Hybrid Quantum Algorithms integrating QAOA, Penalty Dephasing and Zeno Effect for Solving Binary Optimization Problems with Multiple Constraints

ArXiv ID: 2305.08056 “View on arXiv”

Authors: Unknown

Abstract

When tackling binary optimization problems using quantum algorithms, the conventional Ising representation and Quantum Approximate Optimization Algorithm (QAOA) encounter difficulties in efficiently handling errors for large-scale problems involving multiple constraints. To address these challenges, this paper presents a hybrid framework that combines the use of standard Ising Hamiltonians to solve a subset of the constraints, while employing non-Ising formulations to represent and address the remaining constraints. The resolution of these non-Ising constraints is achieved through either penalty dephasing or the quantum Zeno effect. This innovative approach leads to a collection of quantum circuits with adaptable structures, depending on the chosen representation for each constraint. Furthermore, this paper introduces a novel technique that utilizes the quantum Zeno effect by frequently measuring the constraint flag, enabling the resolution of any optimization constraint. Theoretical properties of these algorithms are discussed, and their performance in addressing practical aircraft loading problems is highly promising, showcasing significant potential for a wide range of industrial applications.

Keywords: Quantum Computing, QAOA (Quantum Approximate Optimization Algorithm), Ising Model, Quantum Zeno Effect, Binary Optimization, General / Industrial Applications

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper introduces novel, advanced quantum mechanics concepts like the quantum Zeno effect and hybrid non-Ising formulations, requiring dense theoretical derivations. However, the only empirical validation mentioned is a conceptual application to aircraft loading, lacking specific backtesting results, dataset details, or performance metrics against classical benchmarks.

  flowchart TD
    Start(["Research Goal:<br>Efficient Binary Optimization<br>with Multiple Constraints"]) --> Challenge(Challenge: QAOA/Ising Limitations<br>with Complex Constraints)
    Challenge --> Hybrid["Hybrid Quantum Framework<br>Ising + Non-Ising Representations"]
    Hybrid --> QAOA["Subproblem: Standard QAOA<br>on Ising Hamiltonian"]
    Hybrid --> Methods["Constraint Resolution Methods"]
    Methods --> PD["Penalty Dephasing"]
    Methods --> Zeno["Quantum Zeno Effect<br>Frequent Constraint Measurement"]
    QAOA --> Solve["Hybrid Solution Layer<br>Adaptive Circuit Structure"]
    PD --> Solve
    Zeno --> Solve
    Solve --> Outcome(["Key Findings:<br>Validated on Aircraft Loading<br>High Industrial Potential"])