Over the past several decades, quantum information science has emerged to seek answers to the question: can we gain some advantage by storing, transmitting and processing information encoded in systems that exhibit unique quantum properties? Today it is understood that the answer is yes, and many research groups around the world are working towards the highly ambitious technological goal of building a quantum computer, which would dramatically improve computational power for particular tasks. A number of physical systems, spanning much of modern physics, are being developed for quantum computation. However, it remains unclear which technology, if any, will ultimately prove successful. Here we describe the latest developments for each of the leading approaches and explain the major challenges for the future.

A nanometre-scale superconducting electrode connected to a reservoir via a Josephson junction constitutes an arti®cial twolevel electronic system: a single-Cooper-pair box. The two levels consist of charge states (differing by 2e, where e is the electronic charge) that are coupled by tunnelling of Cooper pairs through the junction. Although the two-level system is macroscopic, containing a large number of electrons, the two charge states can be coherently superposed 1±4 . The Cooper-pair box has therefore been suggested 5±7 as a candidate for a quantum bit or qubit'Ðthe basic component of a quantum computer. Here we report the observation of quantum oscillations in a singleCooper-pair box. By applying a short voltage pulse via a gate electrode, we can control the coherent quantum state evolution: the pulse modi®es the energies of the two charge states nonadiabatically, bringing them into resonance. The resulting stateÐ a superposition of the two charge statesÐis detected by a tunnelling current through a probe junction. Our results demonstrate electrical coherent control of a qubit in a solid-state electronic device.Rapidly improving nanofabrication technologies have made quantum two-level systems in solid-state devices promising for functional quantum circuit integration. To coherently control an individual two-level system as a unit of such circuits, several systems have been examined, such as electronic 8±10 and spin 11 states in quantum dots, nuclear spins of impurity atoms embedded in a substrate 12 , and magnetic-¯ux states in a superconducting ring 13,14 . However, only optical coherent control has been realized experimentally 10 .A single-Cooper-pair box 1 (Fig. 1) is a unique arti®cial solid-state system in the sense that: (1) although there are a large number of electrons in the metal`box' electrode, under superconductivity they all form Cooper pairs and condense into a single macroscopic ground state, |ni, separated by a superconductivity gap ¢ from the excited states with quasiparticles. (Here |ni denotes the chargenumber state with the excess number of electrons n the box, n.) (2) The only low-energy excitations are the transitions between different |ni states due to Cooper-pair tunnelling through the Josephson junction, if ¢ is larger than the single-electron charging energy of the box E C . (3) E C , if larger than the Josephson energy E J and the thermal energy k B T, suppresses a large¯uctuation of n. Hence, we can consider the system an effective two-level system by taking into account the two lowest-energy states which differ by one Cooper pair. (4) In addition, the relative energy of the two levels can be controlled through the gate voltage. For example, as shown in Fig. 2a, the electrostatic energies, E C n 2 Q t =e 2 , of two such charge states |0i and |2i change as a function of the total gate-induced charge Q t and cross each other at Q t =e 1. (The parabolic background energy is subtracted.) In the presence of Josephson coupling, and with weak enough dissipation 15 , these charge states w...

We have observed coherent time evolution between two quantum states of a superconducting flux qubit comprising three Josephson junctions in a loop. The superposition of the two states carrying opposite macroscopic persistent currents is manipulated by resonant microwave pulses. Readout by means of switching-event measurement with an attached superconducting quantum interference device revealed quantum-state oscillations with high fidelity. Under strong microwave driving it was possible to induce hundreds of coherent oscillations. Pulsed operations on this first sample yielded a relaxation time of 900 nanoseconds and a free-induction dephasing time of 20 nanoseconds. These results are promising for future solid-state quantum computing.It is becoming clear that artificially fabricated solidstate devices of macroscopic size may, under certain conditions, behave as single quantum particles. We report on the controlled time-dependent quantum dynamics between two states of a micron-size superconducting ring containing billions of Cooper pairs (1). From a ground state in which all the Cooper pairs circulate in one direction, application of resonant microwave pulses can excite the system to a state where all pairs move oppositely, and make it oscillate coherently between these two states. Moreover, multiple pulses can be used to create quantum operation sequences. This is of strong fundamental interest because it allows experimental studies on decoherence mechanisms of the quantum behavior of a macroscopicsized object. In addition, it is of great significance in the context of quantum computing (2) because these fabricated structures are attractive for a design that can be scaled up to large numbers of quantum bits or qubits (3).Superconducting circuits with mesoscopic Josephson junctions are expected to behave according to the laws of quantum mechanics if they are separated sufficiently from external degrees of freedom, thereby reducing the decoherence. Quantum oscillations of a superconducting two-level system have been observed in the Cooper pair box qubit using the charge degree of freedom (4). An improved version of the Cooper pair box qubit showed that quantum oscillations with a high quality factor could be achieved (5). In addition, a qubit based on the phase degree of freedom in a Josephson junction was presented, consisting of a single, relatively large Josephson junction current-biased close to its critical current (6,7).Our flux qubit consists of three Josephson junctions arranged in a superconducting loop threaded by an externally applied magnetic flux near half a superconducting flux quantum Φ 0 = h/2e [(8); a one-junction flux-qubit is described in (9)]. Varying the flux bias controls the energy level separation of this effectively two-level system. At half a flux quantum, the two lowest states are symmetric and antisymmetric superpositions of two classical states with clockwise and anticlockwise circulating currents. As shown by previous microwave spectroscopy studies, the qubit can be engineered such th...

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In the emerging field of quantum computation 1 and quantum information, superconducting devices are promising candidates for the implementation of solidstate quantum bits or qubits. Single-qubit operations 2−6 , direct coupling between two qubits 7−10 , and the realization of a quantum gate 11 have been reported. However, complex manipulation of entangled states − such as the coupling of a two-level system to a quantum harmonic oscillator, as demonstrated in ion/atom-trap experiments 12,13 or cavity quantum electrodynamics 14 − has yet to be achieved for superconducting devices. Here we demonstrate entanglement between a superconducting flux qubit (a two-level system) and a superconducting quantum interference device (SQUID). The latter provides the measurement system for detecting the quantum states; it is also an effective inductance that, in parallel with an external shunt capacitance, acts as a harmonic oscillator. We achieve generation and control of the entangled state by performing microwave spectroscopy and detecting the resultant Rabi oscillations of the coupled system.The device was realized by electron-beam lithography and metal evaporation. The qubit-SQUID geometry is shown in Fig. 1a: a large loop interrupted by two Josephson junctions (the SQUID) is merged with the smaller loop on the right-hand side comprising three in-line Josephson junctions (the flux qubit) 15 . By applying a perpendicular external magnetic field, the qubit is biased around Φ 0 /2, where Φ 0 = h/2e is the flux quantum. Previous spectroscopy 16 and coherent timedomain experiments 6 have shown that the flux qubit is a controllable two-level system with 'spin-up/spin-down' states corresponding to persistent currents flowing in 'clockwise/anticlockwise' directions and coupled by tunneling. Here we show that a stronger qubit−SQUID coupling allows us to investigate the coupled dynamics of a 'qubit−harmonic oscillator' system.The qubit Hamiltonian is defined by the charging and Josephson energy of the qubit outer junctions (E C = e 2 /2C and E J = hI C /4e where C and I C are their capacitance and critical current) 16 . In a two-level truncation, the Hamiltonian becomes H q /h = −ǫσ z /2−∆σ x /2 where σ z,x are the Pauli matrices in the spin-up/spin-down basis, ∆ is the tunnel splitting and ǫ ∼ = I p Φ 0 (γ q − π)/hπ (I p is the qubit maximum persistent current and γ q is the superconductor phase across the three junctions). The resulting energy level spacing represents the qubit Larmor frequency F L = √ ∆ 2 + ǫ 2 . The SQUID dynamics is characterized by the Josephson inductance of the junctions L J ≈ 80 pH, shunt capacitance C sh ≈ 12 pF (see Fig. 1a) and self-inductances L sl ≈ 170 pH of the SQUID and shunt-lines. In our experiments, the SQUID circuit behaves like a harmonic oscillator described by H sq = hν p (a † a + 1/2), where 2πν p = 1/ (L J + L sl )C sh is called the plasma frequency and a (a † ) is the plasmon annihilation (creation) operator. Henceforth |βn represents the state with the qubit in the ground(β = 0) or excited ...

An atom in open space can be detected by means of resonant absorption and reemission of electromagnetic waves, known as resonance fluorescence, which is a fundamental phenomenon of quantum optics. We report on the observation of scattering of propagating waves by a single artificial atom. The behavior of the artificial atom, a superconducting macroscopic two-level system, is in a quantitative agreement with the predictions of quantum optics for a pointlike scatterer interacting with the electromagnetic field in one-dimensional open space. The strong atom-field interaction as revealed in a high degree of extinction of propagating waves will allow applications of controllable artificial atoms in quantum optics and photonics.A single atom interacting with electromagnetic modes of free space is a fundamental example of an open quantum system (Fig. 1A) [1]. The interaction between the atom (or molecule, quantum dot, et cetera) and a resonant electromagnetic field is particularly important for quantum electronics and quantum information processing. In three-dimensional (3D) space, however, although perfect coupling (with 100% extinction of transmitted power) is theoretically feasible [2], experimentally achieved extinction has not exceeded 12% [3][4][5][6][7] because of spatial mode mismatch between incident and scattered waves. This problem can be avoided by an efficient coupling of the atom to the continuum of electromagnetic modes confined in a 1D transmission line (Fig. 1B) as proposed in [8,9]. Here we demonstrate extinction of 94% on an artificial atom coupled to the open 1D transmission line. The situation with the atom interacting with freely propagating waves is qualitatively different from that of the atom interacting with a single cavity mode; the latter has been used to demonstrate a series of cavity quantum electrodynamics (QED) phenomena [10][11][12][13][14][15][16][17][18]. Moreover in open space, the atom directly reveals such phenomena known from quantum optics as anomalous dispersion and strongly nonlinear behavior in elastic (Rayleigh) scattering near the atomic resonance[1]. Furthermore, spectrum of inelastically scattered radiation is observed and exhibits the resonance fluorescence triplet (the Mollow triplet) [19][20][21][22][23] under a strong drive.Our artificial atom is a macroscopic superconducting loop, interrupted by Josephson junctions (Fig. 1B) [identical to a flux qubit [24]] and threaded by a bias flux Φ b close to a half flux quantum Φ 0 /2, and shares a segment with the transmission line [25], which results in a loop-line mutual inductance M mainly due to kinetic * On leave from Physical-Technical Institute, Tashkent 100012, Uzbekistan † On leave from Lebedev Physical Institute, Moscow 119991, Russia inductance of the shared segment [26]. The two lowest eigenstates of the atom are naturally expressed via superpositions of two states with persistent current, I p , flowing clockwise or counterclockwise. In energy eigenbasis the lowest two levels |g and |e are described by the truncated...

We demonstrate large normal-mode splitting between a magnetostatic mode (the Kittel mode) in a ferromagnetic sphere of yttrium iron garnet and a microwave cavity mode. Strong coupling is achieved in the quantum regime where the average number of thermally or externally excited magnons and photons is less than one. We also confirm that the coupling strength is proportional to the square root of the number of spins. A nonmonotonic temperature dependence of the Kittel-mode linewidth is observed below 1 K and is attributed to the dissipation due to the coupling with a bath of two-level systems.

A practical quantum computer, if built, would consist of a set of coupled two-level quantum systems (qubits). Among the variety of qubits implemented, solid-state qubits are of particular interest because of their potential suitability for integrated devices. A variety of qubits based on Josephson junctions have been implemented; these exploit the coherence of Cooper-pair tunnelling in the superconducting state. Despite apparent progress in the implementation of individual solid-state qubits, there have been no experimental reports of multiple qubit gates--a basic requirement for building a real quantum computer. Here we demonstrate a Josephson circuit consisting of two coupled charge qubits. Using a pulse technique, we coherently mix quantum states and observe quantum oscillations, the spectrum of which reflects interaction between the qubits. Our results demonstrate the feasibility of coupling multiple solid-state qubits, and indicate the existence of entangled two-qubit states.