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arXiv:2306.03238 · IEEE International Conference on Quantum Computing and Engineering (QCE)

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

Elijah Pelofske, Andreas Bärtschi, John K. Golden, Stephan Eidenbenz

Published Sep 17, 2023• 15 citations
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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.

DOI
10.1109/qce57702.2023.00064

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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 MAXkkk-SAT problems, specifically fork=3k=3k=3andk=4k=4k=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 includen=10n=10n=10up top=20p=20p=20, andn=22n=22n=22forp=1p=1p=1andp=2p=2p=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,…,5p=1, \ldots, 5p=1,…,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.
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QAOA with N⋅p≥200N\cdot p\geq 200N⋅p≥200
One of the central goals of the DARPA Optimization with Noisy Intermediate-Scale Quantum (ONISQ) program is to implement a hybrid quantum/classical optimization algorithm with high N⋅pN\cdot pN⋅p, where NNN is the number of qubits and ppp is the number of alternating applications of parameterized quantum operators in the protocol. In this note, we demonstrate the execution of the Quantum Approximate Optimization Algorithm (QAOA) applied to the MaxCut problem on non-planar 3-regular graphs with N⋅pN\cdot pN⋅p of up to 320320320 on the Quantinuum H1-1 and H2 trapped-ion quantum processors. To the best of our knowledge, this is the highest N⋅pN\cdot pN⋅p demonstrated on hardware to date. Our demonstration highlights the rapid progress of quantum hardware.