Cache CircuitToEinsum metadata for repeated observable sweeps

[AbdelStark]

Summary

This change caches CircuitToEinsum forward/inverse metadata for repeated observable-oriented calls and adds focused cache tests plus a small benchmark script.

Problem

CircuitToEinsum already caches the base forward parse through _get_inputs(), but repeated calls to:

• expectation(...)
• reduced_density_matrix(...)
• marginal_probability(...)

still rebuild the forward/inverse metadata in _get_forward_inverse_metadata(...).

For repeated observable sweeps on the same circuit, this adds avoidable Python-side overhead even when:

• the circuit topology is unchanged
• the parser options are unchanged
• the lightcone support is unchanged

What changed

• added a private _forward_inverse_metadata_cache on CircuitToEinsum
• cache key is based on:
  • lightcone
  • normalized coned-qubit positions
  • decompose_gates
  • check_diagonal
• cache entries store:
  • parsed input metadata
  • a copied qubits_frontier
  • next_frontier
  • inverse gates
  • inverse-gate diagonal flags
• cache hits return qubits_frontier.copy() so each call still gets an isolated mutable frontier map
• added focused tests for:
  • repeated identical calls reusing one cache entry
  • equivalent where orderings reusing one cache entry
  • distinct supports creating distinct entries
  • lightcone=True and lightcone=False creating separate entries
• added python/samples/tensornet/circuit_to_einsum_cache_benchmark.py for repeated-call timing

User impact

• reduces repeated metadata construction overhead for observable sweeps
• preserves current public APIs
• preserves numerical behavior
• makes repeated CircuitToEinsum use closer to a reusable compiled artifact instead of a one-shot translator

Validation

Targeted validation was done locally against the pure-Python converter path using real Qiskit and Cirq circuits.

Semantic checks covered:

• cache reuse for repeated identical expectation(...) calls
• cache-key normalization for reordered where arguments
• cache separation by distinct support sets
• cache separation by lightcone mode
• output stability on cache hits

Local timing on a 12-qubit / depth-20 Qiskit circuit:

• expectation(lightcone=True): cached mean 0.000939 s, uncached mean 0.012993 s, 13.84x speedup
• reduced_density_matrix(lightcone=True): cached mean 0.000901 s, uncached mean 0.011013 s, 12.23x speedup