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.

Dielectric loss from two-level states is shown to be a dominant decoherence source in superconducting quantum bits. Depending on the qubit design, dielectric loss from insulating materials or the tunnel junction can lead to short coherence times. We show that a variety of microwave and qubit measurements are well modeled by loss from resonant absorption of two-level defects. Our results demonstrate that this loss can be significantly reduced by using better dielectrics and fabricating junctions of small area . With a redesigned phase qubit employing low-loss dielectrics, the energy relaxation rate has been improved by a factor of 20, opening up the possibility of multiqubit gates and algorithms.

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.