Characterization of hidden modes in networks of superconducting qubits

Abstract

We present a method for detecting electromagnetic (EM) modes that couple to a superconducting qubit in a circuit quantum electrodynamics (circuit-QED) architecture. Based on measurement-induced dephasing, this technique allows the measurement of modes that have a high quality factor (Q) and may be difficult to detect through standard transmission and reflection measurements at the device ports. In this scheme the qubit itself acts as a sensitive phase meter, revealing modes that couple to it through measurements of its coherence time. Such modes are indistinguishable from EM modes that do not couple to the qubit using a vector network analyzer. Moreover, this technique provides useful characterization parameters including the quality factor and the coupling strength of the unwanted resonances. We demonstrate the method for detecting both high-Q coupling resonators in planar devices as well as spurious modes produced by a 3D cavity.Superconducting qubits within a circuit-QED architecture are a prime candidate for quantum computing devices. Qubit coherence times have exceeded 1 100 µs, and gate fidelities have reached over 0.999 2-4 for singleand 0.99 for two-qubit operations 5,6 . Experiments are now moving beyond devices with few qubits and instead involve arrays of connected qubits forming large, complicated networks of qubits and quantum buses or coupling resonators 7-9 . In these systems, there are many high-Q modes that have the potential to couple to the qubits, either by design in the case of bus resonators, or as a result of spurious modes determined by the geometry of the device and packaging 10 . In this letter, we describe a simple method for characterizing these various EM modes by using the qubit as a sensitive phase meter to detect any electromagnetic mode that couples to it. As we will show here, this technique, which we refer to as "coherence spectroscopy", identifies only those modes which couple to the qubit and does so with a sensitivity much greater than that of external port S-parameter measurements.Typically bus resonators are designed to act as a mechanism for coupling two or more qubits but are difficult to detect through the on-chip measurement ports 11 . Quantum fluctuations in the number of photons in a resonator coupled to the qubit can create random phase differences between the |0 and |1 state of the qubit, which leads to dephasing. Measurement-induced-dephasing is a well known phenomenon 12-16 that has been characterized in experimental systems using tunable couplings between the qubit and its environment 17 and has served as a mechanism for measuring thermal noise 18-20 . Various efforts have been made to avoid populating resonators in qubit gates that depend on the qubit-resonator coupling 21,22 , to reduce qubit dephasing through measurement feedback [23][24][25] or tunable coupling to the readout resonator 26 . However, we can also take advantage of this phenomenon to determine the frequency of bus resonators and the strength of bus-qubit coupling. We accomplish this by accurate...

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