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AutoVQE research program

Find the best useful VQE ansatz for the Hamiltonian named by the user. Work as one closed research loop:

understand -> propose -> optimize -> compare -> learn -> keep or discard

Boundary

During a solve, edit only ansatz.py as code. Treat evaluate.py, results.tsv, .autovqe-state.json, and the problem file as immutable. Never run an eigensolver, search for a known answer, insert optimized constants, or encode a solution in the input, initial state, or fixed gates. The evaluator is the only source of energies and optimized parameters.

The gate allowlist is a Pauli word, U1 (XX+YY), GIVENS ((YX-XY)/2), PAIR ((YX+XY)/2), or SU2 (XX+YY+ZZ). GIVENS preserves total Z/Hamming weight; PAIR mixes sectors whose weights differ by two while preserving Hamming parity. Neither implies full SU(2). A freely chosen Pauli word may touch at most two qubits. A higher-weight word is allowed only when it is an input-Hamiltonian term or a component of a rank-one or rank-two fermionic excitation under an explicitly known mapping; expose every component and share its parameter. Arbitrary Pauli sums, higher-rank excitations, custom unitaries, fixed angles, and fitted per-operation scales are forbidden.

Before claiming a symmetry, verify that its generator commutes with the Hamiltonian, the state entering its block occupies a definite target sector, and the complete block preserves it. Full SU(2) requires all three total-spin components, not only magnetization. Translation, reflection, and point-group structure should use parameter sharing across symmetry orbits, not new gates.

Every allowed gate is fully expanded and transpiled to supplied native constraints. U1, GIVENS, PAIR, and SU2 count as two, two, two, and three occurrences. Judge simplicity from occurrences, generator support, two-qubit gates, total gates, and depth—not unique parameter count alone.

Loop

  1. Read the raw Hamiltonian. Inspect coefficients, locality, interaction graph, initial occupation, repeated structure, and verified conserved quantities. A conserving circuit cannot change sector, so preparation must variationally reach the intended sector rather than encode an answer.
  2. If this problem has no result, evaluate the empty or current ansatz once; otherwise use its existing result as the baseline.
  3. Give every candidate the evaluator's fixed default budget max(30, 60*2**(n-16)) seconds; use --seconds only when the user overrides it. State one falsifiable change per run. Continue until the user interrupts; target, convergence, a failed candidate, or a plateau never ends the loop.
  4. Start each candidate with L-BFGS-B; new parameters receive a small deterministic nonzero seed. The evaluator restarts a converged optimizer until the candidate budget expires. If energy does not improve, try one bounded COBYLA or Powell activation, then return it to L-BFGS-B.
  5. Bracket depth with shared parameters in multiplicative jumps instead of sweeping adjacent depths. Change depth or sharing in one comparison, never both. Split names at fixed structure; if useful, keep that scheme while testing further growth.
  6. Derive physical ladders from observed terms, coefficients, graph, and verified symmetries—not a filename or model label. For antiferromagnetic isotropic XX+YY+ZZ graphs, test low-spin Y/GIVENS dimers followed by edge-colored SU2 matching cycles. For ZZ graphs with transverse X, test a shared Y seed and alternating ZZ/X layers, then verified symmetry-orbit name splits.
  7. The evaluator owns current_best and decides every run. Before target, it keeps lower energy, or a Pareto-simpler circuit when |delta_E| <= 1e-8*max(1, |E_current_best|). The first target-reaching candidate is kept. After that, accuracy is a hard constraint: keep only target-reaching candidates that reduce at least one of unique parameters, occurrences, generator support, two-qubit gates, total gates, and depth without increasing another. Otherwise discard and restore current_best. Use failures to choose a genuinely different structure.
  8. Never write optimized numbers into ansatz.py. If an edit or run is interrupted, use evaluate.py ... --restore-best --hypothesis "restore"; otherwise keep running until the user stops the task.

If reference_energy exists, success means meeting the requested relative error. The reference is for scoring only and must never shape or be copied into the ansatz. If no reference exists, report best found, not ground state. A converged optimizer is not success by itself: ansatz quality is the energy it reaches within the shared per-candidate budget. target_reached changes the objective from energy improvement to simplification; it does not end the research loop.