Scientific guide
The terminology, units and comparison rules behind the published results.
Fermion-to-qubit mapping: JW, P, PF and PT
A mapping encodes the electronic Hamiltonian in qubit operators. JW denotes Jordan-Wigner. P denotes parity without reduction. PF uses the known particle numbers to reduce the parity encoding. PT additionally tapers qubits using Hamiltonian symmetries and the selected symmetry sector. These abbreviations are the conventions of these datasets, not universal software names. The number of remaining qubits depends on the molecule and active space.
Active space and basis
An active space selects electrons and spatial orbitals treated explicitly in the correlated calculation. 2e2o and 2e,2o both mean two active electrons in two spatial orbitals. Orbital indices and their selection matter as well as these counts. STO-3G is the orbital basis used in these studies. Different geometries or active spaces define different molecular models.
UCC, initial state and parameters
UCC means unitary coupled cluster, a parameterized circuit family. These studies use a Hartree-Fock initial state with double excitations. The parameter vector specifies one point in that circuit family; parameter ordering must be retained for reproduction.
COBYLA and objective evaluations
COBYLA is a derivative-free classical optimizer. An objective evaluation estimates the energy at a parameter vector; it is not necessarily an optimizer iteration. maxiter is an optimizer budget, and early convergence is possible. Final energy is the final reported objective value. Best observed energy is the lowest sampled value along the trajectory.
Energy, reference error and hartree (Ha)
Hartree is the energy unit; 1 mHa is 0.001 Ha. Signed error is energy minus its stated reference; absolute error is its magnitude. Compare errors only with the matching geometry, basis, Hamiltonian convention, active space and reference method. BeyondH2 compares the active electronic Hamiltonian with active-space CASCI, excluding nuclear-repulsion and inactive-space constants. A lower raw energy across different molecules does not indicate better accuracy. A noisy minimum below the reference can arise from finite-shot selection.
Shots, precision and uncertainty
Shots are repeated circuit measurements. Nominal shots and target precision are requested settings; actual allocation can depend on the primitive and mitigation options. An estimator standard error describes its statistical uncertainty, not all hardware bias or temporal drift. Repeated independent executions are needed to study reproducibility.
IBM resilience settings
Resilience is an IBM Runtime mitigation preset. Level 0 has no resilience mitigation. Levels 1 and 2 request increasingly extensive mitigation, whose exact options depend on the saved Runtime version and resolved settings. The preset number alone is insufficient to reproduce mitigation or establish its cost. Do not assume equal levels are equivalent across software versions or hardware vendors.
Single job, session and QPU time
Single-job execution submits estimator work independently. A session groups iterative work under a Runtime session. Wall time includes waiting and classical overhead. QPU time is saved provider-reported usage, not queue time. For a job containing several fixed-vector measurements, allocated QPU seconds are apportioned according to the release's allocation rule; do not sum the repeated job total once per measurement.
Logical and transpiled circuits
Logical metrics describe the circuit before device compilation. Transpilation maps it to native gates and physical qubits. Depth is the number of sequential gate layers, not duration in seconds. Two-qubit gate counts must state whether they count logical CX or native gates such as CZ. Published H2 circuit metrics are pre-transpilation; BeyondH2 calculation metrics describe device-transpiled circuits.
Fixed-parameter remeasurement and cohorts
A fixed-parameter measurement independently estimates the energy at a saved vector without optimizer updates. theta_best and theta_final label the selected best and final vectors. A later measurement can reflect calibration drift as well as sampling. BeyondH2's primary Heron cohort and post-hoc Phoenix cohort have different roles and remain labelled. Summary means on this site are descriptive, not pooled hypothesis tests.
Dataset releases and missing values
Each release links to an immutable Zenodo dataset and its associated article. Blank fields mean unavailable or not recorded, not zero. The interface includes verified metadata recovered from archived sources; use the cited Zenodo release for the original published files and analysis methods. JSON retains numbers and missing values. CSV exports use explicit column labels, with energies in Ha and times in seconds.
Read the associated articles and release documentation for the full protocols: dataset releases and publications.