| name | quantum-ground-state-preparation-benchmark |
| description | Benchmark methodology for comparing quantum ground state preparation algorithms (cooling, adiabatic, QAOA) under realistic noise conditions. Provides phase-dependent performance analysis using quadratic fermionic Hamiltonians with depolarizing noise. |
Quantum Ground State Preparation Benchmark
Description
Benchmark methodology for comparing quantum ground state preparation algorithms under realistic noise conditions. Based on arXiv:2606.20551 (Molpeceres et al., 2026), which derives scaling laws for achievable relative energy as a function of noise rate across cooling, adiabatic, and optimization algorithms. Key finding: algorithm performance depends critically on the quantum phase — adiabatic evolution dominates in the trivial phase while multi-frequency cooling is superior in the topological phase where gap-closing limits adiabatic protocols.
Activation Keywords
- ground state preparation benchmark
- quantum algorithm benchmark noise
- 量子基态制备基准
- cooling vs adiabatic vs QAOA
- quantum phase transition benchmark
- noisy quantum state preparation
- multi-frequency cooling algorithm
- depolarizing noise benchmark
Tools Used
- terminal: Run numerical simulations of quantum algorithms
- write_file: Create benchmark scripts and analysis code
- skill_view: Reference related quantum algorithm skills
Core Framework
1. Algorithm Categories
| Algorithm | Best Phase | Noise Robustness | Key Advantage |
|---|
| Adiabatic Evolution | Trivial | Moderate | Conceptual simplicity |
| Multi-Frequency Cooling | Topological | High | Gap-closing resilience |
| QAOA | Trivial | Low-Moderate | Competitive with cooling in trivial phase |
2. Benchmark Protocol
Step 1: Define Hamiltonian Family
- Use exactly solvable quadratic fermionic Hamiltonians
- Include a quantum phase transition (trivial vs topological phases)
- Parameterize by gap size and system size
Step 2: Model Noise
- Apply depolarizing noise at varying rates (p)
- Track noise rate as primary parameter
- Include parameter imperfections for robustness testing
Step 3: Run Each Algorithm
- Adiabatic: Vary evolution time, measure energy vs noise
- Cooling: Multi-frequency protocol, compare with single-frequency baseline
- QAOA: Optimize angles, compare with cooling performance
Step 4: Evaluate Metrics
- Achievable relative energy: (E_achieved - E_ground) / E_ground
- Scaling with noise rate: fit energy vs p curves
- Robustness to parameter imperfections
- Phase-dependent performance crossover points
3. Phase-Dependent Analysis
The critical insight: performance depends on the quantum phase:
- Trivial phase: Adiabatic evolution is favorable; QAOA competitive with cooling
- Topological phase: Multi-frequency cooling superior (gap-closing limits adiabatic)
- Near phase transition: All algorithms degrade; cooling shows most graceful degradation
4. Noise Scaling Laws
For quadratic fermionic models with depolarizing noise:
- Derive analytical scaling of achievable energy as function of noise rate
- Validate with numerical simulations
- Identify noise thresholds below which each algorithm is viable
5. Robustness to Parameter Imperfections
- Cooling protocol shows enhanced robustness to parameter imperfections
- This is critical for realistic NISQ-era implementations
- Test by varying Hamiltonian parameters ±10% and measuring energy degradation
Usage Patterns
Pattern 1: Benchmark New Ground State Algorithm
- Implement the algorithm on the standard quadratic fermionic Hamiltonian family
- Test across both trivial and topological phases
- Compare against the three baselines (adiabatic, cooling, QAOA)
- Report phase-dependent performance, not just average
Pattern 2: Noise-Aware Algorithm Selection
- Estimate the noise rate of your quantum hardware
- Identify the phase of your target Hamiltonian
- Select algorithm based on the phase-noise performance map:
- Low noise + trivial phase → adiabatic
- Any noise + topological phase → multi-frequency cooling
- Moderate noise + trivial phase → QAOA or cooling
Pattern 3: Extend to New Model Classes
- Verify the model is exactly solvable (or has known ground state)
- Identify phase transitions and their nature
- Apply the same benchmark protocol
- Compare scaling laws with the fermionic baseline
Error Handling
Algorithm Fails in Topological Phase
- This is expected for adiabatic protocols (gap-closing)
- Switch to multi-frequency cooling
- Report the phase-dependent performance honestly
Noise Rate Too High
- All algorithms will fail to reach ground state
- Report the noise threshold for each algorithm
- Consider error mitigation strategies before benchmarking
Resources
- arXiv:2606.20551: "Benchmark of quantum algorithms for ground state preparation in the presence of noise" (Molpeceres, Lu, Cirac, Kraus, 2026)
