2-qubit conjectures · Selene shot proofs

Track B-Selene turns rule (M)'s matrix-canonical verdict into physical proof. For each of the 10 shortest PROMOTED 2q conjectures, we run the two contrasting representatives through Selene's IdealErrorModel over a 108-cell tomography grid (36 product preps × 3 diagonal basis pairs ZZ/XX/YY) at 256 shots/cell. A PASS means every outcome-probability difference |p_A − p_B| falls below 4·√(0.5/shots).

conjectures

PASS

10/10

grid

108

total time

104.7s

Conjecture #1
PASS
diag≈[0.71+0.00i, 0.71+0.00i, 0.00-0.71i, 0.00-0.71i] nz=8/16
A
S0H0
B
H1S0H0H1
cells
108/108
worst Δp
0.1172
threshold
0.1768
elapsed
148.9s
worst cells
prep basis dmax pass
0+i ZZ 0.1172 ✓
-- ZZ 0.1094 ✓
1- YY 0.1016 ✓
1+ ZZ 0.0977 ✓
1-i YY 0.0898 ✓
+- ZZ 0.0898 ✓
-i+ YY 0.0898 ✓
+1 YY 0.082 ✓
Conjecture #2
PASS
diag≈[0.50+0.50i, 0.50+0.50i, 0.50+0.50i, 0.50+0.50i] nz=8/16
A
H0S0H0
B
H0H1S0H0H1
cells
108/108
worst Δp
0.0898
threshold
0.1768
elapsed
103.8s
worst cells
prep basis dmax pass
0- ZZ 0.0898 ✓
-- ZZ 0.0859 ✓
+1 XX 0.082 ✓
0+i XX 0.0781 ✓
11 YY 0.0781 ✓
-+i ZZ 0.0781 ✓
-i1 XX 0.0781 ✓
++ ZZ 0.0742 ✓
Conjecture #3
PASS
diag≈[0.50+0.00i, -0.50+0.00i, 0.00-0.50i, 0.00+0.50i] nz=16/16
A
H1S0H0
B
H0H0S0H0H1
cells
108/108
worst Δp
0.1211
threshold
0.1768
elapsed
111.4s
worst cells
prep basis dmax pass
-i+i YY 0.1211 ✓
+i+i ZZ 0.1172 ✓
+0 YY 0.1094 ✓
-i0 ZZ 0.1055 ✓
-i+i XX 0.1055 ✓
-- XX 0.1016 ✓
-+i ZZ 0.1016 ✓
01 ZZ 0.0977 ✓
Conjecture #4
PASS
diag≈[0.71+0.00i, 0.71+0.00i, 0.00-0.71i, 0.00+0.71i] nz=8/16
A
S0H0CZ
B
H1S0H0H1CZ
cells
108/108
worst Δp
0.1211
threshold
0.1768
elapsed
104.1s
worst cells
prep basis dmax pass
--i YY 0.1211 ✓
+i0 XX 0.1211 ✓
-i+ YY 0.1211 ✓
1- XX 0.1094 ✓
-+ ZZ 0.1016 ✓
-+i YY 0.1016 ✓
-i+i XX 0.0977 ✓
00 ZZ 0.0898 ✓
Conjecture #5
PASS
diag≈[0.71+0.00i, 0.71+0.00i, 0.71+0.00i, 0.71+0.00i] nz=8/16
A
S0H0S0
B
H1S0H0S0H1
cells
108/108
worst Δp
0.1094
threshold
0.1768
elapsed
105.6s
worst cells
prep basis dmax pass
-- YY 0.1094 ✓
-i+ YY 0.0977 ✓
+- YY 0.0938 ✓
0+ ZZ 0.0859 ✓
-i- XX 0.0859 ✓
-i-i ZZ 0.0859 ✓
-+i YY 0.082 ✓
+i1 YY 0.082 ✓
Conjecture #6
PASS
diag≈[0.71+0.00i, 0.71+0.00i, 0.71+0.00i, 0.71+0.00i] nz=8/16
A
S0S0H0
B
H1S0S0H0H1
cells
108/108
worst Δp
0.1484
threshold
0.1768
elapsed
108.5s
worst cells
prep basis dmax pass
--i ZZ 0.1484 ✓
-i1 XX 0.1016 ✓
00 XX 0.0977 ✓
+i-i ZZ 0.082 ✓
+-i XX 0.0781 ✓
-i0 XX 0.0781 ✓
++i YY 0.0742 ✓
-i+i XX 0.0742 ✓
Conjecture #7
PASS
diag≈[1.00+0.00i, 1.00+0.00i, 0.00-1.00i, 0.00-1.00i] nz=4/16
A
S0S0S0
B
H0S0H0S0H0
cells
108/108
worst Δp
0.1094
threshold
0.1768
elapsed
118.4s
worst cells
prep basis dmax pass
-0 XX 0.1094 ✓
01 XX 0.1055 ✓
0+i XX 0.1055 ✓
-i1 YY 0.1055 ✓
--i XX 0.0859 ✓
0+ YY 0.082 ✓
0+i YY 0.082 ✓
00 XX 0.0781 ✓
Conjecture #8
PASS
diag≈[0.71+0.00i, 0.00-0.71i, 0.00+0.71i, 0.71+0.00i] nz=8/16
A
S0S1H1
B
H0H0S1H1S0
cells
108/108
worst Δp
0.1172
threshold
0.1768
elapsed
105s
worst cells
prep basis dmax pass
-+i YY 0.1172 ✓
1+i YY 0.1094 ✓
-+ XX 0.1055 ✓
-i- YY 0.0977 ✓
0+ YY 0.0938 ✓
0- XX 0.0859 ✓
+i-i YY 0.0859 ✓
-i-i YY 0.0859 ✓
Conjecture #9
PASS
diag≈[0.35+0.35i, -0.35-0.35i, 0.35+0.35i, -0.35-0.35i] nz=16/16
A
H0H1S0H0
B
H0S0H0H1
cells
108/108
worst Δp
0.1367
threshold
0.1768
elapsed
97.2s
worst cells
prep basis dmax pass
+i1 YY 0.1367 ✓
-i- XX 0.1055 ✓
0+i XX 0.0977 ✓
+i- XX 0.0977 ✓
00 XX 0.0938 ✓
-- XX 0.0898 ✓
-i-i XX 0.0859 ✓
0- ZZ 0.082 ✓
Conjecture #10
PASS
diag≈[0.50+0.50i, 0.50+0.50i, -0.50+0.50i, -0.50+0.50i] nz=8/16
A
H0S0H0S0
B
S0S0S0H0
cells
108/108
worst Δp
0.1445
threshold
0.1768
elapsed
104.7s
worst cells
prep basis dmax pass
1-i ZZ 0.1445 ✓
+i+ YY 0.1211 ✓
01 YY 0.1094 ✓
+i+i ZZ 0.1094 ✓
-1 YY 0.1055 ✓
0+ ZZ 0.0977 ✓
++ XX 0.0938 ✓
1- YY 0.0898 ✓

prep	basis	dmax	pass
0+i	ZZ	0.1172	✓
--	ZZ	0.1094	✓
1-	YY	0.1016	✓
1+	ZZ	0.0977	✓
1-i	YY	0.0898	✓
+-	ZZ	0.0898	✓
-i+	YY	0.0898	✓
+1	YY	0.082	✓

prep	basis	dmax	pass
0-	ZZ	0.0898	✓
--	ZZ	0.0859	✓
+1	XX	0.082	✓
0+i	XX	0.0781	✓
11	YY	0.0781	✓
-+i	ZZ	0.0781	✓
-i1	XX	0.0781	✓
++	ZZ	0.0742	✓

prep	basis	dmax	pass
-i+i	YY	0.1211	✓
+i+i	ZZ	0.1172	✓
+0	YY	0.1094	✓
-i0	ZZ	0.1055	✓
-i+i	XX	0.1055	✓
--	XX	0.1016	✓
-+i	ZZ	0.1016	✓
01	ZZ	0.0977	✓

prep	basis	dmax	pass
--i	YY	0.1211	✓
+i0	XX	0.1211	✓
-i+	YY	0.1211	✓
1-	XX	0.1094	✓
-+	ZZ	0.1016	✓
-+i	YY	0.1016	✓
-i+i	XX	0.0977	✓
00	ZZ	0.0898	✓

prep	basis	dmax	pass
--	YY	0.1094	✓
-i+	YY	0.0977	✓
+-	YY	0.0938	✓
0+	ZZ	0.0859	✓
-i-	XX	0.0859	✓
-i-i	ZZ	0.0859	✓
-+i	YY	0.082	✓
+i1	YY	0.082	✓

prep	basis	dmax	pass
--i	ZZ	0.1484	✓
-i1	XX	0.1016	✓
00	XX	0.0977	✓
+i-i	ZZ	0.082	✓
+-i	XX	0.0781	✓
-i0	XX	0.0781	✓
++i	YY	0.0742	✓
-i+i	XX	0.0742	✓

prep	basis	dmax	pass
-0	XX	0.1094	✓
01	XX	0.1055	✓
0+i	XX	0.1055	✓
-i1	YY	0.1055	✓
--i	XX	0.0859	✓
0+	YY	0.082	✓
0+i	YY	0.082	✓
00	XX	0.0781	✓

prep	basis	dmax	pass
-+i	YY	0.1172	✓
1+i	YY	0.1094	✓
-+	XX	0.1055	✓
-i-	YY	0.0977	✓
0+	YY	0.0938	✓
0-	XX	0.0859	✓
+i-i	YY	0.0859	✓
-i-i	YY	0.0859	✓

prep	basis	dmax	pass
+i1	YY	0.1367	✓
-i-	XX	0.1055	✓
0+i	XX	0.0977	✓
+i-	XX	0.0977	✓
00	XX	0.0938	✓
--	XX	0.0898	✓
-i-i	XX	0.0859	✓
0-	ZZ	0.082	✓

prep	basis	dmax	pass
1-i	ZZ	0.1445	✓
+i+	YY	0.1211	✓
01	YY	0.1094	✓
+i+i	ZZ	0.1094	✓
-1	YY	0.1055	✓
0+	ZZ	0.0977	✓
++	XX	0.0938	✓
1-	YY	0.0898	✓

Why this matters

Each PROMOTED 2q conjecture is an identity rule (M) accepts via matrix-canonical residue but the structural rewriter cannot. We confirm rule (M) on Selene shots: the 2q tomography grid (36 product preps × 3 diagonal basis pairs ZZ/XX/YY = 108 cells, or 9 basis pairs = 324 cells in 'full' mode) must agree within 4·√(0.5/shots) per outcome for every cell. PASS = rule (M) is physically real on this conjecture. FAIL = the TS-side matrix oracle disagrees with shot statistics.

A PASS verdict here closes the loop from structural rewriter → matrix oracle → physical shot statistics. The two representatives of each conjecture have different structural residues (rewriter is incomplete) but identical canonical 4×4 unitaries (rule M's oracle) — and Selene confirms they are indistinguishable on actual measurement outcomes.