TY - JOUR AB - Quantum computers are increasing in size and quality but are still very noisy. Error mitigation extends the size of the quantum circuits that noisy devices can meaningfully execute. However, state-of-the-art error mitigation methods are hard to implement and the limited qubit connectivity in superconducting qubit devices restricts most applications to the hardware's native topology. Here we show a quantum approximate optimization algorithm (QAOA) on nonplanar random regular graphs with up to 40 nodes enabled by a machine learning-based error mitigation. We use a swap network with careful decision-variable-to-qubit mapping and a feed-forward neural network to optimize a depth-two QAOA on up to 40 qubits. We observe a meaningful parameter optimization for the largest graph which requires running quantum circuits with 958 two-qubit gates. Our paper emphasizes the need to mitigate samples, and not only expectation values, in quantum approximate optimization. These results are a step towards executing quantum approximate optimization at a scale that is not classically simulable. Reaching such system sizes is key to properly understanding the true potential of heuristic algorithms like QAOA. AU - Sack, Stefan AU - Egger, Daniel J. ID - 15122 IS - 1 JF - Physical Review Research SN - 2643-1564 TI - Large-scale quantum approximate optimization on nonplanar graphs with machine learning noise mitigation VL - 6 ER - TY - JOUR AB - The quantum approximate optimization algorithm (QAOA) is a variational quantum algorithm, where a quantum computer implements a variational ansatz consisting of p layers of alternating unitary operators and a classical computer is used to optimize the variational parameters. For a random initialization, the optimization typically leads to local minima with poor performance, motivating the search for initialization strategies of QAOA variational parameters. Although numerous heuristic initializations exist, an analytical understanding and performance guarantees for large p remain evasive.We introduce a greedy initialization of QAOA which guarantees improving performance with an increasing number of layers. Our main result is an analytic construction of 2p + 1 transition states—saddle points with a unique negative curvature direction—for QAOA with p + 1 layers that use the local minimum of QAOA with p layers. Transition states connect to new local minima, which are guaranteed to lower the energy compared to the minimum found for p layers. We use the GREEDY procedure to navigate the exponentially increasing with p number of local minima resulting from the recursive application of our analytic construction. The performance of the GREEDY procedure matches available initialization strategies while providing a guarantee for the minimal energy to decrease with an increasing number of layers p. AU - Sack, Stefan AU - Medina Ramos, Raimel A AU - Kueng, Richard AU - Serbyn, Maksym ID - 13125 IS - 6 JF - Physical Review A SN - 2469-9926 TI - Recursive greedy initialization of the quantum approximate optimization algorithm with guaranteed improvement VL - 107 ER - TY - THES AU - Sack, Stefan ID - 14622 SN - 2663 - 337X TI - Improving variational quantum algorithms: Innovative initialization techniques and extensions to qudit systems ER - TY - JOUR AB - Quantum impurities exhibit fascinating many-body phenomena when the small interacting impurity changes the physics of a large noninteracting environment. The characterisation of such strongly correlated nonperturbative effects is particularly challenging due to the infinite size of the environment, and the inability of local correlators to capture the buildup of long-ranged entanglement in the system. Here, we harness an entanglement-based observable—the purity of the impurity—as a witness for the formation of strong correlations. We showcase the utility of our scheme by exactly solving the open Kondo box model in the small box limit, and thus describe all-electronic dot-cavity devices. Specifically, we conclusively characterize the metal-to-insulator phase transition in the system and identify how the (conducting) dot-lead Kondo singlet is quenched by an (insulating) intraimpurity singlet formation. Furthermore, we propose an experimentally feasible tomography protocol for the measurement of the purity, which motivates the observation of impurity physics through their entanglement build up. AU - Stocker, Lidia AU - Sack, Stefan AU - Ferguson, Michael S. AU - Zilberberg, Oded ID - 12111 IS - 4 JF - Physical Review Research SN - 2643-1564 TI - Entanglement-based observables for quantum impurities VL - 4 ER - TY - JOUR AB - Variational quantum algorithms are promising algorithms for achieving quantum advantage on nearterm devices. The quantum hardware is used to implement a variational wave function and measure observables, whereas the classical computer is used to store and update the variational parameters. The optimization landscape of expressive variational ansätze is however dominated by large regions in parameter space, known as barren plateaus, with vanishing gradients, which prevents efficient optimization. In this work we propose a general algorithm to avoid barren plateaus in the initialization and throughout the optimization. To this end we define a notion of weak barren plateaus (WBPs) based on the entropies of local reduced density matrices. The presence of WBPs can be efficiently quantified using recently introduced shadow tomography of the quantum state with a classical computer. We demonstrate that avoidance of WBPs suffices to ensure sizable gradients in the initialization. In addition, we demonstrate that decreasing the gradient step size, guided by the entropies allows WBPs to be avoided during the optimization process. This paves the way for efficient barren plateau-free optimization on near-term devices. AU - Sack, Stefan AU - Medina Ramos, Raimel A AU - Michailidis, Alexios AU - Kueng, Richard AU - Serbyn, Maksym ID - 11471 IS - 2 JF - PRX Quantum KW - General Medicine SN - 2691-3399 TI - Avoiding barren plateaus using classical shadows VL - 3 ER - TY - JOUR AB - The quantum approximate optimization algorithm (QAOA) is a prospective near-term quantum algorithm due to its modest circuit depth and promising benchmarks. However, an external parameter optimization required in the QAOA could become a performance bottleneck. This motivates studies of the optimization landscape and search for heuristic ways of parameter initialization. In this work we visualize the optimization landscape of the QAOA applied to the MaxCut problem on random graphs, demonstrating that random initialization of the QAOA is prone to converging to local minima with suboptimal performance. We introduce the initialization of QAOA parameters based on the Trotterized quantum annealing (TQA) protocol, parameterized by the Trotter time step. We find that the TQA initialization allows to circumvent the issue of false minima for a broad range of time steps, yielding the same performance as the best result out of an exponentially scaling number of random initializations. Moreover, we demonstrate that the optimal value of the time step coincides with the point of proliferation of Trotter errors in quantum annealing. Our results suggest practical ways of initializing QAOA protocols on near-term quantum devices and reveal new connections between QAOA and quantum annealing. AU - Sack, Stefan AU - Serbyn, Maksym ID - 9760 JF - Quantum TI - Quantum annealing initialization of the quantum approximate optimization algorithm VL - 5 ER -