The geometric aspects of quantum mechanics are underlined most prominently by the concept of geometric phases, which are acquired whenever a quantum system evolves along a closed path in Hilbert space. The geometric phase is determined only by the shape of this path [1][2][3][4] and is -in its simplest form -a real number. However, if the system contains degenerate energy levels, matrix-valued geometric phases, termed non-abelian holonomies, can emerge 5 . They play an important role for the creation of synthetic gauge fields in cold atomic gases 6 and the description of non-abelian anyon statistics 7 . Moreover, it has been proposed to exploit non-abelian holonomic gates for robust quantum computation [8][9][10] . In contrast to abelian geometric phases 11 , nonabelian ones have been observed only in nuclear quadrupole resonance experiments with a large number of spins and without fully characterizing the geometric process and its non-commutative nature 12,13 . Here, we realize non-abelian holonomic quantum operations 14,15 on a single superconducting artificial three-level atom 16 by applying a well controlled two-tone microwave drive. Using quantum process tomography, we determine fidelities of the resulting non-commuting gates exceeding 95%. We show that a sequence of two paths in Hilbert space traversed in different order yields inequivalent transformations, which is an evidence for the non-abelian character of the implemented holonomic quantum gates. In combination with two-qubit operations, they form a universal set of gates for holonomic quantum computation.A cyclic evolution of a non-degenerate quantum system is in general accompanied by a phase change of its wave function. The acquired abelian phase can be divided into two parts: The dynamical phase which is proportional to the evolution time and the energy of the system, and the geometric phase which depends only on the path of the system in Hilbert space. This characteristic feature leads to a resilience of the geometric phase to certain fluctuations during the evolution 17-19 , a property which has attracted particular attention in the field of quantum information processing 20 . However, universal quantum computation cannot be based on simple phase gates, which modify only the relative phase of a superposition state, unless they act on specific basis states 21 . Furthermore, geometric operations acting on degenerate subspaces have * abdumalikov@phys.ethz.ch † Now at Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA 91125, USA been proposed for holonomic quantum computation fully based on geometric concepts 8 . In this scheme, quantum bits are encoded in a doubly degenerate eigenspace of the system hamiltonian h( λ). The parameters λ are varied to induce a cyclic evolution of the system. When the system returns back to its initial state, it can acquire not only a simple geometric phase factor, but also undergoes a path-dependent unitary transformation, a non-abelian holonomy, which causes a transition bet...

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 µs. The presented scheme is also expected to be suitable for integration into a multiplexed readout architecture.

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 . 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 . Here we implement deterministic state-transfer and entanglement protocols between two superconducting qubits fabricated on separate chips. Superconducting circuits constitute a universal quantum node that is capable of sending, receiving, storing and processing quantum information. Our implementation is based on an all-microwave cavity-assisted Raman process , which entangles or transfers the qubit state of a transmon-type artificial atom 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.

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.

Active qubit reset is a key operation in many quantum algorithms, and particularly in quantum error correction. Here, we experimentally demonstrate a reset scheme for a three-level transmon artificial atom coupled to a large bandwidth resonator. The reset protocol uses a microwave-induced interaction between the |f,0⟩ and |g,1⟩ states of the coupled transmon-resonator system, with |g⟩ and |f⟩ denoting the ground and second excited states of the transmon, and |0⟩ and |1⟩ the photon Fock states of the resonator. We characterize the reset process and demonstrate reinitialization of the transmon-resonator system to its ground state in less than 500 ns and with 0.2% residual excitation. Our protocol is of practical interest as it has no additional architectural requirements beyond those needed for fast and efficient single-shot readout of transmons, and does not require feedback.