Quantum Annealing vs. QAOA: 127 Qubit Higher-Order Ising Problems on NISQ Computers

Abstract

Quantum annealing (QA) and Quantum Alternating Operator Ansatz (QAOA) are both heuristic quantum algorithms intended for sampling optimal solutions of combinatorial optimization problems. In this article we implement a rigorous direct comparison between QA on D-Wave hardware and QAOA on IBMQ hardware. These two quantum algorithms are also compared against classical simulated annealing. The studied problems are instances of a class of Ising models, with variable assignments of $+1$ or $-1$, that contain cubic $ZZZ$ interactions (higher order terms) and match both the native connectivity of the Pegasus topology D-Wave chips and the heavy hexagonal lattice of the IBMQ chips. The novel QAOA implementation on the heavy hexagonal lattice has a CNOT depth of $6$ per round and allows for usage of an entire heavy hexagonal lattice. Experimentally, QAOA is executed on an ensemble of randomly generated Ising instances with a grid search over $1$ and $2$ round angles using all 127 programmable superconducting transmon qubits of ibm_washington. The error suppression technique digital dynamical decoupling is also tested on all QAOA circuits. QA is executed on the same Ising instances with the programmable superconducting flux qubit devices D-Wave Advantage_system4.1 and Advantage_system6.1 using modified annealing schedules with pauses. We find that QA outperforms QAOA on all problem instances. We also find that dynamical decoupling enables 2-round QAOA to marginally outperform 1-round QAOA, which is not the case without dynamical decoupling.

Accepted at ISC HPC 2023

References in corpus (4)

• Mathematical Foundation of Quantum Annealing
• Coherent quantum annealing in a programmable 2000-qubit Ising chain
• Constrained Quantum Optimization for Extractive Summarization on a Trapped-ion Quantum Computer
• Effects of Dynamical Decoupling and Pulse-level Optimizations on IBM Quantum Computers

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• Provable bounds for noise-free expectation values computed from noisy samples
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• Scaling Whole-Chip QAOA for Higher-Order Ising Spin Glass Models on Heavy-Hex Graphs
• High-Round QAOA for MAX $k$-SAT on Trapped Ion NISQ Devices
• Bias-Field Digitized Counterdiabatic Quantum Algorithm for Higher-Order Binary Optimization
• Multi-Objective Optimization and Network Routing with Near-Term Quantum Computers
• Higher-Order Portfolio Optimization with Quantum Approximate Optimization Algorithm
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• Increasing the Hardness of Posiform Planting Using Random QUBOs for Programmable Quantum Annealer Benchmarking
• Efficient Online Quantum Circuit Learning with No Upfront Training