The superposition principle is a fundamental tenet of quantum mechanics. It allows a quantum system to be 'in two places at the same time', because the quantum state of a physical system can simultaneously include measurably different physical states. The preparation and use of such superposed states forms the basis of quantum computation and simulation. The creation of complex superpositions in harmonic systems (such as the motional state of trapped ions, microwave resonators or optical cavities) has presented a significant challenge because it cannot be achieved with classical control signals. Here we demonstrate the preparation and measurement of arbitrary quantum states in an electromagnetic resonator, superposing states with different numbers of photons in a completely controlled and deterministic manner. We synthesize the states using a superconducting phase qubit to phase-coherently pump photons into the resonator, making use of an algorithm that generalizes a previously demonstrated method of generating photon number (Fock) states in a resonator. We completely characterize the resonator quantum state using Wigner tomography, which is equivalent to measuring the resonator's full density matrix.

We measured Kondo-assisted tunneling via C60 molecules in contact with ferromagnetic nickel electrodes. Kondo correlations persisted despite the presence of ferromagnetism, but the Kondo peak in the differential conductance was split by an amount that decreased (even to zero) as the moments in the two electrodes were turned from parallel to antiparallel alignment. The splitting is too large to be explained by a local magnetic field. However, the voltage, temperature, and magnetic field dependence of the signals agree with predictions for an exchange splitting of the Kondo resonance. The Kondo effect leads to negative values of magnetoresistance, with magnitudes much larger than the Julliere estimate.

Nature 454, 310 (2008) Recommended and Commentary by Steven M. Girvin, Yale University Microwaves, despite their name, are particles. However the photon quanta of microwave fields are rather pusillanimous. They carry four to five orders of magnitude less energy than optical photons and are correspondingly vastly more difficult to detect and count. Nevertheless, recent progress in atomic cavity QED [1] and superconducting circuit QED [2] has achieved this. Single-photons-on-demand as well as coherent superpositions of 0 and 1 photons have been generated in a microwave resonator electrical circuit.[3]A classical signal generator produces a sine wave of constant amplitude, frequency and phase. The quantum equivalent (produced by a laser or a microwave signal generator) is a so-called coherent state. Because the phase is sharply defined, the photon number (which is the conjugate variable), is necessarily ill-defined. The number of photons to be found in a coherent pulse is in fact Poisson distributed. As a result, a coherent pulse which contain N photons on average will have a variance in photon number of √N. These closest cousins to classical waves are of course useful but not terribly exciting. There is great current interest in generating highly non-classical states of the electromagnetic field for purposes of quantum communication and quantum information processing. One interesting and highly non-classical class of states are the Fock states. These are electromagnetic pulses which contain exactly n photons where n is some specified integer. Because they have definite photon number, the phase suffers complete quantum uncertainty. Hence the electric field of such pulses is completely uncertain, a fact which has recently been verified. [3] Hofheinz et al. have made a tour-de-force advance by deterministically generating photon number Fock states containing up to N = 6 photons (N = 15 in recent unpublished work) using a superconducting qubit coupled to a resonator.The resonator supports discrete modes at integer multiples of the fundamental. Because the modes are widely spaced in frequency for short res-1

Demonstration of quantum entanglement, a key resource in quantum computation arising from a nonclassical correlation of states, requires complete measurement of all states in varying bases. By using simultaneous measurement and state tomography, we demonstrated entanglement between two solid-state qubits. Single qubit operations and capacitive coupling between two super-conducting phase qubits were used to generate a Bell-type state. Full two-qubit tomography yielded a density matrix showing an entangled state with fidelity up to 87%. Our results demonstrate a high degree of unitary control of the system, indicating that larger implementations are within reach.

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.

A quantum computer will require quantum bits (qubits) with good coherence that can be coupled together to form logic gates 1,2 . Superconducting circuits offer a novel solution [3][4][5][6][7][8][9] because qubits can be connected in elaborate ways through simple wiring, much like that of conventional integrated circuits. However, this ease of coupling is offset by coherence times shorter than those observed in molecular and atomic systems. Hybrid architectures could help skirt this fundamental trade-off between coupling and coherence by using macroscopic qubits for coupling and atom-based qubits for coherent storage 10,11 . Here, we demonstrate the first quantum memory operation 12 on a Josephson-phase qubit by transferring an arbitrary quantum state to a two-level state 13 (TLS), storing it there for some time, and later retrieving it. The qubit is used to probe the coherence of the TLS by measuring its energy relaxation and dephasing times. Quantum process tomography 2,14 completely characterizes the memory operation, yielding an overall process fidelity of 79%. Although the uncontrolled distribution of TLSs precludes their direct use in a scalable architecture, the ability to coherently couple a macroscopic device with an atomic-sized system motivates a search for designer molecules that could replace the TLS in future hybrid qubits.In quantum computation, coupling atomic qubits over macroscopic distances is a long-standing technological challenge. In ion-trap architectures, qubits are physically moved to regions where they can be positioned close to each other and coupled electrostatically 15 . Approaches based on cavity QED eliminate the difficulty of moving atoms, but instead use a resonant electromagnetic cavity to couple over macroscopic distances via guided photons 5,6,16 . Several recent proposals meet this challenge using further novel approaches 10,11,17,18 . Superconducting wires are a natural medium for coupling between macroscopic and atomic states because currents and voltages obey quantum mechanics over length scales from macroscopic to atomic dimensions. At the macroscopic scale, the coupling remains coherent because superconductors have small dissipation. At the atomic scale, coupling is possible because the tunnel junction has a dielectric thickness ∼2 nm that approaches atomic size. When an atom carrying a single elementary charge moves by one atomic bond length inside such a tunnel junction, it produces a substantial image charge in the junction electrodes,