Universal two-qubit interactions, measurement, and cooling for quantum simulation and computing

By coupling pairs of superconducting qubits through a small Josephson junction with a time-dependent flux bias, we show that arbitrary interactions involving any combination of Pauli matrices can be generated with a small number of drive tones applied through the flux bias of the coupling junction. We then demonstrate that similar (though not fully universal) results can be achieved in capacitively coupled qubits by exploiting the higher energy states of the devices through multiphoton drive signals applied to the qubits' flux degrees of freedom. By using this mechanism to couple a qubit to a detuned resonator, the qubit's rotating-frame state can be nondestructively measured along any direction on the Bloch sphere. Finally, we describe how the frequency-converting nature of the couplings can be used to engineer a mechanism analogous to dynamic nuclear polarization in NMR systems, capable of cooling an array of qubits well below the ambient temperature, and outline how higher-order interactions, such as local three-body terms, can be engineered through the same couplings. Our results demonstrate that a programmable quantum simulator for large classes of interacting spin models could be engineered with the same physical hardware.

Figure 1

Basic coupling types considered in this work. (a) We demonstrate a flux-biased Josephson junction coupling between two transmon qubits (blue dashed regions), discussed in Sec. 2, each of which has its primary Josephson junction split into a superconducting quantum interference device (SQUID) loop for optional flux tuning. By tuning the flux signal $F\left(t\right)$ threaded through the loop made by the smaller junction and the bridged ground, all possible two-body interactions between the qubits can be dynamically generated. Similar results can be derived for flux and fluxonium qubits in the appropriate parameter regimes. This coupling can be used to implement the cooling protocol of Sec. 4. (b) We depict a transmon qubit coupled to a resonator through a simple capacitive coupling, as discussed in Sec. 3. The grounds are bridged in this figure, though unlike case (a) this is not required to obtain the desired behavior. A flux signal is applied through the transmon's SQUID loop to generate couplings which allow for the transmon's rotating-frame state to be measured along any direction on the Bloch sphere. This setup can also be used to couple qubits, though without as much flexibility as the small junction in (a).