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A quantum computer can solve hard problems -such as prime factoring 1,2 , database searching 3,4 , and quantum simulation 5 -at the cost of needing to protect fragile quantum states from error. Quantum error correction 6 provides this protection, by distributing a logical state among many physical qubits via quantum entanglement. Superconductivity is an appealing platform, as it allows for constructing large quantum circuits, and is compatible with microfabrication. For superconducting qubits the surface code 7 is a natural choice for error correction, as it uses only nearest-neighbour coupling and rapidly-cycled entangling gates. The gate fidelity requirements are modest: The per-step fidelity threshold is only about 99%. Here, we demonstrate a universal set of logic gates in a superconducting multi-qubit processor, achieving an average single-qubit gate fidelity of 99.92% and a two-qubit gate fidelity up to 99.4%. This places Josephson quantum computing at the fault-tolerant threshold for surface code error correction. Our quantum processor is a first step towards the surface code, using five qubits arranged in a linear array with nearest-neighbour coupling. As a further demonstration, we construct a five-qubit GreenbergerHorne-Zeilinger (GHZ) state 8,9 using the complete circuit and full set of gates. The results demonstrate that Josephson quantum computing is a high-fidelity technology, with a clear path to scaling up to large-scale, fault-tolerant quantum circuits.The high fidelity performance we demonstrate here is achieved through a combination of highly coherent qubits, a straightforward interconnection architecture, and a novel implementation of the two-qubit controlled-phase (CZ) entangling gate. The CZ gate uses a fast but adiabatic frequency tuning of the qubits 10 , which is easily adjusted yet minimises decoherence and leakage from the computational basis [Martinis, J., et al., in preparation]. We note that previous demonstrations of two-qubit gates achieving better than 99% fidelity used fixed-frequency qubits: Systems based on nuclear magnetic resonance and ion traps have shown two-qubit gates with fidelities of 99.5% 11 and 99.3% 12 . Here, the tuneable nature of the qubits and their entangling gates provides, remarkably, both high fidelity and fast control.Superconducting integrated circuits give flexibility in building quantum systems due to the macroscopic nature of the electron condensate. As shown in Fig. 1, we have designed a processor consisting of five Xmon qubits with nearestneighbour coupling, arranged in a linear array. The crossshaped qubit 14 offers a nodal approach to connectivity while maintaining a high level of coherence (see Supplementary Information for decoherence times). Here, the four legs of the cross allow for a natural segmentation of the design into coupling, control and readout. We chose a modest inter-qubit capacitive coupling strength of g/2π = 30 MHz and use alternating qubit idle frequencies of 5.5 and 4.7 GHz, enabling a CZ gate in 40 ns when two qubits are brough...

We consider the continuous measurement of a double quantum dot by a weakly coupled detector (tunnel point contact nearby). While the conventional approach describes the gradual system decoherence due to the measurement, we study the situation when the detector output is explicitly recorded that leads to the opposite effect: gradual purification of the doubledot density matrix. Nonlinear Langevin equation is derived for the random evolution of the density matrix which is reflected and caused by the stochastic detector output. Gradual collapse, gradual purification, and quantum Zeno effect are naturally described by the equation. We also discuss the possible experiments to confirm the theory.The problem of quantum measurements has a long history, however, it still attracts considerable attention and even causes some controversy, mainly concerning the wavefunction "collapse" (see, e.g., 1,2 ). Among various modern approaches to this problem let us mention the idea of replacing the collapse postulate by the gradual decoherence of the density matrix due to the interaction with the detector 3 and the approach of a stochastic evolution of the wavefunction (see, e.g., 4-11 ). The latter approach (which is used in the present paper) can describe the selective measurements for which the system evolution is conditioned on the particular measurement result (other keywords of the approach are: quantum trajectories, quantum state diffusion, quantum jumps, etc.). The renewed interest in the measurement problem is justified by the development of experimental technique, which allows more and more experimental studies of quantum measurement in optics and mesoscopic structures. [12][13][14][15][16][17] The problem also has a close connection to the rapidly growing fields of quantum cryptography and quantum computing. 18 In the recent experiment 15 with "which-path" interferometer the suppression of Aharonov-Bohm interference due to the detection of which path an electron chooses, was observed. The weakly coupled quantum point contact was used as a detector. The interference suppression in this experiment can be quantitatively described by the decoherence due to the measurement process. [19][20][21][22] We will consider a somewhat different setup: two quantum dots occupied by one electron and a weakly coupled detector (point contact nearby) measuring the position of the electron. The decoherence of the double-dot density matrix due to continuous measurement in this setup has been analyzed in Refs. 19,22 . However, the decoherence approach cannot describe the detector output that is a separate problem analyzed in the present paper. We answer two interrelated questions: how the detector current behaves in time and what is the proper double-dot density matrix for a particular detector output. We show that the models of point contact considered in Refs. [19][20][21] describe an ideal detector. In this case the density matrix decoherence is just a consequence of averaging over all possible measurement results. For any particular detecto...