Quantum computers could be used to solve certain problems exponentially faster than classical computers, but are challenging to build because of their increased susceptibility to errors. However, it is possible to detect and correct errors without destroying coherence, by using quantum error correcting codes. The simplest of these are three-quantum-bit (three-qubit) codes, which map a one-qubit state to an entangled three-qubit state; they can correct any single phase-flip or bit-flip error on one of the three qubits, depending on the code used. Here we demonstrate such phase- and bit-flip error correcting codes in a superconducting circuit. We encode a quantum state, induce errors on the qubits and decode the error syndrome--a quantum state indicating which error has occurred--by reversing the encoding process. This syndrome is then used as the input to a three-qubit gate that corrects the primary qubit if it was flipped. As the code can recover from a single error on any qubit, the fidelity of this process should decrease only quadratically with error probability. We implement the correcting three-qubit gate (known as a conditional-conditional NOT, or Toffoli, gate) in 63 nanoseconds, using an interaction with the third excited state of a single qubit. We find 85 ± 1 per cent fidelity to the expected classical action of this gate, and 78 ± 1 per cent fidelity to the ideal quantum process matrix. Using this gate, we perform a single pass of both quantum bit- and phase-flip error correction and demonstrate the predicted first-order insensitivity to errors. Concatenation of these two codes in a nine-qubit device would correct arbitrary single-qubit errors. In combination with recent advances in superconducting qubit coherence times, this could lead to scalable quantum technology.

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 ...

Thorough control of quantum measurement is key to the development of quantum information technologies. Many measurements are destructive, removing more information from the system than they obtain. Quantum non-demolition (QND) measurements allow repeated measurements that give the same eigenvalue 1 . They could be used for several quantum information processing tasks such as error correction 2 , preparation by measurement 3 and one-way quantum computing 4 . Achieving QND measurements of photons is especially challenging because the detector must be completely transparent to the photons while still acquiring information about them 5,6 . Recent progress in manipulating microwave photons in superconducting circuits [7][8][9] has increased demand for a QND detector that operates in the gigahertz frequency range. Here we demonstrate a QND detection scheme that measures the number of photons inside a high-quality-factor microwave cavity on a chip. This scheme maps a photon number, n, onto a qubit state in a single-shot by means of qubit-photon logic gates. We verify the operation of the device for n = 0 and 1 by analysing the average correlations of repeated measurements, and show that it is 90% QND. It differs from previously reported detectors 5,8-11 because its sensitivity is strongly selective to chosen photon number states. This scheme could be used to monitor the state of a photon-based memory in a quantum computer.Several teams have engineered detectors that are sensitive to single microwave photons by strongly coupling atoms (or qubits) to high-quality-factor (high-Q) cavities. This architecture, known as cavity quantum electrodynamics (cavity QED), can be used in various ways to detect photons. One destructive method measures quantum Rabi oscillations of an atom or qubit resonantly coupled to the cavity [8][9][10] . The oscillation frequency is proportional to √ n, where n is the number of photons in the cavity, so this method essentially measures the time-domain swap frequency.Another method uses a dispersive interaction to map the photon number in the cavity onto the phase difference of a superposition of atomic states (|g +e iφ |e )/ √ 2. Each photon number n corresponds to a different phase φ, so repeated Ramsey experiments 5 can be used to estimate the phase and extract n. This method is QND, because it does not exchange energy between the atom and photon. However, as the phase cannot be measured in a single operation, it does not extract full information about a particular Fock state |n in a single interrogation. Nonetheless, using Rydberg atoms in cavity QED, remarkable experiments have shown quantum jumps of light and the collapse of the photon number by measurement 5,12 . Here we report a new method that implements a set of programmable controlled-NOT (CNOT) operations between an n-photon Fock state and a qubit, asking the question 'are there exactly n photons in the cavity?' A single interrogation consists of applying one such CNOT operation and reading-out the resulting qubit state. To do this we u...

Spontaneous emission through a coupled cavity can be a significant decay channel for qubits in circuit quantum electrdynamics. We present a circuit design that effectively eliminates spontaneous emission due to the Purcell effect while maintaining strong coupling to a low Q cavity. Excellent agreement over a wide range in frequency is found between measured qubit relaxation times and the predictions of a circuit model. Using fast (nanosecond time-scale) flux biasing of the qubit, we demonstrate in-situ control of qubit lifetime over a factor of 50. We realize qubit reset with 99.9% fidelity in 120 ns.

We demonstrate a qubit readout scheme that exploits the Jaynes-Cummings nonlinearity of a superconducting cavity coupled to transmon qubits. We find that in the strongly-driven dispersive regime of this system, there is the unexpected onset of a high-transmission "bright" state at a critical power which depends sensitively on the initial qubit state. A simple and robust measurement protocol exploiting this effect achieves a single-shot fidelity of 87% using a conventional sample design and experimental setup, and at least 61% fidelity to joint correlations of three qubits.Circuit quantum electrodynamics (cQED) is the study of the interaction of light and matter where superconducting qubits playing the role of atoms are strongly coupled to microwave transmission line resonators acting as cavities [1]. This architecture offers advantages over cavity QED with atomic systems with regard to both coupling strength and accessibility of strongly driven nonlinear regimes [2][3][4]. For example, the high-power response of a cavity with a qubit in resonance has recently been studied, demonstrating the appearance of additional photon number (n) resonances with characteristic √ n spacing, in excellent agreement with theory [4]. In this Letter, we investigate the behavior of a strongly driven cQED system in the dispersive regime, where four strongly coupled transmon qubits [5] are far detuned from the cavity. We find that for increasing drive strength, the cavity response initially becomes strongly nonlinear and continuously shifts down in frequency. At a critical power, it reaches its bare frequency and transmission rapidly rises to a "bright state". Importantly, this critical power is strongly dependent on the initial state of the qubit, providing for a simple high-fidelity qubit readout mechanism. This scheme is also applicable to the joint measurement of several qubits simultaneously.There are two commonly used cQED readout schemes. The first employs the state-dependent dispersive shift of the coupled cavity's resonance frequency [ Fig. 1(a)] to infer the qubit state by measuring transmission [6,7]. This must be done in the low-power, linear response regime of the cavity in part because system anharmonicity inhibits higher population. The signal-to-noise ratio (SNR) and fidelity of this weak measurement is thus limited (to typically 40%-60% [7,8]) by the relatively high noise temperature (T sys N ≈ 10 K ∼ 20 photons) of conventional commercial amplifiers and short integration time mandated by qubit relaxation (T 1 ≈ 1 µs) [9]. A specialized superconducting low-noise amplifier [10][11][12] could improve the SNR, but at a cost of additional complexity. The second scheme uses some nonlinearity to project the qubit state onto a classically distinguishable system and yield high discrimination [13]. The Josephson bifurcation amplifier (JBA) is one such example, exploiting cavity bistability caused by the Kerr-Duffing nonlinearity of an additional Josephson junction [14][15][16]. These schemes have, however, not yet taken advant...

We demonstrate improved operation of exchange-coupled semiconductor quantum dots by substantially reducing the sensitivity of exchange operations to charge noise. The method involves biasing a double dot symmetrically between the charge-state anticrossings, where the derivative of the exchange energy with respect to gate voltages is minimized. Exchange remains highly tunable by adjusting the tunnel coupling. We find that this method reduces the dephasing effect of charge noise by more than a factor of 5 in comparison to operation near a charge-state anticrossing, increasing the number of observable exchange oscillations in our qubit by a similar factor. Performance also improves with exchange rate, favoring fast quantum operations. DOI: 10.1103/PhysRevLett.116.110402 Gated semiconductor quantum dots are a leading candidate for quantum information processing due to their high speed, density, and compatibility with mature fabrication technologies [1,2]. Quantum dots are formed by spatially confining individual electrons using a combination of material interfaces and nanoscale metallic gates. Although several quantized degrees of freedom are available [3][4][5], the electron spin is often employed as a qubit due to its long coherence time [6,7]. Spin-spin coupling may be controlled via the kinetic exchange interaction, which has the benefit of short range and electrical controllability. Numerous qubit proposals use exchange, including as a two-qubit gate between ESR-addressed spins [8], a single axis of control in a two dot system also employing gradient magnetic fields [9] or spin-orbit couplings [10], or as a means of full qubit control on a restricted subspace of at least three coupled spins [11][12][13]. However, since exchange relies on electron motion, it is susceptible to electric field fluctuations, or charge noise. Limiting the consequence of this noise is critical to attaining performance of exchange-based qubits adequate for quantum information processing.Charge noise in semiconductor quantum dots may originate from a variety of sources including electric defects at interfaces and in dielectrics [14]. These defects typically result in electric fields that exhibit an approximate 1=f noise spectral density. Conventional routes for reducing charge noise include improving materials and interfaces [15] and dynamical decoupling [16][17][18][19]. In this Letter, rather than addressing the microscopic origins or detailed spectrum of charge noise, we introduce a "symmetric" mode of operation where the exchange interaction is less susceptible to that noise. This is done by biasing the device to a regime where the strength of the exchange interaction is first-order insensitive to dot chemical potential fluctuations but is still controllable by modulating the interdot tunnel barrier. This dramatically reduces the effects of charge noise.The principle of symmetric operation can be understood by treating charge noise as equivalent to voltage fluctuations on confinement gates. This approximation is valid when materi...

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Although epidemiologic data strongly suggest a role for inhaled environmental pollutants in modulating the susceptibility to respiratory infection in humans, the underlying cellular and molecular mechanisms have not been well studied in experimental systems. The current study assessed the impact of inhaled diesel engine emissions (DEE) on the host response in vivo to a common pediatric respiratory pathogen, respiratory syncytial virus (RSV). Using a relatively resistant mouse model of RSV infection, prior exposure to either 30 microg/m3 particulate matter (PM) or 1,000 microg/m3 PM of inhaled DEE (6 h/d for seven consecutive days) increased lung inflammation to RSV infection as compared with air-exposed RSV-infected C57Bl/6 mice. Inflammatory cells in bronchoalveolar lavage fluid were increased in a dose-dependent manner with regard to the level of DEE exposure, concomitant with increased levels of inflammatory mediators. Lung histology analysis indicated pronounced peribronchial and peribronchiolar inflammation concordant with the level of DEE exposure during infection. Mucous cell metaplasia was markedly increased in the airway epithelium of DEE-exposed mice following RSV infection. Interestingly, both airway and alveolar host defense and immunomodulatory proteins were attenuated during RSV infection by prior DEE exposure. DEE-induced changes in inflammatory and lung epithelial responses to infection were associated with increased RSV gene expression in the lungs following DEE exposure. These findings are consistent with the concept that DEE exposure modulates the lung host defense to respiratory viral infections and may alter the susceptibility to respiratory infections leading to increased lung disease.