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Scaling trapped-ion quantum computing will require robust trapping of at least hundreds of ions over long periods, while increasing the complexity and functionality of the trap itself. Symmetric 3D structures enable high trap depth, but microfabrication techniques are generally better suited to planar structures that produce less ideal conditions for trapping. We present an ion trap fabricated on stacked 8-inch wafers in a large-scale MEMS microfabrication process that provides reproducible traps at a large volume. Electrodes are patterned on the surfaces of two opposing wafers bonded to a spacer, forming a 3D structure with 2.5 micrometer standard deviation in alignment across the stack. We implement a design achieving a trap depth of 1 eV for a calcium-40 ion held at 200 micrometers from either electrode plane. We characterize traps, achieving measurement agreement with simulations to within +/-5% for mode frequencies spanning 0.6--3.8 MHz, and evaluate stray electric field across multiple trapping sites. We measure motional heating rates over an extensive range of trap frequencies, and temperatures, observing 40 phonons/s at 1 MHz and 185 K. This fabrication method provides a highly scalable approach for producing a new generation of 3D ion traps., Comment: 29 pages, 5 figures

As superconductors are cooled below their critical temperature, stray magnetic flux can become trapped in regions that remain normal. The presence of trapped flux facilitates dissipation of ac current in a superconductor, leading to losses in superconducting elements of microwave devices. In type II superconductors, dissipation is well-understood in terms of the dynamics of vortices hosting a single flux quantum. In contrast, the ac response of type I superconductors with trapped flux has not received much attention. Building on Andreev's early work [Sov. Phys. JETP 24, 1019 (1967)], here we show theoretically that the dominant dissipation mechanism is the absorption of the ac field at the exposed surfaces of the normal regions, while the deformation of the superconducting/normal interfaces is unimportant. We use the developed theory to estimate the degradation of the quality factors in field-cooled cavities, and we satisfactorily compare these theoretical estimates to the measured field dependence of the quality factors of two aluminum cavities., Comment: 9 pages, 3 figures

A quantum computer has the potential to effciently solve problems that are intractable for classical computers. Constructing a large-scale quantum processor, however, is challenging due to errors and noise inherent in real-world quantum systems. One approach to this challenge is to utilize modularity--a pervasive strategy found throughout nature and engineering--to build complex systems robustly. Such an approach manages complexity and uncertainty by assembling small, specialized components into a larger architecture. These considerations motivate the development of a quantum modular architecture, where separate quantum systems are combined via communication channels into a quantum network. In this architecture, an essential tool for universal quantum computation is the teleportation of an entangling quantum gate, a technique originally proposed in 1999 which, until now, has not been realized deterministically. Here, we experimentally demonstrate a teleported controlled-NOT (CNOT) operation made deterministic by utilizing real-time adaptive control. Additionally, we take a crucial step towards implementing robust, error-correctable modules by enacting the gate between logical qubits, encoding quantum information redundantly in the states of superconducting cavities. Such teleported operations have significant implications for fault-tolerant quantum computation, and when realized within a network can have broad applications in quantum communication, metrology, and simulations. Our results illustrate a compelling approach for implementing multi-qubit operations on logical qubits within an error-protected quantum modular architecture., Comment: Main text: 7 pages, 4 figures; Supplementary Information: 26 pages, 13 figures

Large-scale quantum information processing networks will most probably require the entanglement of distant systems that do not interact directly. This can be done by performing entangling gates between standing information carriers, used as memories or local computational resources, and flying ones, acting as quantum buses. We report the deterministic entanglement of two remote transmon qubits by Raman stimulated emission and absorption of a traveling photon wavepacket. We achieve a Bell state fidelity of 73 %, well explained by losses in the transmission line and decoherence of each qubit.

Manipulating the state of a logical quantum bit usually comes at the expense of exposing it to decoherence. Fault-tolerant quantum computing tackles this problem by manipulating quantum information within a stable manifold of a larger Hilbert space, whose symmetries restrict the number of independent errors. The remaining errors do not affect the quantum computation and are correctable after the fact. Here we implement the autonomous stabilization of an encoding manifold spanned by Schroedinger cat states in a superconducting cavity. We show Zeno-driven coherent oscillations between these states analogous to the Rabi rotation of a qubit protected against phase-flips. Such gates are compatible with quantum error correction and hence are crucial for fault-tolerant logical qubits.

We present a device demonstrating a lithographically patterned transmon integrated with a micromachined cavity resonator. Our two-cavity, one-qubit device is a multilayer microwave integrated quantum circuit (MMIQC), comprising a basic unit capable of performing circuit-QED (cQED) operations. We describe the qubit-cavity coupling mechanism of a specialized geometry using an electric field picture and a circuit model, and finally obtain specific system parameters using simulations. Fabrication of the MMIQC includes lithography, etching, and metallic bonding of silicon wafers. Superconducting wafer bonding is a critical capability that is demonstrated by a micromachined storage cavity lifetime $34.3~\mathrm{\mu s}$, corresponding to a quality factor of 2 million at single-photon energies. The transmon coherence times are $T_1=6.4~\mathrm{\mu s}$, and $T_2^{Echo}= 11.7~\mathrm{\mu s}$. We measure qubit-cavity dispersive coupling with rate $\chi_{q\mu}/2\pi=-1.17~$MHz, constituting a Jaynes-Cummings system with an interaction strength $g/2\pi=49~$MHz. With these parameters we are able to demonstrate cQED operations in the strong dispersive regime with ease. Finally, we highlight several improvements and anticipated extensions of the technology to complex MMIQCs.

We present a method for relieving aluminum 3D transmon qubits from a silicon substrate using micromachining. Our technique is a high yield, one-step deep reactive ion etch that requires no additional fabrication processes, and results in the suspension of the junction area and edges of the aluminum film. The drastic change in the device geometry affects both the dielectric and flux noise environment experienced by the qubit. In particular, the participation ratios of various dielectric interfaces are significantly modified, and suspended qubits exhibited longer $T_1$'s than non-suspended ones. We also find that suspension increases the flux noise experienced by tunable SQUID-based qubits., Comment: Main text: 4 pages, 3 figures. Supplementary materials: 6 pages, 5 figures

There are two general requirements to harness the computational power of quantum mechanics: the ability to manipulate the evolution of an isolated system and the ability to faithfully extract information from it. Quantum error correction and simulation often make a more exacting demand: the ability to perform non-destructive measurements of specific correlations within that system. We realize such measurements by employing a protocol adapted from [S. Nigg and S. M. Girvin, Phys. Rev. Lett. 110, 243604 (2013)], enabling real-time selection of arbitrary register-wide Pauli operators. Our implementation consists of a simple circuit quantum electrodynamics (cQED) module of four highly-coherent 3D transmon qubits, collectively coupled to a high-Q superconducting microwave cavity. As a demonstration, we enact all seven nontrivial subset-parity measurements on our three-qubit register. For each we fully characterize the realized measurement by analyzing the detector (observable operators) via quantum detector tomography and by analyzing the quantum back-action via conditioned process tomography. No single quantity completely encapsulates the performance of a measurement, and standard figures of merit have not yet emerged. Accordingly, we consider several new fidelity measures for both the detector and the complete measurement process. We measure all of these quantities and report high fidelities, indicating that we are measuring the desired quantities precisely and that the measurements are highly non-demolition. We further show that both results are improved significantly by an additional error-heralding measurement. The analyses presented here form a useful basis for the future characterization and validation of quantum measurements, anticipating the demands of emerging quantum technologies., Comment: 10 pages, 5 figures, plus supplement

Three-dimensional microwave cavities have recently been combined with superconducting qubits in the circuit quantum electrodynamics (cQED) architecture. These cavities should have less sensitivity to dielectric and conductor losses at surfaces and interfaces, which currently limit the performance of planar resonators. We expect that significantly (>10^3) higher quality factors and longer lifetimes should be achievable for 3D structures. Motivated by this principle, we have reached internal quality factors greater than 0.5x10^9 and intrinsic lifetimes of 0.01 seconds for multiple aluminum superconducting cavity resonators at single photon energies and millikelvin temperatures. These improvements could enable long lived quantum memories with submicrosecond access times when strongly coupled to superconducting qubits., Comment: 4 pages, 2 figures