From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz

The next few years will be exciting as prototype universal quantum processors emerge, enabling implementation of a wider variety of algorithms. Of particular interest are quantum heuristics, which require experimentation on quantum hardware for their evaluation, and which have the potential to significantly expand the breadth of quantum computing applications. A leading candidate is Farhi et al.'s Quantum Approximate Optimization Algorithm, which alternates between applying a cost-function-based Hamiltonian and a mixing Hamiltonian. Here, we extend this framework to allow alternation between more general families of operators. The essence of this extension, the Quantum Alternating Operator Ansatz, is the consideration of general parametrized families of unitaries rather than only those corresponding to the time-evolution under a fixed local Hamiltonian for a time specified by the parameter. This ansatz supports the representation of a larger, and potentially more useful, set of states than the original formulation, with potential long-term impact on a broad array of application areas. For cases that call for mixing only within a desired subspace, refocusing on unitaries rather than Hamiltonians enables more efficiently implementable mixers than was possible in the original framework. Such mixers are particularly useful for optimization problems with hard constraints that must always be satisfied, defining a feasible subspace, and soft constraints whose violation we wish to minimize. More efficient implementation enables earlier experimental exploration of an alternating operator approach to a wide variety of approximate optimization, exact optimization, and sampling problems. Here, we introduce the Quantum Alternating Operator Ansatz, lay out design criteria for mixing operators, detail mappings for eight problems, and provide brief descriptions of mappings for diverse problems.Comment: 51 pages, 2 figures. Revised to match journal pape

Charting the circuit QED design landscape using optimal control theory

With recent improvements in coherence times, superconducting transmon qubits have become a promising platform for quantum computing. They can be flexibly engineered over a wide range of parameters, but also require us to identify an efficient operating regime. Using state-of-the-art quantum optimal control techniques, we exhaustively explore the landscape for creation and removal of entanglement over a wide range of design parameters. We identify an optimal operating region outside of the usually considered strongly dispersive regime, where multiple sources of entanglement interfere simultaneously, which we name the quasi-dispersive straddling qutrits (QuaDiSQ) regime. At a chosen point in this region, a universal gate set is realized by applying microwave fields for gate durations of 50 ns, with errors approaching the limit of intrinsic transmon coherence. Our systematic quantum optimal control approach is easily adapted to explore the parameter landscape of other quantum technology platforms.Comment: 13 pages, 5 figures, 2 pages supplementary, 1 supplementary figur

Several fitness functions and entanglement gates in quantum kernel generation

Quantum machine learning (QML) represents a promising frontier in the realm of quantum technologies. In this pursuit of quantum advantage, the quantum kernel method for support vector machine has emerged as a powerful approach. Entanglement, a fundamental concept in quantum mechanics, assumes a central role in quantum computing. In this paper, we study the necessities of entanglement gates in the quantum kernel methods. We present several fitness functions for a multi-objective genetic algorithm that simultaneously maximizes classification accuracy while minimizing both the local and non-local gate costs of the quantum feature map's circuit. We conduct comparisons with classical classifiers to gain insights into the benefits of employing entanglement gates. Surprisingly, our experiments reveal that the optimal configuration of quantum circuits for the quantum kernel method incorporates a proportional number of non-local gates for entanglement, contrary to previous literature where non-local gates were largely suppressed. Furthermore, we demonstrate that the separability indexes of data can be effectively leveraged to determine the number of non-local gates required for the quantum support vector machine's feature maps. This insight can significantly aid in selecting appropriate parameters, such as the entanglement parameter, in various quantum programming packages like https://qiskit.org/ based on data analysis. Our findings offer valuable guidance for enhancing the efficiency and accuracy of quantum machine learning algorith