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. The studied problems are instances of a class of Ising problems, 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 (DDD) 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 DDD enables 2-round QAOA to outperform 1-round QAOA, which is not the case without DDD.

Variational Amplitude Amplification for Solving QUBO Problems

“…The QUBO problem has many connections to important fields of computer science [39][40][41][42][43], making it relevant for demonstrating quantum's potential for obtaining solutions. To date, the two most successful quantum approaches to solving QUBOs are annealing [13][14][15][16] and QAOA [10,11,44,45], with a great deal of interest in comparing the two [46][47][48]. Shown below in Equation ( 1) is the QUBO cost function, C(X), which we seek to solve using our quantum algorithm.…”

Quantum-enhanced greedy combinatorial optimization solver

“…The QAOA has been implemented on several experimental platforms to solve a range of combinatorial optimization problems (13)(14)(15)(16)(17)(18)(19)(20)(21)(22). However, a major challenge in these demonstrations has been the stringent technical requirement of reducing hardware noise to provide good quality solutions that are well-separated from trivial classical approaches such as random sampling.…”