Quantum circuit theory has emerged as an essential tool for the study of the dynamics of superconducting circuits. Recently, the problem of accounting for time-dependent driving viaexternal magnetic fields was addressed by Riwar-DiVincenzo in their paper – ‚Circuit quantization with time-dependent magnetic fields for realistic geometries‘ in which they proposed a technique to construct a low-energy Hamiltonian for a given circuit geometry, taking as input the external magnetic field interacting with the geometry. This result generalises previous efforts that dealt only with discrete circuits. Moreover, it shows through the example of a parallel-plate SQUID circuit that assigning individual, discrete capacitances to each individual Josephson junction, as proposed by treatments of discrete circuits, is only possible if we allow for negative, time-dependent and even singular capacitances. In this report, we provide numerical evidence to substantiate this result by performing finite-difference simulations on a parallel-plate SQUID. We furnish continuous geometries with a uniform magnetic field whose distribution we vary such that the capacitances that are to be assigned to each Josephson junction must be negative and even singular. Thus, the necessity for time-dependent capacitances for appropriate quantization emerges naturally when we allow the distribution of the magnetic field to change with time.
We present the design of an inductively shunted transmon qubit with flux-tunable coupling to an embedded harmonic mode. This circuit construction offers the possibility to flux-choosebetween pure transverse and pure longitudinal coupling, that is coupling to the σx or σz degree of freedom of the qubit. While transverse coupling is the coupling type that is most commonly used for superconducting qubits, the inherently different longitudinal coupling has some remarkable advantages both for readout and for the scalability of a circuit. Being able to choose between both kinds of coupling in the same circuit provides the flexibility to use one for coupling to the next qubit and one for readout, or vice versa. We provide a detailed analysis of the system’s behavior using realistic parameters, along with a proposal for the physical implementation of a prototype device.
We consider the direct three-qubit parity measurement scheme with two measurement resonators, using circuit quantum electrodynamics to analyze its functioning for several differenttypes of superconducting qubits. We find that for the most common, transmon-like qubit, the presence of additional qubit-state dependent coupling terms of the two resonators hinders the possibility of performing the direct parity measurement. We show how this problem can be solved by employing the Tunable Coupling Qubit (TCQ) in a particular designed configuration. In this case, we effectively engineer the original model Hamiltonian by cancelling the harmful terms. We further develop an analysis of the measurement in terms of information gains and provide some estimates of the typical parameters for optimal operation with TCQs.
We present a circuit construction for a new fixed-frequency superconducting qubit and show how it can be scaled up to a grid with strictly local interactions. The circuit QED realizationwe propose implements σz-type coupling between a superconducting qubit and any number of LC resonators. The resulting \textit{longitudinal coupling} is inherently different from the usual σx-type \textit{transverse coupling}, which is the one that has been most commonly used for superconducting qubits. In a grid of fixed-frequency qubits and resonators with a particular pattern of always-on interactions, coupling is strictly confined to nearest and next-nearest neighbor resonators; there is never any direct qubit-qubit coupling. We note that just four distinct resonator frequencies, and only a single unique qubit frequency, suffice for the scalability of this scheme. A controlled phase gate between two neighboring qubits can be realized with microwave drives on the qubits, without affecting the other qubits. This fact is a supreme advantage for the scalability of this scheme.