Update Kipu Iskay Quantum Optimizer Doc with new features

[HuangJunye]

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https://quantum.cloud.ibm.com/docs/en/guides/kipu-optimization

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Kipu Iskay Quantum optimizer function has added new features in a recent update. The guide should be updated accordingly.

Below is the changelog provided by Kipu team which can be used as the source materials for the update.

Enhanced Transpilation System and Smarter Optimization with User Control

New features

Preprocessing Levels (0-3): Specially important for larger problems that cannot currently fit on the coherence times of the hardware. While higher preprocessing levels achieve shallower circuit depths by approximations in the problem transpilation:

• Level 0: Exact, longer circuits
• Level 1: Good balance between accuracy and approximation, cutting out only the gates with angles in the lowest 10 percentile.
• Level 2: Slightly higher approximation, cutting out the gates with angles in the lowest 20 percentile and using approximation_degree=0.95 in the transpilation.
• Level 3: Maximum approximation level, cutting out the gates in the lowest 30 percentile and using approximation_degree=0.90 in the transpilation.

Transpilation Levels (0-5): Control the advanced transpiler optimization trials for quantum circuit compilation:

• Level 0: Optimization of the decomposed DCQO circuit (layout, routing, scheduling)
• Level 1: Optimization of PauliEvolutionGate and then the decomposed DCQO circuit (max_trials=10)
• Level 2: Optimization of PauliEvolutionGate and then the decomposed DCQO circuit (max_trials=15)
• Level 3: Optimization of PauliEvolutionGate and then the decomposed DCQO circuit (max_trials=20)
• Level 4: Optimization of PauliEvolutionGate and then the decomposed DCQO circuit (max_trials=25)
• Level 5: Optimization of PauliEvolutionGate and then the decomposed DCQO circuit (max_trials=50)

Postprocessing Levels (0-2): Control how much classical optimization, compensating for bitflip errors with different number of greedy passes of a local search:

• Level 0: 1 pass
• Level 1: 2 passes
• Level 2: 3 passes

Transpile-Only Mode: Now available for users who want to analyze circuit optimization without running the full quantum algorithm execution.

How to Use the New Options

Here's how to use the new level-based controls in your input:

arguments = {
    "problem": your_problem_dict,
    "problem_type": "binary",  # or "spin"
    "backend_name": "ibm_sherbrooke",
    "instance": your_instance,
    "credentials": your_credentials,
    "options": {
        "shots": 10000,
        "preprocessing_level": 2,    # Faster optimization with good accuracy. Defaults to 0.
        "postprocessing_level": 1,   # Moderate classical optimization. Defaults to 2. 
        "transpilation_level": 3,    # Enhanced quantum circuit optimization. Defaults to 2.
        "transpilation_only": False, # Set to True for circuit analysis without execution
        # seed_transpiler: None by default - allows automatic optimization 
        # to find the best transpilation seed across multiple trials
    }
}

Note: seed_transpiler is set to None by default to enable the transpiler's automatic optimization process. When None, the system will try multiple seeds and select the one that produces the best circuit depth, leveraging the full power of the max_trials parameter for each transpilation level.

Important: Transpilation levels may not always change the final circuit - this depends heavily on the specific circuit structure and complexity. For some circuits/problems, the difference between 10 trials (level 1) and 50 trials (level 5) can be dramatic.

Real Performance Impact

Comprehensive benchmark testing shows the dramatic impact of different optimization levels:

Circuit Depth Results

Preprocessing\Transpilation    0     1     2     3     4     5
---------------------------------------------------------------
                    0        749   579   579   579   579   579
                    1        749   664   664   664   664   664
                    2        749   370   370   370   370   370
                    3        749   387   387   387   387   387

Two-Qubit Gates Results

Preprocessing\Transpilation    0     1     2     3     4     5
---------------------------------------------------------------
                    0       1183  1249  1249  1249  1249  1249
                    1       1183  1171  1171  1171  1171  1171
                    2       1183   536   536   536   536   536
                    3       1183   521   521   521   521   521

Key Achievements:

Preprocessing Level 2 + Transpilation Level 1 delivers optimal results:

• 51% reduction in circuit depth (370 vs 749 gates) = Significantly faster quantum execution
• 55% reduction in two-qubit gates (536 vs 1183 gates) = Lower error rates and better fidelity

Smart Optimization Strategy:

• Transpilation levels 1+ provide substantial improvements over level 0
• Preprocessing levels 2-3 offer the most dramatic circuit reductions
• Combined optimization delivers compound benefits for quantum algorithm performance

Business Value

• Faster Development: Comprehensive optimization levels enable rapid circuit analysis and iteration
• Lower Costs: Up to 55% reduction in two-qubit gates means shorter quantum execution times and lower error rates
• Better Accessibility: Simple level controls make optimization accessible to all users, from beginners to experts
• Proven Results: Extensive benchmark data demonstrates significant improvements across multiple metrics
• Flexible Analysis: Transpile-only mode enables circuit optimization analysis without full execution overhead

Easy Migration

• Drop-in compatibility: Existing code continues to work unchanged.
• Gradual adoption: Users can migrate to new features at their own pace.
• Best of both worlds: Simple levels for ease-of-use, custom parameters for experts.

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[HuangJunye]

The plan is to update it after QDC.