Building Hamiltonians with Josephson Phase-Slip Qubits

Tunable Josephson phase-slip qubits (JPSQs) present the possibility of constructing effective spin-1/2 Hamiltonians with arbitrary 2-local interactions using superconducting technology. Here, we discuss how this mapping is made, presenting a Pauli-operator breakdown of the current and voltage dipoles of a JPSQ along a qubit annealing path that allows for preparation and readout in addition to the engineered couplings. As an example of the possibilities inherent in these devices, we present a system of JPSQs that adiabatically encodes or decodes a logical qubit in a [[4,1,2]] Bacon-Shor code.