noise-directed-adaptive-remapping

name	noise-directed-adaptive-remapping
description	Noise-directed adaptive remapping methodology for integer optimization — encoding qubit-based problems into qudit representations with noise-aware adaptation. Use when optimizing quantum integer optimization on NISQ hardware, converting qubit encodings to qudit representations, mitigating hardware noise through adaptive remapping, or solving scheduling/resource allocation problems with quantum qudit systems.
metadata	{"arxiv_id":"2606.28234","published":"2026-06-26","tags":["quantum","optimization","qudit","NISQ","integer-optimization","noise-mitigation"]}

Context

Noise-directed adaptive remapping converts qubit-based integer optimization into qudit representations that exploit hardware noise characteristics to improve solution quality.

Core Methodology

Qubit-to-Qudit Encoding

1. Problem Formulation: Express integer optimization as QUBO on qubit registers
2. Qudit Mapping: Group qubits into qudit registers — each qudit represents log₂(d) qubits
3. Noise Characterization: Measure hardware noise profiles (T1, T2, gate fidelities) per physical qudit
4. Adaptive Assignment: Map logical qudit variables to physical qudits with lowest noise for critical variables
5. Error Mitigation: Apply noise-adaptive compilation — schedule high-fidelity gates on sensitive variables

Optimization Pipeline

1. Classical Preprocessing: Reduce problem size via constraint propagation
2. Qudit Encoding: Select optimal qudit dimension d based on hardware constraints
3. Noise-Aware Mapping: Use hardware calibration data to optimize variable-to-qudit assignment
4. Circuit Compilation: Generate parameterized qudit circuits with noise-adaptive gate decomposition
5. Measurement & Post-processing: Extract integer solutions with noise-aware readout correction

Key Advantages

• Reduced circuit depth: Qudit encoding compresses multi-bit integers into fewer physical systems
• Noise resilience: Adaptive remapping exploits noise heterogeneity across hardware
• Hardware efficiency: Fewer physical systems needed vs binary qubit encoding
• Natural integer representation: Qudits natively represent discrete integer variables

Implementation Steps

1. Profile hardware noise (T1, T2, gate fidelities) for all physical qudits
2. Formulate integer optimization as QUBO
3. Determine optimal qudit dimension d = min(available levels, problem domain size)
4. Apply noise-aware variable assignment heuristic
5. Compile to hardware-native qudit gates
6. Execute with noise-adaptive readout correction

Pitfalls

• Qudit availability: Not all quantum hardware supports native qudit operations
• Gate decomposition overhead: Qudit gate decomposition may increase circuit depth
• Noise calibration freshness: Calibration data must be recent — noise profiles drift
• Encoding overhead: Some problems lose structure when mapped from qubits to qudits
• Readout complexity: Qudit readout requires more sophisticated discrimination than qubit

Verification

• Problem encoding preserves integer constraints
• Qudit mapping respects hardware connectivity
• Noise-aware assignment improves over random assignment
• Solution quality validated against classical baseline

Activation

noise-directed adaptive remapping, qubit to qudit encoding, quantum integer optimization, qudit quantum computing, noise-aware quantum mapping, NISQ qudit optimization, quantum scheduling optimization, qudit resource allocation