High-Round QAOA for MAX $k$-SAT on Trapped Ion NISQ Devices

TL;DR

This paper develops optimized QAOA circuits for MAX k-SAT problems and tests them on multiple trapped ion quantum computers, revealing that current NISQ devices perform best at low circuit depths due to noise limitations.

Contribution

It introduces novel QAOA circuit constructions for MAX 3- and 4-SAT, including measurement-based uncomputation, and demonstrates large-scale circuit execution on NISQ hardware.

Findings

NISQ devices perform optimally at low QAOA rounds (p=1 to 5).

Performance degrades with increased circuit depth due to noise.

Largest QAOA circuits on NISQ devices include over 9,000 gates.

Abstract

The Quantum Alternating Operator Ansatz (QAOA) is a hybrid classical-quantum algorithm that aims to sample the optimal solution(s) of discrete combinatorial optimization problems. We present optimized QAOA circuit constructions for sampling MAX $k$-SAT problems, specifically for $k=3$ and $k=4$. The novel $4$-SAT QAOA circuit construction we present uses measurement based uncomputation, followed by classical feed forward conditional operations. The QAOA circuit parameters for $3$-SAT are optimized via exact classical (noise-free) simulation, using HPC resources to simulate up to $20$ rounds on $10$ qubits. In order to explore the limits of current NISQ devices we execute these optimized QAOA circuits for random $3$-SAT test instances with clause-to-variable ratio $4$ on four trapped ion quantum computers: Quantinuum H1-1 (20 qubits), IonQ Harmony (11 qubits), IonQ Aria 1 (25 qubits), and IonQ Forte (30 qubits). The QAOA circuits that are executed include $n=10$ up to $p=20$, and $n=22$ for $p=1$ and $p=2$. The high round circuits use upwards of 9,000 individual gate instructions, making these some of the largest QAOA circuits executed on NISQ devices. Our main finding is that current NISQ devices perform best at low round counts (i.e., $p = 1,\ldots, 5$) and then -- as expected due to noise -- gradually start returning satisfiability truth assignments that are no better than randomly picked solutions as the number of QAOA rounds are further increased.