Characterizing and calibrating physical qubits is essential for maintaining the performance of quantum processors. A key challenge in this process is the presence of crosstalk thatcomplicates the estimation of individual qubit detunings. In this work, we derive optimal strategies for estimating detuning and crosstalk parameters by optimizing Ramsey interference experiments using Fisher information and the Cramer-Rao bound. We compare several calibration protocols, including measurements of a single quadrature at multiple times and of two quadratures at a single time, for a fixed number of total measurements. Our results predict that the latter approach yields the highest precision and robustness in both cases of isolated and coupled qubits. We validate experimentally our approach using a single NV center as well as superconducting transmons. Our approach enables accurate parameter extraction with significantly fewer measurements, resulting in up to a 50\% reduction in calibration time while maintaining estimation accuracy.
We propose an analog superconducting quantum simulator for a one-dimensional model featuring momentum-dependent (nonlocal) electron-phonon couplings of Su-Schrieffer-Heeger and „breathing-mode“types. Because its corresponding vertex function depends on both the electron- and phonon quasimomenta, this model does not belong to the realm of validity of the Gerlach-L\“{o}wen theorem that rules out any nonanalyticities in single-particle properties. The superconducting circuit behind the proposed simulator entails an array of transmon qubits and microwave resonators. By applying microwave driving fields to the qubits, a small-polaron Bloch state with an arbitrary quasimomentum can be prepared in this system within times several orders of magnitude shorter than the typical qubit decoherence times. We demonstrate that in this system — by varying the circuit parameters — one can readily reach the critical coupling strength required for observing the sharp transition from a nondegenerate (single-particle) ground state corresponding to zero quasimomentum (Kgs=0) to a twofold-degenerate small-polaron ground state at nonzero quasimomenta Kgs and −Kgs. Through exact numerical diagonalization of our effective Hamiltonian, we show how this nonanalyticity is reflected in the relevant single-particle properties (ground-state energy, quasiparticle residue, average number of phonons). The proposed setup provides an ideal testbed for studying quantum dynamics of polaron formation in systems with strongly momentum-dependent electron-phonon interactions.
We propose to use an ancilla fluxonium qubit to interact with a Majorana
qubit hosted by a topological 1D wire. The coupling is obtained using the
Majorana qubit controlled $4pi$ Josephsoneffect to flux bias the fluxonium
qubit. We demonstrate how this coupling can be used to sensitively identify
topological superconductivity, to measure the state of the Majorana qubit, to
construct 2-qubit operations, and to implement quantum memories with
topological protection.