Analog quantum simulation of bosonic and anyonic models with flux-driven transmons

How can superconducting transmon circuits, typically used for gate-based quantum computing, be repurposed as analog quantum simulators for complex many-body lattice models like the Bose-Hubbard (BH) and anyon-Hubbard (AH) models? The authors seek a protocol that avoids the limitations of previous transmon-based simulations, which were often restricted to hard-core bosons or limited particle numbers.

The researchers propose a protocol based on the sinusoidal modulation of transmon frequencies. By applying this modulation in an alternating pattern across the lattice, they resonantly drive specific many-body transitions between neighboring transmons. By carefully choosing the drive frequencies and amplitudes, they can match the effective transition amplitudes to the hopping parameters of the target models. Furthermore, by introducing phase offsets to the drives, they can engineer complex-valued hopping amplitudes, which are essential for simulating the fractional statistics of anyons.

The study demonstrates that this frequency-modulation scheme allows for the simulation of the BH model with up to three particles per site and the AH model with up to two particles per site. Numerical simulations confirm that the transmon array accurately reproduces key physical phenomena, such as interaction-dependent localization in the BH model and the statistics-dependent asymmetry of quantum walks in the AH model. The protocol is shown to be robust across a range of interaction strengths and statistical phases, provided the system remains within the specified excitation manifold.

This work expands the utility of existing superconducting quantum hardware by enabling the study of many-body physics that is difficult to simulate classically. By providing a general, flexible protocol for analog simulation, the authors offer a path to explore exotic phases of matter and anyonic dynamics on platforms that are already widely available and highly controllable. This approach complements digital quantum computing by leveraging the intrinsic dynamics of the hardware to probe complex quantum systems.