feynman-clock-error-mitigation

name	feynman-clock-error-mitigation
description	BBGKY-ISM quantum error mitigation using Feynman's clock Hamiltonian with polynomial overhead (arXiv: 2607.06752)

Feynman's Clock and Hierarchy-Informed Sampling for Quantum Error Mitigation

Overview

Novel quantum error mitigation technique extending BBGKY-ISM scheme from spin chain simulations to arbitrary quantum circuits. Maps circuit executions using Feynman's clock Hamiltonian to Hamiltonian dynamics obeying BBGKY-like hierarchy, enabling systematic error reduction with polynomial overhead.

Key Innovation: Uses Feynman's clock Hamiltonian to map quantum circuit execution to physical system dynamics, enabling hierarchy-informed error mitigation.

Core Methodology

1. Theoretical Framework

• Feynman's Clock Hamiltonian: Maps quantum circuit execution to time evolution
• BBGKY Hierarchy: Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy of equations
• BBGKY-ISM: Information Subspace Method for error mitigation
• Generalization: Extends from spin chains to arbitrary quantum circuits

2. Error Mitigation Pipeline

1. Map quantum circuit to Feynman clock Hamiltonian
2. Derive BBGKY-like hierarchy for the mapped system
3. Use hierarchy to inform error mitigation strategy
4. Apply BBGKY-ISM to reduce noise effects
5. Extract mitigated expectation values

3. Key Results

• Polynomial Overhead: Both classical and quantum resources scale polynomially
  • Polynomial in circuit size
  • Polynomial in number of qubits
• Systematic Reduction: Controllable quantum error reduction
• Validation: Tested on tunable Bell state preparation under state-of-the-art noise

Technical Details

BBGKY-ISM Extension

• Original Domain: Quantum simulations of spin chains
• New Domain: Arbitrary quantum circuits via clock Hamiltonian mapping
• Mechanism: Hierarchy equations inform which observables to track
• Advantage: Structured approach vs ad-hoc mitigation

Complexity Analysis

• Classical Cost: Polynomial in circuit depth and width
• Quantum Cost: Polynomial number of circuit executions
• Scalability: Favorable compared to exponential-cost methods

Use Cases

• Near-Term Quantum Computing: NISQ-era error mitigation
• Bell State Preparation: High-fidelity entangled state generation
• Variational Algorithms: VQE/QAOA with noise reduction
• Quantum Simulation: Error-mitigated dynamics simulation

Implementation Notes

• Requirements: Ability to execute parameterized circuits
• Overhead Management: Polynomial scaling makes it practical for moderate sizes
• Tunability: Systematic and controllable error reduction
• Noise Model: Validated under state-of-the-art quantum noise models

Activation Keywords

Feynman clock Hamiltonian, BBGKY hierarchy, quantum error mitigation, BBGKY-ISM, polynomial overhead, Bell state preparation, quantum noise reduction, hierarchy-informed sampling, circuit-to-Hamiltonian mapping

References

• arXiv: 2607.06752 (2026)
• Author: Theo Saporiti
• Subject: Quantum Physics (quant-ph)