Quantum bits have been under intense development since the late 1990s, due to the discovery of a number of potential applications for engineered quantum systems to problems in computation or communication. As superconducting circuits provide a straightforward path to scaling up to large numbers of qubits and are exible in terms of their application to a range of different problems, This chapter focuses on the problem of coupling superconducting qubits to other systems, in particular to microwave frequency electromagnetic resonators as well as mechanical resonators. It begins by introducing the topics of piezoelectricity and its role in solid mechanics, then turns to a description of one flavour of superconducting qubit, the phase qubit. It then describes how the phase qubit can be used to control and measure a superconducting electromagnetic resonator, and concludes by describing how a phase qubit can also be used to control and measure a piezomechanical resonator.
Quantum bits have been under intense development since the late 1990s, due to the discovery of a number of potential applications for engineered quantum systems to problems in computation or communication. As superconducting circuits provide a straightforward path to scaling up to large numbers of qubits and are exible in terms of their application to a range of different problems, This chapter focuses on the problem of coupling superconducting qubits to other systems, in particular to microwave frequency electromagnetic resonators as well as mechanical resonators. It begins by introducing the topics of piezoelectricity and its role in solid mechanics, then turns to a description of one flavour of superconducting qubit, the phase qubit. It then describes how the phase qubit can be used to control and measure a superconducting electromagnetic resonator, and concludes by describing how a phase qubit can also be used to control and measure a piezomechanical resonator.
This chapter describes a method to control and measure quantum cavities, achieved using a superconducting phase qubit, a type of electronic atom. The phase qubit has been under intensive development for use as a quantum processing element in a quantum computer. It has recently been used to demonstrate the quantum control and measurement of excitations in resonant cavities, including controlling photons in superconducting microwave resonators, as well as phonons in microwave-frequency mechanical resonators. The discussion here focuses on the quantum control of electromagnetic resonators.
Circuit quantum electrodynamics (cQED), exemplified by a coupled system of a superconducting qubit and a microwave cavity, is a powerful framework for the quantum control and measurement of macroscopic quantum states in solid-state circuits. Quantum circuits based on superconducting qubits have emerged as one of the leading platforms in the pursuit of fault-tolerant quantum computing. Despite significant progress in extending qubit lifetimes, refining experimental protocols, and scaling up quantum processors, errors arising from the control and measurement of superconducting qubits continue to hinder the realization of a universal quantum computer. To investigate the error mechanisms for state-of-the-art qubits, we realize long-lived superconducting transmon qubits that exhibit fluctuating lifetimes, with an average of 0.2 ms and a maximum exceeding 0.4 ms. We then investigate their dominant error mechanism. By introducing novel time-resolved error measurements that are synchronized with the operation of the pulse tube cooler in a dilution refrigerator, we find that mechanical vibrations from the pulse tube induce nonequilibrium dynamics in highly coherent qubits, leading to their correlated bit-flip errors. Our findings not only deepen our understanding of qubit error mechanisms but also provide valuable insights into potential error-mitigation strategies for achieving fault tolerance by decoupling superconducting qubits from their mechanical environments. We also present a novel scheme for operating a cQED system in a regime where the cavity is largely displaced. We find that a qubit drive at the bare cavity frequency can effectively displace the cavity field while minimizing the cavity-drive-induced dephasing and the ac Stark shift. Furthermore, we demonstrate that standard cQED protocols, such as qubit control, readout, and cavity single-photon generation, remain compatible with largely displaced cavity fields, even beyond the critical photon number. These findings open new pathways for exploring cQED dynamics in large-photon-number regimes, including the study of nonlinear phenomena in microwave cavities, the saturation of two-level system baths for extending the coherence of microwave quantum states, and the acceleration of the dispersive readout. Finally, mechanical resonators have emerged as integral components in quantum computing for storing and transducing quantum information. Low-frequency mechanical resonators, with extremely low energy dissipation rates, are particularly interesting for extending the lifetimes of stored quantum information. However, integrating low-frequency mechanical resonators with qubits is challenging because their small energy gaps make coherent energy exchange and ground-state preparation difficult. In this thesis, we report the first steps towards the characterization of a hybrid quantum device, consisting of a Transmon qubit and a circuit optomechanical system, both coupled to a 3D microwave cavity.
Nanomechanical systems can support highly coherent microwave-frequency excitations at cryogenic temperatures. However, generating sufficient coupling between these devices and superconducting quantum circuits is challenging due to the vastly different length scales of acoustic and electromagnetic excitations. Here we demonstrate a general method for calculating piezoelectric interactions between quantum circuits and arbitrary phononic nanostructures. We illustrate our technique by studying the coupling between a transmon qubit and bulk acoustic-wave, Lamb-wave, and phononic crystal resonators, and show that very large coupling rates are possible in all three cases. Our results suggest a route to phononic circuits and systems that are nonlinear at the single-phonon level.
Phonon modes at microwave frequencies can be cooled to their quantum ground state using conventional cryogenic refrigeration, providing a convenient way to study and manipulate quantum states at the single phonon level. Phonons are of particular interest because mechanical deformations can mediate interactions with a wide range of different quantum systems, including solid-state defects, superconducting qubits, and optical photons when using optomechanically active constructs. Phonons, thus, hold promise for quantum-focused applications as diverse as sensing, information processing, and communication. Here, we describe a piezoelectric quantum bulk acoustic resonator (QBAR) with a 4.88 GHz resonant frequency, which, at cryogenic temperatures, displays large electromechanical coupling strength combined with a high intrinsic mechanical quality factor, Qi≈4.3×104. Using a recently developed flip-chip technique, we couple this QBAR resonator to a superconducting qubit on a separate die and demonstrate the quantum control of the mechanics in the coupled system. This approach promises a facile and flexible experimental approach to quantum acoustics and hybrid quantum systems.
Superconducting qubits, realized by incorporating Josephson junctions into superconducting circuits, behave as artificial atoms with anharmonic energy spectra and can be precisely controlled and measured using microwave cavities within the framework of circuit quantum electrodynamics (cQED). Since its emergence in the early 2000s, cQED has established superconducting qubits as leading candidates for scalable quantum devices and has enabled the exploration of hybrid quantum systems that integrate disparate physical platformsThis review surveys superconducting hybrid quantum electromechanical systems in which mechanical resonators are coupled to superconducting qubits, with a focus on two widely used qubit platforms: the transmon and the fluxonium. We provide an overview of the underlying coupling mechanisms arising from interactions through the phase and charge degrees of freedom of the qubit, and discuss how these mechanisms give rise to both longitudinal and transverse qubit-mechanical interactions. We further review extensions of electromechanical platforms to electro-optomechanical architectures, in which optical cavities are integrated to enable coherent interfacing between superconducting circuits and optical photons. This review aims to present a unified framework and perspective on qubit-mechanical and qubit-mechanical-optical hybrid systems in superconducting quantum technologies and applications related to sensors.
The leading approach to attempt quantum computing is based on superconductors. In particular, Circuit Quantum Electrodynamic systems (circuit QED) are used to couple photons stored in a microwave resonator to a quantum bit (qubit), allowing the qubit to be controlled and measured. A lumped element parallel RLC circuit will be used to model a superconducting coplanar microwave resonator, in order to gain an intuitive understanding of how various parameters affect its electromagnetic properties, and how they can be optimised to provide desired specifications. Resonator quality factors will also be realised, which describe the effects of coupling the microwave resonator to external input/output transmission lines. The qubit is generated by a superconducting capacitively shunted Josephson Junction; the transmon, and its operation and non-linear behaviour will be discussed in this report. The transmon is integrated with a microwave resonator to generate the circuit QED system, and the derivation of the systems Hamiltonian will allow us to determine the equations describing the behaviour of the system, and therefore how it may be controlled and measured. The Bloch sphere will be introduced, which provides a useful geometric representation of the state space of a two-level quantum system. Mapping the derived Hamiltonian to the time-dependent Schrodinger equation facilitates realisation of control mechanisms of the qubit based on rotations about the Bloch sphere.