Topological two-dimensional Floquet lattice on a single superconducting qubit

Current noisy intermediate-scale quantum (NISQ) devices constitute powerful platforms for analogue quantum simulation. The exquisite level of control offered by state-of-the-art quantum computers make them especially promising to implement time-dependent Hamiltonians. We implement quasiperiodic driving of a single qubit in the IBM Quantum Experience and thus experimentally realize a temporal version of the half-Bernevig-Hughes-Zhang Chern insulator. Using simple error mitigation, we achieve consistently high fidelities of around 97%. From our data we can infer the presence of a topological transition, thus realizing an earlier proposal of topological frequency conversion by Martin, Refael, and Halperin. Motivated by these results, we theoretically study the many-qubit case, and show that one can implement a wide class of Floquet Hamiltonians, or time-dependent Hamiltonians in general. Our study highlights promises and limitations when studying many-body systems through multi-frequency driving of quantum computers. Introduction.-Noisy intermediate-scale quantum (NISQ) computers may not yet offer fully fault-tolerant quantum computing facilities, but they nevertheless constitute a versatile experimental platform with the potential for fundamental research , small-scale computation or quantum simulation [1]. The typical model of a quantum computer is that of a quantum circuit, which is a sequence of gates applied to the qubits [2]. In principle, the time-evolution of any many-body quantum systems can be simulated by applying a Trotterization, which turns continuous time evolution into a discrete local quantum circuit [3]. This results in a digital quantum simulation, which has been benchmarked for a range of different models on existing quantum computers [4-7]. In superconducting circuits, the currently leading technology , quantum circuits are constructed from a set of available gates, which correspond to a set of carefully calibrated microwave pulses applied to its input ports [8]. The abstraction into quantum circuits hides the complexity of the underlying many-body system, whose continuous evolution offers exciting directions in analogue quantum simulation [9, 10], which potentially incurs significantly less overhead. This perspective has been explored in a series of theoretical and experimental works [11-15]. If the intrinsic many-body nature of quantum computers is combined with the capacity to apply essentially arbitrary drives, they may serve also as powerful analogue quantum simulators for very large classes of time-dependent Hamiltonians. The evolution under time-dependent Hamiltonians is incredibly rich and exhibits many novel phenomena, even at the level of individual qubits. A particular example is the temporal topological transition that occurs in the presence of quasiperiodic driving, theoretically predicted by Martin, Re-fael, and Halperin in 2017 [16]. Using a Floquet treatment of the driven qubit, the dynamics is related to the properties o