Multi-angle quantum approximate optimization algorithm

Abstract

The quantum approximate optimization algorithm (QAOA) generates an approximate solution to combinatorial optimization problems using a variational ansatz circuit defined by parameterized layers of quantum evolution. In theory, the approximation improves with increasing ansatz depth but gate noise and circuit complexity undermine performance in practice. Here, we investigate a multi-angle ansatz for QAOA that reduces circuit depth and improves the approximation ratio by increasing the number of classical parameters. Even though the number of parameters increases, our results indicate that good parameters can be found in polynomial time for a test dataset we consider. This new ansatz gives a 33% increase in the approximation ratio for an infinite family of MaxCut instances over QAOA. The optimal performance is lower bounded by the conventional ansatz, and we present empirical results for graphs on eight vertices that one layer of the multi-angle anstaz is comparable to three layers of the traditional ansatz on MaxCut problems. Similarly, multi-angle QAOA yields a higher approximation ratio than QAOA at the same depth on a collection of MaxCut instances on fifty and one-hundred vertex graphs. Many of the optimized parameters are found to be zero, so their associated gates can be removed from the circuit, further decreasing the circuit depth. These results indicate that multi-angle QAOA requires shallower circuits to solve problems than QAOA, making it more viable for near-term intermediate-scale quantum devices.

Error Mitigation for Quantum Approximate Optimization

“…There are several adaptions to the simple p-level QAOA method described in the main text in Sec. II A [38,42,[66][67][68][69][70][71][72][73]. For instance, the Quantum Alternation Operator Ansatz [38] (QAOA+) provides a more expressive variational state by modifying the definitions of U x (β) and U p (γ).…”

Quantum Local Search with the Quantum Alternating Operator Ansatz

“…Prior work, investigating the application of the QAOA to MaxCut problems, has shown that allowing the partial mixers to be uniquely parameterized in this way can lead to increased approximation ratio and reduced circuit depth at the expense of an increased number of variational parameters [14]. However, the QLS ansatz differs from that considered in [14] because the partial mixers do not commute with one another. This allows us to randomize over different permutations of the partial mixers to escape local minima.…”

FrozenQubits: Boosting Fidelity of QAOA by Skipping Hotspot Nodes

“…We evaluate the application fidelity of QAOA circuits using Approximation Ratio Gap (ARG) from prior works [8,41,60], as defined in Equation ( 4).…”