Superconducting circuits are promising candidates for constructing quantum bits (qubits) in a quantum computer; single-qubit operations are now routine 1,2 , and several examples 3,4,5,6,7,8,9 of two qubit interactions and gates having been demonstrated. These experiments show that two nearby qubits can be readily coupled with local interactions. Performing gates between an arbitrary pair of distant qubits is highly desirable for any quantum computer architecture, but has not yet been demonstrated. An efficient way to achieve this goal is to couple the qubits to a quantum bus, which distributes quantum information among the qubits. Here we show the implementation of such a quantum bus, using microwave photons confined in a transmission line cavity, to couple two superconducting qubits on opposite sides of a chip. The interaction is mediated by the exchange of virtual rather than real photons, avoiding cavity induced loss. Using fast control of the qubits to switch the coupling effectively on and off, we demonstrate coherent transfer of quantum states between the qubits. The cavity is also used to perform multiplexed control and measurement of the qubit states. This approach can be expanded to more than two qubits, and is an attractive architecture for quantum information processing on a chip.There are several physical systems in which one could realize a quantum bus. A particular example is trapped ions 10,11 in which a variety of quantum operations and algorithms have been performed using the quantized motion of the ions (phonons) as the bus. Photons are another natural candidate as a carrier of quantum information 12,13 , because they are highly coherent and can mediate interactions between distant objects. To create a photon bus, it is helpful to utilize the increased interaction strength provided by the techniques of cavity quantum electrodynamics, where an atom is coupled to a single cavity mode. In the strong coupling limit 14 the interaction is coherent, permitting the transfer of quantum information between the atom and the photon. Entanglement between atoms has been demonstrated with Rydberg atom cavity QED 15,16,17 . Circuit QED 18 is a realization of the physics of cavity QED with superconducting qubits coupled to a microwave cavity on a chip. Previous circuit QED experiments with single qubits have achieved 19 the strong coupling limit and have demonstrated 20 the transfer of quantum information from qubit to photon. Here we perform a circuit QED experiment with two qubits strongly coupled to a cavity, and demonstrate a coherent, non-local coupling between the qubits via this bus.Operations with multiple superconducting qubits have been performed and are a subject of current research. The first solid-state quantum gate has been demonstrated with charge qubits 3 . For flux qubits, two-qubit coupling 5 and a controllable coupling mechanism have been realized 7,8,9 . Two phase qubits have also been successfully coupled 4 and the entanglement between them has been observed 6 . All of these interactions h...

Quantum computers, which harness the superposition and entanglement of physical states, could outperform their classical counterparts in solving problems with technological impact-such as factoring large numbers and searching databases. A quantum processor executes algorithms by applying a programmable sequence of gates to an initialized register of qubits, which coherently evolves into a final state containing the result of the computation. Building a quantum processor is challenging because of the need to meet simultaneously requirements that are in conflict: state preparation, long coherence times, universal gate operations and qubit readout. Processors based on a few qubits have been demonstrated using nuclear magnetic resonance, cold ion trap and optical systems, but a solid-state realization has remained an outstanding challenge. Here we demonstrate a two-qubit superconducting processor and the implementation of the Grover search and Deutsch-Jozsa quantum algorithms. We use a two-qubit interaction, tunable in strength by two orders of magnitude on nanosecond timescales, which is mediated by a cavity bus in a circuit quantum electrodynamics architecture. This interaction allows the generation of highly entangled states with concurrence up to 94 per cent. Although this processor constitutes an important step in quantum computing with integrated circuits, continuing efforts to increase qubit coherence times, gate performance and register size will be required to fulfil the promise of a scalable technology.

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.

Electromagnetic signals are always composed of photons, although in the circuit domain those signals are carried as voltages and currents on wires, and the discreteness of the photon's energy is usually not evident. However, by coupling a superconducting quantum bit (qubit) to signals on a microwave transmission line, it is possible to construct an integrated circuit in which the presence or absence of even a single photon can have a dramatic effect. Such a system can be described by circuit quantum electrodynamics (QED)-the circuit equivalent of cavity QED, where photons interact with atoms or quantum dots. Previously, circuit QED devices were shown to reach the resonant strong coupling regime, where a single qubit could absorb and re-emit a single photon many times. Here we report a circuit QED experiment in the strong dispersive limit, a new regime where a single photon has a large effect on the qubit without ever being absorbed. The hallmark of this strong dispersive regime is that the qubit transition energy can be resolved into a separate spectral line for each photon number state of the microwave field. The strength of each line is a measure of the probability of finding the corresponding photon number in the cavity. This effect is used to distinguish between coherent and thermal fields, and could be used to create a photon statistics analyser. As no photons are absorbed by this process, it should be possible to generate non-classical states of light by measurement and perform qubit-photon conditional logic, the basis of a logic bus for a quantum computer.

We present an experimental realization of the transmon qubit, an improved superconducting charge qubit derived from the Cooper pair box. We experimentally verify the predicted exponential suppression of sensitivity to 1/f charge noise [J. Koch et al., Phys. Rev. A 76, 042319 (2007)]. This removes the leading source of dephasing in charge qubits, resulting in homogenously broadened transitions with relaxation and dephasing times in the microsecond range. Our systematic characterization of the qubit spectrum, anharmonicity, and charge dispersion shows excellent agreement with theory, rendering the transmon a promising qubit for future steps towards solid-state quantum information processing. PACS numbers: 03.67.Lx, 74.50.+r, Over the last decade, superconducting qubits have gained substantial interest as an attractive option for quantum information processing, cf. Refs. [1,2,3] for recent reviews. Although there already exist different realizations of superconducting qubits [4,5,6,7], all their coherence times are several orders of magnitude too short for large-scale quantum computation. Fortunately, an increase of coherence times from 2 ns in the first superconducting qubit [4] to microsecond times in present experiments [8,9,10,11] has already been shown, giving rise to hope that the remaining gap can be overcome by optimized quantum circuits and better materials. Coherence times can be either limited by dissipation (T 1 ) or dephasing (T * 2 ). Most superconducting qubits have dephasing times much shorter than the limit T * 2 = 2T 1 imposed by dissipation, because they are plagued by the influence of 1/f noise in charge, flux, or critical current. The transmon qubit is an improved design [12] derived from the original charge qubit [13] that renders it immune to its primary source of noise, 1/f charge noise, without making it more susceptible to either flux or critical current noise.The transmon consists of two superconducting islands connected by a Josephson tunnel junction. The tunneling of Cooper pairs between the two islands is governed by two energy scales: the charging energy E C and the Josephson energy E J . The transmon has a Hamiltonian identical to the Cooper pair box (CPB),wheren denotes the number of excess Cooper pairs on one of the islands and n g the offset charge due to the electrostatic environment. Because there are no dc connections to the qubit, n is integer-valued like an angular momentum, and the conjugate variableφ is a compact angle. Despite its basic CPB nature, the transmon is operated in a vastly different param-The primary benefit of this new regime is a suppression of the sensitivity to charge noise, which is exponential in the ratio E J /E C . The qubit spectrum becomes more uniformly spaced in the transmon, but it has been shown in [12] that the anharmonicity in the spectrum only decays as a weak alge-braic function of E J /E C , allowing it to be used as an effective two-level system. One of the reasons for the long coherence times of the design is that the state of the transmon q...

Traditionally, quantum entanglement has played a central role in foundational discussions of quantum mechanics. The measurement of correlations between entangled particles can exhibit results at odds with classical behavior. These discrepancies increase exponentially with the number of entangled particles 1 . When entanglement is extended from just two quantum bits (qubits) to three, the incompatibilities between classical and quantum correlation properties can change from a violation of inequalities 2 involving statistical averages to sign differences in deterministic observations 3 . With the ample confirmation of quantum mechanical predictions by experiments 4-7 , entanglement has evolved from a philosophical conundrum to a key resource for quantum-based technologies, like quantum cryptography and computation 8 . In particular, maximal entanglement of more than two qubits is crucial to the implementation of quantum error correction protocols. While entanglement of up to 3, 5, and 8 qubits has been demonstrated among spins 9 , photons 7 , and ions 10 , respectively, entanglement in engineered solid-state systems has been limited to two qubits [11][12][13][14][15] . Here, we demonstrate three-qubit entanglement in a superconducting circuit, creating Greenberger-HorneZeilinger (GHZ) states with fidelity of 88%, measured with quantum state tomography.Several entanglement witnesses show violation of biseparable bounds by 830 ± 80%. Our entangling sequence realizes the first step of basic quantum error correction, namely the encoding of a logical qubit into a manifold of GHZ-like states using a repetition code. The integration of encoding, decoding and error-correcting steps in a feedback loop will be the next milestone for quantum computing with integrated circuits.With steady improvements in qubit coherence, control, and readout over a decade, superconducting quantum circuits 16 have recently attained two milestones for solidstate two-qubit entanglement. The first is the violation of Bell inequalities without a detection loophole, realized with phase qubits by minimizing cross-talk between high-fidelity individual qubit readouts 14 . Second is the realization of simple quantum algorithms 13 , achieved through improved two-qubit gates and coherence in cir- (inset) to Q4] inside a meandering coplanar waveguide resonator. Local flux-bias lines allow qubit tuning on nanosecond timescales with room-temperature voltages Vi. Microwave pulses at qubit transition frequencies f1, f2, and f3 realize single-qubit x-and y-rotations in 8 ns. Q4 (operational but unused) is biased at its maximal frequency of 12.27 GHz to minimize its interaction with the qubits employed. Pulsed measurement of cavity homodyne voltage VH (at the bare cavity frequency fc = 9.070 GHz) allows joint qubit readout. A detailed schematic of the measurement setup is shown in Supplementary Fig. S2. b, Grey-scale images of cavity transmission and qubit spectroscopy versus local tuning of Q1 show avoided crossings with Q2 (66 MHz splitting), with Q3 (128 ...

We present a detailed characterization of coherence in seven transmon qubits in a circuit QED architecture. We find that spontaneous emission rates are strongly influenced by far off-resonant modes of the cavity and can be understood within a semiclassical circuit model. A careful analysis of the spontaneous qubit decay into a microwave transmission-line cavity can accurately predict the qubit lifetimes over 2 orders of magnitude in time and more than an octave in frequency. Coherence times T1 and T_{2};{*} of more than a microsecond are reproducibly demonstrated.

Electromagnetic signals in circuits consist of discrete photons [1], though conventional voltage sources can only generate classical fields with a coherent superposition of many different photon numbers. While these classical signals can control and measure bits in a quantum computer (qubits), single photons can carry quantum information, enabling non-local quantum interactions, an important resource for scalable quantum computing [2]. Here, we demonstrate an on-chip single photon source in a circuit quantum electrodynamics (QED) architecture [3], with a microwave transmission line cavity that collects the spontaneous emission of a single superconducting qubit with high efficiency. The photon source is triggered by a qubit rotation, as a photon is generated only when the qubit is excited. Tomography of both qubit and fluorescence photon shows that arbitrary qubit states can be mapped onto the photon state, demonstrating an ability to convert a stationary qubit into a flying qubit. Both the average power and voltage of the photon source are characterized to verify performance of the system. This single photon source is an important addition to a rapidly growing toolbox for quantum optics on a chip.Numerous approaches to generating single photons, particularly optical photons, have been proposed and demonstrated in recent years [4]. The underlying principle for generating single photons from atoms or qubits is straightforward: an excited qubit can relax to its ground state by emitting a photon [5,6], A pulse that excites the qubit can therefore trigger a single photon emission, as long as the control and emission photons can be separated. Early experiments demonstrated this photon generation from single ions [7], atoms [8], molecules[9, 10, 11], nitrogen vacancies [12], and quantum dots [13,14], though radiation in all directions made efficient collection difficult. In a cavity QED source, the atom or qubit is coupled to a single photonic mode of a cavity, enhancing the rate of decay to that mode through the Purcell effect [15] and allowing a source where photons are emitted into a controlled channel. Atoms [16,17,18,19], ions [20], and quantum dots [14,21,22] have been used to generate optical photons efficiently in this manner.Here, we implement a cavity QED system in a circuit [23,24], where a superconducting qubit and transmission line cavity are coupled such that the dominant channel for relaxation of the qubit is to spontaneously emit a photon into the cavity. Each time the qubit is excited, the most likely outcome is the generation of one (and only one) photon at a random time, with the distribution of times characterized by the decay rate of the qubit. The challenge is to create a system where spontaneous emission dominates other relaxation channels. This spontaneous emission rate can be determined from the Hamiltonian of the system, the well-known JaynesCummings Hamiltonian, H =hω a σ z /2+hω r (a † a+1/2)+ * Authors with contributed equally to this work.h g(a † σ − + aσ + ). The first two terms represent...