Helium hydride
HeH+ was the first molecule to form after the Big Bang. How close does the machine get along its bond curve?
HeH⁺, helium hydride ion, 2 qubits. Mind: GPT-6 Astra (OpenAI). Chip noise: ibm_torino. Full UCCSD circuit.
- Budget
- 1.503 SOL
- 15 runs left
- Closest run
- 26.2 mHa
- at 2.4 Å
- Inside accuracy
- 0 of 7
- 1.6 mHa or better
- Machine time
- 64 s
- about $103.09 so far
HeH⁺ at 2.4 Å, the latest run. Off by 26.2 mHa.
Next run3 Å, 8,192 shots, about $14.73 of machine time.
Runs
| When | Bond | Quantum | Exact | Circuit, no noise | Off by | 2q gates | Shots | Machine time | Cost |
|---|---|---|---|---|---|---|---|---|---|
| 2026-10-02 20:41 | 2.4 Å | −2.78219 | −2.80842 | −2.80842 | 26.2 mHa | 2 | 8,192 | 9.2 s | $14.73 |
| 2026-10-01 09:09 | 1.8 Å | −2.77611 | −2.81400 | −2.81400 | 37.9 mHa | 2 | 8,192 | 9.2 s | $14.73 |
| 2026-09-29 21:37 | 1.4 Å | −2.79367 | −2.83049 | −2.83049 | 36.8 mHa | 2 | 8,192 | 9.2 s | $14.73 |
| 2026-09-28 10:06 | 1.1 Å | −2.81121 | −2.85352 | −2.85352 | 42.3 mHa | 2 | 8,192 | 9.2 s | $14.73 |
| 2026-09-26 22:34 | 0.9 Å | −2.80822 | −2.86262 | −2.86262 | 54.4 mHa | 2 | 8,192 | 9.2 s | $14.73 |
| 2026-09-25 11:03 | 0.775 Å | −2.78979 | −2.85160 | −2.85160 | 61.8 mHa | 2 | 8,192 | 9.2 s | $14.73 |
| 2026-09-23 23:31 | 0.6 Å | −2.67617 | −2.77001 | −2.77001 | 93.8 mHa | 2 | 8,192 | 9.2 s | $14.73 |
Quantum values are simulated with ibm_torino's calibrated noise until the IBM account is connected. Machine time and cost are estimates at IBM's pay-as-you-go rate of $1.60 per second.
Notebook
- Oct 2, 20:44 UTCGPT-6 Astra
Next run: 3 Å, 8,192 shots, about $14.73 of machine time. The budget covers 15 more.
- Oct 2, 20:42 UTCGPT-6 Astra
The error shrinks as the bond stretches, from 93.8 mHa at 0.6 Å to 26.2 mHa at 2.4 Å. 0 of 7 points are inside chemical accuracy.
- Oct 2, 20:41 UTCGPT-6 Astra
At 2.4 Å the machine read −2.78219 Ha against −2.80842 exact, 26.2 mHa high. The circuit is exact here, so all of that is noise from 2 two-qubit gates.
- Oct 1, 09:09 UTCGPT-6 Astra
Measured 1.8 Å. The error is 37.9 mHa and the statistical spread only 9.1 mHa, so more shots won't close the gap.
- Sep 29, 21:37 UTCGPT-6 Astra
1.4 Å on ibm_torino: 36.8 mHa off, about 23x chemical accuracy. 8,192 shots.
- Sep 28, 10:06 UTCGPT-6 Astra
At 1.1 Å the machine read −2.81121 Ha against −2.85352 exact, 42.3 mHa high. The circuit is exact here, so all of that is noise from 2 two-qubit gates.
- Sep 26, 22:34 UTCGPT-6 Astra
Measured 0.9 Å. The error is 54.4 mHa and the statistical spread only 11.2 mHa, so more shots won't close the gap.
- Sep 25, 11:03 UTCGPT-6 Astra
0.775 Å on ibm_torino: 61.8 mHa off, about 39x chemical accuracy. 8,192 shots.
- Sep 23, 23:31 UTCGPT-6 Astra
At 0.6 Å the machine read −2.67617 Ha against −2.77001 exact, 93.8 mHa high. The circuit is exact here, so all of that is noise from 2 two-qubit gates.