Alignment between initial state and mixer improves QAOA performance for constrained optimization

Abstract

Quantum alternating operator ansatz (QAOA) has a strong connection to the adiabatic algorithm, which it can approximate with sufficient depth. However, it is unclear to what extent the lessons from the adiabatic regime apply to QAOA as executed in practice with small to moderate depth. In this paper, we demonstrate that the intuition from the adiabatic algorithm applies to the task of choosing the QAOA initial state. Specifically, we observe that the best performance is obtained when the initial state of QAOA is set to be the ground state of the mixing Hamiltonian, as required by the adiabatic algorithm. We provide numerical evidence using the examples of constrained portfolio optimization problems with both low (p ≤ 3) and high (p = 100) QAOA depth. Additionally, we successfully apply QAOA with XY mixer to portfolio optimization on a trapped-ion quantum processor using 32 qubits and discuss our findings in near-term experiments.

Hybrid Gate-Based and Annealing Quantum Computing for Large-Size Ising Problems

“…( 19) and (20), which is the lower left part of the plot, the performance ratio is quite good (> 0.9) compared to other regimes. The plot also shows that condition (19) is more restrict than condition (20) as when | h|/ J (%) > 100, the performance ratio can still be larger than 0.9. Similar behaviors can also be observed in Figs.…”

“…We find that the portfolio optimization problems we test satisfies the good performance conditions Eqs. (19) and (20) of LSSA. This is why the performance of LSSA on the portfolio optimization problems could be expected to be quite good compared to that on the fully-connected random Ising problems.…”

“…To find the optimal solution of the corresponding Hamiltonian, the gate-based quantum computing with variational quantum eigensolver (VQE) uses parameterized gates to construct a trial state and optimizes the best set of parameters that can approximate the ground state of the Ising Hamiltonian [14][15][16]. Another commonly used gate-based variational quantum algorithm (VQA) is the quantum approximate optimization algorithm (QAOA), where the trotterization of the adiabatic evolution makes it a scalable approach [17][18][19][20][21][22][23][24][25][26][27][28][29]. However, QAOA and VQE are designed to solve the Ising Hamiltonian problems with N p variables on an N p -qubit gate-based quantum computer.…”

Evidence of scaling advantage for the quantum approximate optimization algorithm on a classically intractable problem

“…Recent progress in trapped-ion platforms based on the quantum charge-coupled device (QCCD) architecture (26,27) has led to a rapid increase in the number of qubits while maintaining high fidelity, enabling large-scale QAOA demonstrations (34,35), These systems implement two-qubit gates between arbitrary pairs of qubits by transporting ions into physically separate gate zones, resulting in high-fidelity two-qubit gates with low cross-talk. We leverage this progress to execute QAOA circuits for the LABS problem on Quantinuum H-series trapped-ion systems.…”