Analysis of Quantum Approximate Optimization Algorithm under Realistic Noise in Superconducting Qubits

Abstract

The quantum approximate optimization algorithm (QAOA) is a promising quantum-classical hybrid technique to solve combinatorial optimization problems in near-term gate-based noisy quantum devices. In QAOA, the objective is a function of the quantum state, which itself is a function of the gate parameters of a multi-level parameterized quantum circuit (PQC). A classical optimizer varies the continuous gate parameters to generate distributions (quantum state) with significant support to the optimal solution. Even at the lowest circuit depth, QAOA offers non-trivial provable performance guarantee which is expected to increase with the circuit depth. However, the existing analysis fails to consider non-idealities in the qubit quality i.e., short lifetime and imperfect gate operations in realistic quantum hardware. In this article, we investigate the impact of various noise sources on the performance of QAOA both in simulation and on a real quantum computer from IBM. Our analyses indicate that the optimal number of stages (p-value) for any QAOA instance is limited by the noise characteristics (gate error, coherence time, etc.) of the target hardware as opposed to the current perception that higher-depth QAOA will provide monotonically better performance for a given problem compared to the low-depth implementations.

References in corpus (8)

• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• A Quantum Approximate Optimization Algorithm
• Quantum generative adversarial networks
• QAOA for Max-Cut requires hundreds of qubits for quantum speed-up
• Practical optimization for hybrid quantum-classical algorithms
• Quantum Algorithms for Fixed Qubit Architectures
• Performance of the Quantum Approximate Optimization Algorithm on the Maximum Cut Problem
• For Fixed Control Parameters the Quantum Approximate Optimization Algorithm's Objective Function Value Concentrates for Typical Instances

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• Investigating the effect of circuit cutting in QAOA for the MaxCut problem on NISQ devices
• An Expressive Ansatz for Low-Depth Quantum Approximate Optimisation
• What do QAOA energies reveal about graphs?
• Error Analysis of the Variational Quantum Eigensolver Algorithm
• QPack: Quantum Approximate Optimization Algorithms as universal benchmark for quantum computers
• Resiliency Analysis and Improvement of Variational Quantum Factoring in Superconducting Qubit
• Finding the optimal Nash equilibrium in a discrete Rosenthal congestion game using the Quantum Alternating Operator Ansatz