A
Quantum hardware
Fire Opal + IBM
The original unitary QASM receives full Z-basis measurements and separate all-0/all-1 readout calibration.
- 120 qubits
- SCV and meson states
- Raw and corrected counts
Quantum simulation · SU(2) lattice gauge theory
When does a
hadron become measurable?
A reproducible workbench for non-Abelian hadron dynamics — from 120-qubit QASM on IBM hardware to tensor networks and an explicitly validated LSH Hamiltonian.
LSH chainN = 60
120qubits
x = 100coupling
20Trotter steps
Not one algorithm on three machines, but three complementary lines of evidence: hardware execution, the same compiled circuits on classical MPS simulators, and independent small-system validation of the underlying Hamiltonian.
01 · Architecture
Three routes, one control question
Each route answers a different part of the reproducibility question.
B
Circuit level
Aer + ITensor MPS
The same compiled QASM is simulated locally as a matrix-product state.
- Apples-to-apples circuit check
- Explicit bond dimension and cutoff
- Not the full paper TDVP
C
Physical validation
LSH dense → MPO → TDVP
Local LSH operators are embedded in Gauss-law-valid sectors and checked against exact evolution.
- Hermiticity and sector conservation
- Dense-versus-MPO check
- Build-up toward N = 60
02 · Physics
Gauge-invariant building blocks
The Loop-String-Hadron representation rewrites the local degrees of freedom as one bosonic loop variable and two binary fermion occupations.
|nℓ, ni, no⟩
- nℓ
- bosonic flux, truncated numerically
- ni, no
- incoming and outgoing fermion occupations
- Q
- conserved total charge; target value Q = 60
Dimensionless Hamiltonian
H = HE + μHM + xHI
Abelian Gauss Law on every link
NL(r) = NR(r + 1)
NL = nℓ + no(1 − ni)NR = nℓ + ni(1 − no)From Z-basis counts
n = ½(1 − ⟨Z⟩)
The local signal is Δnf = nfmeson − nfSCV.
03 · Results
Step 5 in perspective
The timings below use different scopes. That distinction is part of the result.
Fire Opal main circuits
0.987shardware-only · 512 shots · ibm_fezAer MPS · compiled QASM34.281 s34.7×
ITensor MPS · compiled QASM174.611 s176.9×
Paper · Pauli Propagation CPU477.447 s483.7×
Paper · Pauli Propagation GPU547.581 s554.7×
Paper · ITensor/TDVP TN584.092 s591.7×
Fire Opal smoke runs
Signal across Trotter depth
| Step | Depth | Raw Δnf | Readout-corrected | Hardware time |
|---|---|---|---|---|
| 05 | 66 | −0.75195 | −0.76425 | 0.987 s |
| 10 | 125 | +0.32422 | +0.33484 | 1.581 s |
| 15 | 177 | −0.06836 | −0.05441 | 2.175 s |
| 20 | 237 | −0.38672 | −0.39000 | 2.769 s |
Hardware time = estimated circuit duration × shots. Queueing, compilation, API wait and local decoding are excluded.
Dense ↔ MPO/TDVP · N = 4
1.20 × 10−8RMSE in local Q profileEnergy difference
1.11 × 10−11exact versus TDVP evolutionNorm difference
2.50 × 10−13small-system smoke test04 · Claim boundaries
What this repository does — and does not yet — demonstrate
A fast execution time is compelling only when task, accuracy and time definition are matched.
Reproducible technical route
- Fire Opal actions and metadata are captured locally.
- The same QASM is tested classically at MPS level.
- The small LSH-MPO route agrees with exact evolution.
- Global charge Q acts as a physical diagnostic.
Full quantum-advantage claim
- Local Δnf and tracker nf(t) do not yet share a matched normalization.
- The N = 60 LSH-TDVP reproduction has not been run locally.
- Hardware-only time is not end-to-end wall-clock time.
- The 512-shot runs are smoke tests, not a precision campaign.
05 · Start here
Read the repository in this order
- 01README.md
Purpose, directories and current claim boundary.
- 02HADRON_FIRE_OPAL.md
Hardware route, runtimes and benchmark results.
- 03hadron_observable_analyzer.py
From Z-basis counts to Q and Δnf.
- 04lsh_mpo_build_notes.md
The route from the local LSH basis to MPO/TDVP.
- 05hadron_quantum_win_boundary.md
The compact, current timing interpretation.
Open, inspectable, bounded