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Sharing information coherently between nodes of a quantum network is fundamental to distributed quantum information processing. In this scheme, the computation is divided into subroutines and performed on several smaller quantum registers that are connected by classical and quantum channels 1 . A direct quantum channel, which connects nodes deterministically rather than probabilistically, achieves larger entanglement rates between nodes and is advantageous for distributed fault-tolerant quantum computation 2 . Here we implement deterministic state-transfer and entanglement protocols between two superconducting qubits fabricated on separate chips. Superconducting circuits 3 constitute a universal quantum node 4 that is capable of sending, receiving, storing and processing quantum information 5 – 8 . Our implementation is based on an all-microwave cavity-assisted Raman process 9 , which entangles or transfers the qubit state of a transmon-type artificial atom 10 with a time-symmetric itinerant single photon. We transfer qubit states by absorbing these itinerant photons at the receiving node, with a probability of 98.1 ± 0.1 per cent, achieving a transfer-process fidelity of 80.02 ± 0.07 per cent for a protocol duration of only 180 nanoseconds. We also prepare remote entanglement on demand with a fidelity as high as 78.9 ± 0.1 per cent at a rate of 50 kilohertz. Our results are in excellent agreement with numerical simulations based on a master-equation description of the system. This deterministic protocol has the potential to be used for quantum computing distributed across different nodes of a cryogenic network. Deterministic quantum state transfer and entanglement generation is demonstrated between superconducting qubits on distant chips using single photons.

Microwave stimulation of a superconducting artificial three-level atom is used to demonstrate high-fidelity, non-Abelian geometric transformations, the results of which depend on the order in which they are performed. Gateways to quantum computing Geometric phases are acquired whenever a quantum system evolves along a path. If the system contains degenerate energy levels, these can take the form of matrix-valued geometric transformations called non-Abelian holonomies. It has been proposed that such holonomies could be exploited for noise-resilient quantum computation. The authors realize non-Abelian holonomic quantum operations on a single superconducting artificial three-level atom. In combination with a non-trivial two-qubit gate, the results may suggest a route to universal holonomic quantum computing. The geometric aspects of quantum mechanics are emphasized most prominently by the concept of geometric phases, which are acquired whenever a quantum system evolves along a path in Hilbert space, that is, the space of quantum states of the system. The geometric phase is determined only by the shape of this path 1 , 2 , 3 and is, in its simplest form, a real number. However, if the system has degenerate energy levels, then matrix-valued geometric state transformations, known as non-Abelian holonomies—the effect of which depends on the order of two consecutive paths—can be obtained 4 . They are important, for example, for the creation of synthetic gauge fields in cold atomic gases 5 or the description of non-Abelian anyon statistics 6 , 7 . Moreover, there are proposals 8 , 9 to exploit non-Abelian holonomic gates for the purposes of noise-resilient quantum computation. In contrast to Abelian geometric operations 10 , non-Abelian ones have been observed only in nuclear quadrupole resonance experiments with a large number of spins, and without full characterization of the geometric process and its non-commutative nature 11 , 12 . Here we realize non-Abelian non-adiabatic holonomic quantum operations 13 , 14 on a single, superconducting, artificial three-level atom 15 by applying a well-controlled, two-tone microwave drive. Using quantum process tomography, we determine fidelities of the resulting non-commuting gates that exceed 95 per cent. We show that two different quantum gates, originating from two distinct paths in Hilbert space, yield non-equivalent transformations when applied in different orders. This provides evidence for the non-Abelian character of the implemented holonomic quantum operations. In combination with a non-trivial two-quantum-bit gate, our method suggests a way to universal holonomic quantum computing.

Large-scale quantum information processors or quantum communication networks will require reliable exchange of information between spatially separated nodes. The links connecting these nodes can be established using traveling photons that need to be absorbed at the receiving node with high efficiency. This is achievable by shaping the temporal profile of the photons and absorbing them at the receiver by time reversing the emission process. Here, we demonstrate a scheme for creating shaped microwave photons using a superconducting transmon-type three-level system coupled to a transmission line resonator. In a second-order process induced by a modulated microwave drive, we controllably transfer a single excitation from the third level of the transmon to the resonator and shape the emitted photon. We reconstruct the density matrices of the created single-photon states and show that the photons are antibunched. We also create multipeaked photons with a controlled amplitude and phase. In contrast to similar existing schemes, the one we present here is based solely on microwave drives, enabling operation with fixed frequency transmons.

In circuit-based quantum computing the available gate set typically consists of single-qubit gates acting on each individual qubit and at least one entangling gate between pairs of qubits. In certain physical architectures, however, some qubits may be “hidden” and lacking direct addressability through dedicated control and readout lines, for instance, because of limited on-chip routing capabilities, or because the number of control lines becomes a limiting factor for many-qubit systems. In this case, no single-qubit operations can be applied to the hidden qubits and their state cannot be measured directly. Instead, they may be controlled and read out only via single-qubit operations on connected “control” qubits and a suitable set of two-qubit gates. We first discuss the impact of such restricted control capabilities on the performance of specific qubit coupling networks. We then experimentally demonstrate full control and measurement capabilities in a superconducting two-qubit device with local single-qubit control and iswap and controlled-phase two-qubit interactions enabled by a tunable coupler. We further introduce an iterative tune-up process required to completely characterize the gate set used for quantum process tomography and evaluate the resulting gate fidelities.

Physical systems reach thermal equilibrium through energy exchange with their environment, and for spins in solids the relevant environment is almost always their host lattice. However, recent studies 1 motivated by observations by Purcell 2 have shown how radiative emission into a microwave cavity can become the dominant relaxation path for spins if the spin–cavity coupling is sufficiently large (such as for small-mode-volume cavities). In this regime, the cavity electromagnetic field overrides the lattice as the dominant environment, inviting the prospect of controlling the spin temperature independently from that of the lattice, by engineering a suitable cavity field. Here, we report on precisely such control over spin temperature, illustrating a novel and universal method to increase the electron spin polarization above its thermal equilibrium value (termed hyperpolarization). By switching the cavity input between resistive loads at different temperatures we can control the electron spin polarization, cooling it below the lattice temperature. Our demonstration uses donor spins in silicon coupled to a superconducting microresonator and we observe more than a twofold increase in spin polarization. This approach provides a general route to signal enhancement in electron spin resonance, or nuclear magnetic resonance through dynamical nuclear spin polarization 3 , 4 . Electron spins in solid usually relax their energy through the coupling with phonons in the host lattice. By using the coupling to microwave photons in a cavity as an alternative relaxation path, it is demonstrated that spins can be cooled below the lattice temperature.

A quantum system interacting with its environment is subject to dephasing, which ultimately destroys the information it holds. Here we use a superconducting qubit to experimentally show that this dephasing has both dynamic and geometric origins. It is found that geometric dephasing, which is present even in the adiabatic limit and when no geometric phase is acquired, can either reduce or restore coherence depending on the orientation of the path the qubit traces out in its projective Hilbert space. It accompanies the evolution of any system in Hilbert space subjected to noise. Open quantum systems are subject to dephasing that ultimately destroys the information they hold. Here, the authors use a superconducting qubit to show that dephasing also has a geometric origin, which can either reduce or restore coherence depending on the path of the quantum system in its Hilbert space.

In circuit-based quantum computing, the available gate set typically consists of single-qubit gates acting on each individual qubit and at least one entangling gate between pairs of qubits. In certain physical architectures, however, some qubits may be 'hidden' and lacking direct addressability through dedicated control and readout lines, for instance because of limited on-chip routing capabilities, or because the number of control lines becomes a limiting factor for many-qubit systems. In this case, no single-qubit operations can be applied to the hidden qubits and their state cannot be measured directly. Instead, they may be controlled and read out only via single-qubit operations on connected 'control' qubits and a suitable set of two-qubit gates. We first discuss the impact of such restricted control capabilities on the quantum volume of specific qubit coupling networks. We then experimentally demonstrate full control and measurement capabilities in a superconducting two-qubit device with local single-qubit control and iSWAP and controlled-phase two-qubit interactions enabled by a tunable coupler. We further introduce an iterative tune-up process required to completely characterize the gate set used for quantum process tomography and evaluate the resulting gate fidelities.

The possibility to utilize different types of two-qubit gates on a single quantum computing platform adds flexibility in the decomposition of quantum algorithms. A larger hardware-native gate set may decrease the number of required gates, provided that all gates are realized with high fidelity. Here, we benchmark both controlled-Z (CZ) and exchange-type (iSWAP) gates using a parametrically driven tunable coupler that mediates the interaction between two superconducting qubits. Using randomized benchmarking protocols we estimate an error per gate of \\(0.9\\pm0.03\\%\\) and \\(1.3\\pm0.4\\%\\) fidelity for the CZ and the iSWAP gate, respectively. We argue that spurious \\(ZZ\\)-type couplings are the dominant error source for the iSWAP gate, and that phase stability of all microwave drives is of utmost importance. Such differences in the achievable fidelities for different two-qubit gates have to be taken into account when mapping quantum algorithms to real hardware.

A switch capable of routing microwave signals at cryogenic temperatures is a desirable component for state-of-the-art experiments in many fields of applied physics, including but not limited to quantum information processing, communication and basic research in engineered quantum systems. Conventional mechanical switches provide low insertion loss but disturb operation of dilution cryostats and the associated experiments by heat dissipation. Switches based on semiconductors or microelectromechanical systems have a lower thermal budget but are not readily integrated with current superconducting circuits. Here we design and test an on-chip switch built by combining tunable transmission-line resonators with microwave beam-splitters. The device is superconducting and as such dissipates a negligible amount of heat. It is compatible with current superconducting circuit fabrication techniques, operates with a bandwidth exceeding \\(100\\,\\mathrm{MHz}\\), is capable of handling photon fluxes on the order of \\(10^{5}\\,\\mu\\mathrm{s}^{-1}\\), equivalent to powers exceeding \\(-90\\,\\mathrm{dBm}\\), and can be switched within approximately \\(6-8\\,\\mathrm{ns}\\). We successfully demonstrate operation of the device in the quantum regime by integrating it on a chip with a single-photon source and using it to route non-classical itinerant microwave fields at the single-photon level.

The speed of quantum gates and measurements is a decisive factor for the overall fidelity of quantum protocols when performed on physical qubits with finite coherence time. Reducing the time required to distinguish qubit states with high fidelity is therefore a critical goal in quantum information science. The state-of-the-art readout of superconducting qubits is based on the dispersive interaction with a readout resonator. Here, we bring this technique to its current limit and demonstrate how the careful design of system parameters leads to fast and high-fidelity measurements without affecting qubit coherence. We achieve this result by increasing the dispersive interaction strength, by choosing an optimal linewidth of the readout resonator, by employing a Purcell filter, and by utilizing phase-sensitive parametric amplification. In our experiment, we measure 98.25% readout fidelity in only 48 ns, when minimizing read-out time, and 99.2% in 88 ns, when maximizing the fidelity, limited predominantly by the qubit lifetime of 7.6 us. The presented scheme is also expected to be suitable for integration into a multiplexed readout architecture.