The measurement process plays an awkward role in quantum mechanics, because measurement forces a system to 'choose' between possible outcomes in a fundamentally unpredictable manner. Therefore, hidden classical processes have been considered as possibly predetermining measurement outcomes while preserving their statistical distributions. However, a quantitative measure that can distinguish classically determined correlations from stronger quantum correlations exists in the form of the Bell inequalities, measurements of which provide strong experimental evidence that quantum mechanics provides a complete description. Here we demonstrate the violation of a Bell inequality in a solid-state system. We use a pair of Josephson phase qubits acting as spin-1/2 particles, and show that the qubits can be entangled and measured so as to violate the Clauser-Horne-Shimony-Holt (CHSH) version of the Bell inequality. We measure a Bell signal of 2.0732 +/- 0.0003, exceeding the maximum amplitude of 2 for a classical system by 244 standard deviations. In the experiment, we deterministically generate the entangled state, and measure both qubits in a single-shot manner, closing the detection loophole. Because the Bell inequality was designed to test for non-classical behaviour without assuming the applicability of quantum mechanics to the system in question, this experiment provides further strong evidence that a macroscopic electrical circuit is really a quantum system.

Entanglement is one of the key resources required for quantum computation, so the experimental creation and measurement of entangled states is of crucial importance for various physical implementations of quantum computers. In superconducting devices, two-qubit entangled states have been demonstrated and used to show violations of Bell's inequality and to implement simple quantum algorithms. Unlike the two-qubit case, where all maximally entangled two-qubit states are equivalent up to local changes of basis, three qubits can be entangled in two fundamentally different ways. These are typified by the states |GHZ>= (|000+ |111>)/ sqrt [2] and |W>= (|001> + |010> + |100>)/ sqrt [3]. Here we demonstrate the operation of three coupled superconducting phase qubits and use them to create and measure |GHZ> and |W>states. The states are fully characterized using quantum state tomography and are shown to satisfy entanglement witnesses, confirming that they are indeed examples of three-qubit entanglement and are not separable into mixtures of two-qubit entanglement.

The von Neumann architecture for a classical computer comprises a central processing unit and a memory holding instructions and data. We demonstrate a quantum central processing unit that exchanges data with a quantum random-access memory integrated on a chip, with instructions stored on a classical computer. We test our quantum machine by executing codes that involve seven quantum elements: Two superconducting qubits coupled through a quantum bus, two quantum memories, and two zeroing registers. Two vital algorithms for quantum computing are demonstrated, the quantum Fourier transform, with 66% process fidelity, and the three-qubit Toffoli-class OR phase gate, with 98% phase fidelity. Our results, in combination especially with longer qubit coherence, illustrate a potentially viable approach to factoring numbers and implementing simple quantum error correction codes.

Superconducting microwave resonators are reliable circuits widely used for detection and as test devices for material research. A reliable determination of their external and internal quality factors is crucial for many modern applications, which either require fast measurements or operate in the single photon regime with small signal to noise ratios. Here, we use the circle fit technique with diameter correction and provide a step by step guide for implementing an algorithm for robust fitting and calibration of complex resonator scattering data in the presence of noise. The speedup and robustness of the analysis are achieved by employing an algebraic rather than an iterative fit technique for the resonance circle.

Quantum entanglement, one of the defining features of quantum mechanics, has been demonstrated in a variety of nonlinear spin-like systems. Quantum entanglement in linear systems has proven significantly more challenging, as the intrinsic energy level degeneracy associated with linearity makes quantum control more difficult. Here we demonstrate the quantum entanglement of photon states in two independent linear microwave resonators, creating N -photon NOON states as a benchmark demonstration. We use a superconducting quantum circuit that includes Josephson qubits to control and measure the two resonators, and we completely characterize the entangled states with bipartite Wigner tomography. These results demonstrate a significant advance in the quantum control of linear resonators in superconducting circuits.Quantum superposition and entanglement have been demonstrated experimentally using spin-like physical systems ranging from atoms to electronic circuits [1][2][3][4][5][6][7]. These systems all display strong nonlinearity, and are used because this nonlinearity allows straightforward quantum control by classical means. The quantum control of linear systems, exemplified by the harmonic oscillator, is by contrast more difficult, and has only been achieved using nonlinear intermediaries: Atoms [1,8] to control optical cavities, ions to control ion motion [9,10], and superconducting qubits to control photons in microwave resonators [11][12][13][14]. Quantum entanglement of cavity photons still presents a significant challenge: Experiments have demonstrated maximally-entangled photons in different polarization modes of the same cavity [15,16], but the entanglement of photons in two physically distinct cavities [17][18][19] has proven more elusive.Here we show the deterministic generation of entangled photon states in two spatially-separated microwave resonators, achieved by manipulating the photon states with a pair of superconducting phase qubits. We use as a benchmark the generation of NOON states [20][21][22][23][24], comprising a total of N photons in the two resonators (A and B), entangled in the quantum statewith N photons in resonator A and zero in B, superposed with the state with the occupation numbers reversed. Such a state has the same degree of entanglement as the Bell state, but with N excitations. We also generate MOON states, in which, e.g., resonator A has M or zero quanta, entangled with resonator B with zero or N quanta.We fully characterize the two-resonator photon states using bipartite Wigner tomography, which represents a non-trivial extension of single-cavity Wigner to- mography [1,9,[12][13][14], and allows us to distinguish entanglement from an incoherent ensemble.To accomplish this goal, we developed a new quantum circuit comprising two superconducting phase qubits [25] and three microwave resonators. A sketch of the circuit topology is shown in Figs. 1(a). The circuit includes a coupling resonator C, connected to both qubits, and two state storage resonators A and B, each coupled to one q...