Hamiltonian extrema of an arbitrary flux-biased Josephson circuit

Flux-biased loops hosting one or more Josephson junctions are ubiquitous elements in quantum information processing based on superconducting hardware. These circuits can be tuned to implement a variety of Hamiltonians, with applications ranging from advanced qubits to quantum limited converters and amplifiers. In particular, the Hamiltonian extrema of these superconducting loops are of special interest for understanding their local and global properties. However, the theory of superconducting quantum circuits still lacks a systematic method to compute the series expansion of the Hamiltonian around these extrema for an arbitrary non-linear superconducting circuit. In this talk, we present such method. It naturally captures the properties of single- and multi-minima Hamiltonians and can be generalized to networks consisting of multiple loops. With the steady advance of design and fabrication techniques of quantum processors, this approach can facilitate the advent of the next generations of superconducting quantum circuits with enhanced functionalities.