Superconducting quantum circuits based on Josephson junctions have made rapid progress in demonstrating quantum behavior and scalability. However, the future prospects ultimately depend upon the intrinsic coherence of Josephson junctions, and whether superconducting qubits can be adequately isolated from their environment. We introduce a new architecture for superconducting quantum circuits employing a three-dimensional resonator that suppresses qubit decoherence while maintaining sufficient coupling to the control signal. With the new architecture, we demonstrate that Josephson junction qubits are highly coherent, with T2 ∼ 10 to 20  μs without the use of spin echo, and highly stable, showing no evidence for 1/f critical current noise. These results suggest that the overall quality of Josephson junctions in these qubits will allow error rates of a few 10(-4), approaching the error correction threshold.

Photons are ideal carriers for quantum information as they can have a long coherence time and can be transmitted over long distances. These properties are a consequence of their weak interactions within a nearly linear medium. To create and manipulate nonclassical states of light, however, one requires a strong, nonlinear interaction at the single photon level. One approach to generate suitable interactions is to couple photons to atoms, as in the strong coupling regime of cavity QED systems [1, 2]. In these systems, however, one only indirectly controls the quantum state of the light by manipulating the atoms [3]. A direct photon-photon interaction occurs in so-called Kerr media, which typically induce only weak nonlinearity at the cost of significant loss. So far, it has not been possible to reach the single-photon Kerr regime, where the interaction strength between individual photons exceeds the loss rate. Here, using a 3D circuit QED architecture [4], we engineer an artificial Kerr medium which enters this regime and allows the observation of new quantum effects. We realize a Gedankenexperiment proposed by Yurke and Stoler [5], in which the collapse and revival of a coherent state can be observed. This time evolution is a consequence of the quantization of the light field in the cavity and the nonlinear interaction between individual photons. During this evolution non-classical superpositions of coherent states, i.e. multi-component Schrödinger cat states, are formed. We visualize this evolution by measuring the Husimi Q-function and confirm the non-classical properties of these transient states by Wigner tomography. The ability to create and manipulate superpositions of coherent states in such a high quality factor photon mode opens perspectives for combining the physics of continuous variables [6] with superconducting circuits. The single-photon Kerr effect could be employed in QND measurement of photons [7], single photon generation [8], autonomous quantum feedback schemes [9] and quantum logic operations [10].A material whose refractive index depends on the intensity of the light field is called a Kerr medium. A light beam traveling through such a material acquires a phase shift φ Kerr = Kτ I [11] where I is the intensity of the beam, τ is the interaction time of the light field with the material, and K is the Kerr constant. The Kerr effect is a widely used phenomenon in nonlinear quantum optics and has been successfully employed to generate quadrature and amplitude squeezed states [12], parametrically convert frequencies [13], and create ultra-fast pulses [14]. In the field of quantum optics with microwave circuits, the direct analog of the Kerr effect is naturally created by the nonlinear inductance of a Josephson junction (specifically the4 term in the Taylor expansion of the cos φ of the Josephson energy relation) [15,16]. This effect has been used to create Josephson parametric amplifiers [17][18][19] and to generate squeezing of microwave fields [20]. However, in both the microwave and optical dom...

We present a semi-classical method for determining the effective low-energy quantum Hamiltonian of weakly anharmonic superconducting circuits containing mesoscopic Josephson junctions coupled to electromagnetic environments made of an arbitrary combination of distributed and lumped elements. A convenient basis, capturing the multi-mode physics, is given by the quantized eigenmodes of the linearized circuit and is fully determined by a classical linear response function. The method is used to calculate numerically the low-energy spectrum of a 3D-transmon system, and quantitative agreement with measurements is found.

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 (>103 ) higher quality factors and longer lifetimes should be achievable for 3D structures. Motivated by this principle, we have reached internal quality factors greater than 0.5×10 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.In circuit quantum electrodynamics (cQED), microwave resonators protect superconducting qubits from decoherence, suppress spontaneous emission 1 , allow for quantum non-demolition measurements 2,3 , and serve as quantum memories 4 . Single photon lifetimes between 10-50 µs (Q≈10 6 ) have been achieved in thin film resonators with careful surface preparation and geometrical optimization 5-7 . The route toward an optimal geometry also sheds light on the physical mechanisms responsible for damping. Planar resonators with larger features are generally found to be higher quality, which is interpreted as loss dominated by surface elements 5-9 , as the relative energy stored in surface defects is inversely proportional to the size of the resonator.Three dimensional, macroscopic cavity resonators are at the extreme limit of this trend and historically exhibit remarkable lifetimes 10 . Progress with superconducting niobium cavities for particle acceleration has led to dwell times of seconds for RF field strengths of 10 MeV/m at 2 K bath temperatures 11 . At the much lower drive powers corresponding to single-photon excitations, or fields of ∼1 µV/m, storage time in excess of 100 ms has been achieved in three dimensional, niobium Fabry Perot resonators at 51 GHz and 0.8 K 12 , and also in 3D, niobium micromaser cavities at 22 GHz and 0.15 K 13 . The coupling of superconducting qubits to 3D microwave cavities 14 could lead to cQED-type experiments with coherence on these timescales.We have set out to construct very high quality microwave cavities (Q≫10 6 ) in superconducting aluminum while focusing on geometries that may be compatible a) Electronic mail: robert.schoelkopf@yale.edu with single-photon cQED experiments at ∼10 GHz and 20 mK. We study two types of waveguide cavities (rectangular and cylindrical) that support a diversity of modes to test the effects of material purity and surface treatment on cavity lifetimes in the quantum regime. We find that pure, chemically etched aluminum produces the best results, with rectangular resonators reaching lifetimes, τ int =Q int /ω of 1.2 ms (Q int =6.9×10 7 ) and cylindrical resonators as long as 10.4 ms (Q int =7.4×10 8 ). Realizing these timescales in cQED experime...

Quantum computing hardware technologies have advanced during the past two decades, with the goal of building systems that can solve problems that are intractable on classical computers. The ability to realize large-scale systems depends on major advances in materials science, materials engineering, and new fabrication techniques. We identify key materials challenges that currently limit progress in five quantum computing hardware platforms, propose how to tackle these problems, and discuss some new areas for exploration. Addressing these materials challenges will require scientists and engineers to work together to create new, interdisciplinary approaches beyond the current boundaries of the quantum computing field.

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We study the photon shot noise dephasing of a superconducting transmon qubit in the strong-dispersive limit, due to the coupling of the qubit to its readout cavity. As each random arrival or departure of a photon is expected to completely dephase the qubit, we can control the rate at which the qubit experiences dephasing events by varying in situ the cavity mode population and decay rate. This allows us to verify a pure dephasing mechanism that matches theoretical predictions, and in fact explains the increased dephasing seen in recent transmon experiments as a function of cryostat temperature. We investigate photon dynamics in this limit and observe large increases in coherence times as the cavity is decoupled from the environment. Our experiments suggest that the intrinsic coherence of small Josephson junctions, when corrected with a single Hahn echo, is greater than several hundred microseconds.

The resonator-induced phase (RIP) gate is an all-microwave multiqubit entangling gate that allows a high degree of flexibility in qubit frequencies, making it attractive for quantum operations in large-scale architectures. We experimentally realize the RIP gate with four superconducting qubits in a three-dimensional circuit-QED architecture, demonstrating high-fidelity controlled-z (cz) gates between all possible pairs of qubits from two different 4-qubit devices in pair subspaces. These qubits are arranged within a wide range of frequency detunings, up to as large as 1.8 GHz. We further show a dynamical multiqubit refocusing scheme in order to isolate out 2-qubit interactions, and combine them to generate a 4-qubit Greenberger-Horne-Zeilinger state.