As quantum information technologies advance they face challenges in scaling and connectivity. In particular, two necessities remain independent of the technological implementation:the need for connectivity between distant qubits and the need for efficient generation of entanglement. Perfect State Transfer is a technique which realises the time optimal transfer of a quantum state between distant nodes of qubit lattices with only nearest-neighbour couplings, hence providing an important tool to improve device connectivity. Crucially, the transfer protocol results in effective parity-dependent non-local interactions, extending its utility to the efficient generation of entangled states. Here, we experimentally demonstrate Perfect State Transfer and the generation of multi-qubit entanglement on a chain of superconducting qubits. The system consists of six fixed-frequency transmon qubits connected by tunable couplers, where the couplings are controlled via parametric drives. By simultaneously activating all couplings and engineering their individual amplitudes and frequencies, we implement Perfect State Transfer on up to six qubits and observe the respective single-excitation dynamics for different initial states. We then apply the protocol in the presence of multiple excitations and verify its parity-dependent property, where the number of excitations within the chain controls the phase of the transferred state. Finally, we utilise this property to prepare a multi-qubit Greenberger-Horne-Zeilinger state using only a single transfer operation, demonstrating its application for efficient entanglement generation.

By strongly driving a transmon-resonator system, the transmon qubit may eventually escape from its cosine-shaped potential. This process is called transmon ionization (TI) and knownto be detrimental to the qubit coherence and operation. In this work, we investigate the onset of TI in an irreversible, parametrically-driven, frequency conversion process in a system consisting of a superconducting 3D-cavity coupled to a fixed-frequency transmon qubit. Above a critical pump power we find a sudden increase in the transmon population. Using Renyi entropy, Floquet modes, and Husimi Q functions, we infer that this abrupt change can be attributed to a quantum-to-classical phase transition. Furthermore, in the context of the single-photon detection, we measure a TI-uncorrected detection efficiency of up to 86% and estimate a TI-corrected value of up to 78% by exploiting the irreversible frequency conversion. Our numerical simulations suggest that increasing the detuning between the pump and qubit frequencies and increasing the qubit anharmonicity can suppress the TI impact. Our findings highlight the general importance of the TI process when operating coupled qubit-cavity systems.

To control and measure the state of a quantum system it must necessarily be coupled to external degrees of freedom. This inevitably leads to spontaneous emission via the Purcell effect,photon-induced dephasing from measurement back-action, and errors caused by unwanted interactions with nearby quantum systems. To tackle this fundamental challenge, we make use of the design flexibility of superconducting quantum circuits to form a multi-mode element — an artificial molecule — with symmetry-protected modes. The proposed circuit consists of three superconducting islands coupled to a central island via Josephson junctions. It exhibits two essential non-linear modes, one of which is flux-insensitive and used as the protected qubit mode. The second mode is flux-tunable and serves via a cross-Kerr type coupling as a mediator to control the dispersive coupling of the qubit mode to the readout resonator. We demonstrate the Purcell protection of the qubit mode by measuring relaxation times that are independent of the mediated dispersive coupling. We show that the coherence of the qubit is not limited by photon-induced dephasing when detuning the mediator mode from the readout resonator and thereby reducing the dispersive coupling. The resulting highly protected qubit with tunable interactions may serve as a basic building block of a scalable quantum processor architecture, in which qubit decoherence is strongly suppressed.

Understanding the non-deterministic behavior of deterministic nonlinear systems has been an implicit dream since Lorenz named it the „butterfly effect“. A prominent exampleis the hysteresis and bistability of the Duffing oscillator, which in the classical description is attributed to the coexistence of two steady states in a double-well potential. However, this interpretation fails in the quantum-mechanical perspective, where a single unique steady state is allowed in the whole parameter space. Here, we measure the non-equilibrium dynamics of a superconducting Duffing oscillator and reconcile the classical and quantum descriptions in a unified picture of quantum metastability. We demonstrate that the two classically regarded steady states are in fact metastable states. They have a remarkably long lifetime in the classical hysteresis regime but must eventually relax into a single unique steady state allowed by quantum mechanics. By engineering the lifetime of the metastable states sufficiently large, we observe a first-order dissipative phase transition, which mimics a sudden change of the mean field in a 11-site Bose-Hubbard lattice. We also reveal the two distinct phases of the transition by quantum state tomography, namely a coherent-state phase and a squeezed-state phase separated by a critical point. Our results reveal a smooth quantum state evolution behind a sudden dissipative phase transition, and they form an essential step towards understanding hysteresis and instability in non-equilibrium systems.

We describe a unified quantum approach for analyzing the scattering coefficients of superconducting microwave resonators with a variety of geometries. We also generalize the methodto a chain of resonators in either hanger- or necklace-type, and reveal interesting transport properties similar to a photonic crystal. It is shown that both the quantum and classical analyses provide consistent results, and they together form a solid basis for analyzing the decoherence effect in a general microwave resonator. These results pave the way for designing and applying superconducting microwave resonators in complex circuits, and should stimulate the interest of distinguishing different decoherence mechanisms of a resonator mode beyond free energy relaxation.

We describe a unified classical approach for analyzing the scattering coefficients of superconducting microwave resonators with a variety of geometries. To fill the gap between experimentand theory, we also consider the influences of small circuit asymmetry and the finite length of the feedlines, and describe a procedure to correct them in typical measurement results. We show that, similar to the transmission coefficient of a hanger-type resonator, the reflection coefficient of a necklace- or bridge-type resonator does also contain a reference point which can be used to characterize the electrical properties of a microwave resonator in a single measurement. Our results provide a comprehensive understanding of superconducting microwave resonators from the design concepts to the characterization details.

We propose a tunable coupler consisting of N off-resonant and fixed-frequency qubits that can tune and even amplify the effective interaction between two general circuit components.The tuning range of the interaction is proportional to N, with a minimum value of zero and a maximum that can exceed the physical coupling rates in the system. The effective coupling rate is determined by the collective magnetic quantum number of the qubit ensemble, which takes only discrete values and is free from collective decay and decoherence. Using single-photon pi-pulses, the coupling rate can be switched between arbitrary initial and final values within the dynamic range in a single step without going through intermediate values. A cascade of the couplers for amplifying small interactions or weak signals is also discussed. These results should not only stimulate interest in exploring the collective effects in quantum information processing, but also enable development of applications in tuning and amplifying the interactions in a general cavity-QED system.

Nano-electromechanical systems implement the opto-mechanical interaction combining electromagnetic circuits and mechanical elements. We investigate an inductively coupled nano-electromechanicalsystem, where a superconducting quantum interference device (SQUID) realizes the coupling. We show that the resonance frequency of the mechanically compliant string embedded into the SQUID loop can be controlled in two different ways: (i) the bias magnetic flux applied perpendicular to the SQUID loop, (ii) the magnitude of the in-plane bias magnetic field contributing to the nano-electromechanical coupling. These findings are quantitatively explained by the inductive interaction contributing to the effective spring constant of the mechanical resonator. In addition, we observe a residual field dependent shift of the mechanical resonance frequency, which we attribute to the finite flux pinning of vortices trapped in the magnetic field biased nanostring.

We have fabricated and studied a system of two tunable and coupled nonlinear superconducting resonators. The nonlinearity is introduced by galvanically coupled dc-SQUIDs. We simulatethe system response by means of a circuit model, which includes an additional signal path introduced by the electromagnetic environment. Furthermore, we present two methods allowing us to experimentally determine the nonlinearity. First, we fit the measured frequency and flux dependence of the transmission data to simulations based on the equivalent circuit model. Second, we fit the power dependence of the transmission data to a model that is predicted by the nonlinear equation of motion describing the system. Our results show that we are able to tune the nonlinearity of the resonators by almost two orders of magnitude via an external coil and two on-chip antennas. The studied system represents the basic building block for larger systems, allowing for quantum simulations of bosonic many-body systems with a larger number of lattice sites.

Quantum Fourier transform (QFT) is a key ingredient of many quantum algorithms. In typical applications such as phase estimation, a considerable number of ancilla qubits and gates areused to form a Hilbert space large enough for high-precision results. Qubit recycling reduces the number of ancilla qubits to one, but it is only applicable to semi-classical QFT and requires repeated measurements and feedforward within the coherence time of the qubits. In this work, we explore a novel approach based on resonators that forms a high-dimensional Hilbert space for the realization of QFT. By employing the perfect state-transfer method, we map an unknown multi-qubit state to a single resonator, and obtain the QFT state in the second oscillator through cross-Kerr interaction and projective measurement. A quantitive analysis shows that our method allows for high-dimensional and fully-quantum QFT employing the state-of-the-art superconducting quantum circuits. This paves the way for implementing various QFT related quantum algorithms.