Evolved operator functions

[Cryoris]

Summary

Part of #13046: The evolved_operator_ansatz and qaoa_ansatz functions.

This is based on #13295, so that PR will need merging first.

Details and comments

• After Prepare PauliEvolutionGate for Rustiq & port it to Rust #13295, the EvolvedOperatorAnsatz is already pretty performant since it does the Pauli evolution in Rust. However, with these functions we still gain a speedup since we can do all evolution at once in Rust and don't need go back and forth.

  This benchmarks the construction of an evolved operator ansatz for an Ising Hamiltonian on a square grid with side length n
  (so n ** 2 qubits), which has 2 operators; the ZZ-interactions and the X-field. For 100 qubits we get a speedup of 1.33x,
  which is increasing with the number of qubits (e.g. we get 1.83x at 10'000 qubits).

  -- n = 10, speedup 1.33x
  main: 0.033 +- 0.014
  this: 0.025 +- 0.009
  
  -- n = 50, speedup 1.64x
  main: 6.218 +- 0.200
  this: 3.792 +- 0.105
  
  -- n = 100, speedup 1.83x
  main: 100.487 +- 2.275
  this: 55.007 +- 1.139
  

• This also adds a new function called hamiltonian_variational_ansatz (HVA), which automatically splits an input Hamiltonian into commuting terms. This is slightly different to evolved_operator_ansatz, which requires you to manually do this split, but IMO the HVA is the form most users would be interested in. We could've changed the default behavior of evolved_operator_ansatz to do the splitting, but I didn't want to change behavior for a class that users are already used to.

[qiskit-bot]

One or more of the following people are relevant to this code:

• @Cryoris
• @Qiskit/terra-core
• @ajavadia

[coveralls]

Pull Request Test Coverage Report for Build 11483287578

Details

• 379 of 421 (90.02%) changed or added relevant lines in 16 files are covered.
• 20 unchanged lines in 6 files lost coverage.
• Overall coverage decreased (-0.03%) to 88.653%

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Changes Missing Coverage	Covered Lines	Changed/Added Lines	%
qiskit/synthesis/evolution/suzuki_trotter.py	18	20	90.0%
qiskit/circuit/library/n_local/evolved_operator_ansatz.py	69	73	94.52%
qiskit/synthesis/evolution/product_formula.py	41	45	91.11%
qiskit/synthesis/evolution/qdrift.py	14	18	77.78%
crates/circuit/src/operations.rs	1	6	16.67%
crates/accelerate/src/circuit_library/pauli_evolution.rs	179	185	96.76%
crates/accelerate/src/circuit_library/utils.rs	9	26	34.62%

Files with Coverage Reduction	New Missed Lines	%
qiskit/synthesis/evolution/product_formula.py	1	93.15%
crates/qasm2/src/expr.rs	1	94.02%
qiskit/transpiler/passes/synthesis/unitary_synthesis.py	2	61.59%
crates/qasm2/src/lex.rs	3	92.23%
crates/qasm2/src/parse.rs	6	97.62%
qiskit/synthesis/two_qubit/xx_decompose/decomposer.py	7	90.77%

Totals
Change from base Build 11481266566:	-0.03%
Covered Lines:	75031
Relevant Lines:	84634

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💛 - Coveralls