of definition of stabilizer coordinates, over Q(i).
  19. Peleg, Shir, Shpilka, Amir, Volk, Ben Lee. Lower Bounds on Stabilizer Rank. Quantum, vol. 6, p. 652, 2022 · arXiv:2106.03214 · DOI
    Subset-sum route; needs amplitudes attaining different values across Hamming-weight layers.
  20. Koch, Mark, Yeung, Richie, Wang, Quanlong. Speedy Contraction of {ZX} Diagrams with Triangles via Stabiliser Decompositions. 2023 · arXiv:2307.01803
    Tensored ZX star edges (triangle nodes, each of stabilizer rank 2) decomposed with 2^{0.774 t} terms; the only sub-product bound found for a CCZ-like resource, transfer to chi(|CCZ>^k) unconfirmed.
  21. Kliuchnikov, Vadym, Sch{\"o}nnenbeck, Sebastian. Stabilizer operators and {Barnes-Wall} lattices. 2024 · arXiv:2404.17677
    Minimal vectors of the Barnes-Wall lattices are stabilizer states; the lattice input to the Kalra-Sinha bounds.
  22. Mehraban, Saeed, Tahmasbi, Mehrdad. Quadratic Lower Bounds on the Approximate Stabilizer Rank. Proceedings of the 56th Annual ACM Symposium on Theory of Computing (STOC), 2024 · arXiv:2305.10277
    Omega~(n^2) for approximate rank, which carries to exact rank.
  23. de Silva, Nadish, Yin, Ming, Strelchuk, Sergii. Bases for optimising stabiliser decompositions of quantum states. 2024 · arXiv:2311.17384
    The space of linear dependencies of n-qubit stabilizer states has a basis of three-term dependencies; every decomposition is reachable by adding dependent triples. Qubit only.
  24. Camillo, Giulio, Peres, Filipa C. R., Heinrich, Markus, Bermejo-Vega, Juani. Symmetry-Accelerated Classical Simulation of Clifford-Dominated Circuits. 2025 · arXiv:2510.18977
    Optimal extent decompositions of real, diagonal and real-diagonal unitaries lie in the matching Clifford subgroup; extents up to seven qubits. Extent, not exact rank.
  25. Codsi, Julien, Laakkonen, Tuomas. Unifying Graph Measures and Stabilizer Decompositions for the Classical Simulation of Quantum Circuits. 2026 · arXiv:2603.06377
    Tree-width and rank-width simulation bounds; no exact-rank value.
  26. Kalra, Arnav, Sinha, Makrand. Stabilizer Ranks, Barnes Wall Lattices and Magic Monotones. Quantum, vol. 10, p. 2179, 2026 · arXiv:2503.04101
    Omega(n / log n) lower bound on the approximate rank of the H-type state via a quantitative stabilizer-fidelity bound.
  27. Labib, Farrokh, Russo, Vincent. Stabilizer rank bounds for magic-state orbits. 2026 · arXiv:2605.28586
    Per-copy exponents for the four qutrit orbits; the baselines this challenge is measured against.
  28. de Colnet, Alexis, Geerts, Floris, Hai, Rihan, Laarman, Alfons, Lee, Joon Hyung, P{\'e}rez, Guillermo A.. Quadratic Sums-of-Powers for Fixed-Parameter Tractable Quantum-Circuit Simulation. 2026 · arXiv:2605.29944
    Rank-width dynamic program with a stabilizer-rank optimization that takes the QPG decomposition as a black box.
  29. {dring-05}. qutrit-t3-structural-obstructions: exact structural obstructions for four-copy qutrit {T} stabilizer rank. 2026
    Two restricted theorems on decompositions of |T3>^4 (fixed-foliation and unique-crossing); does not claim chi(T3^4) >= 9. Not a paper; not re-run here.