Integrated multi-wavelength control of an ion qubit.

Monolithic integration of control technologies for atomic systems is a promising route to the development of quantum computers and portable quantum sensors1-4. Trapped atomic ions form the basis of high-fidelity quantum information processors5,6 and high-accuracy optical clocks7. However, current implementations rely on free-space optics for ion control, which limits their portability and scalability. Here we demonstrate a surface-electrode ion-trap chip8,9 using integrated waveguides and grating couplers, which delivers all the wavelengths of light required for ionization, cooling, coherent operations and quantum state preparation and detection of Sr+ qubits. Laser light from violet to infrared is coupled onto the chip via an optical-fibre array, creating an inherently stable optical path, which we use to demonstrate qubit coherence that is resilient to platform vibrations. This demonstration of CMOS-compatible integrated photonic surface-trap fabrication, robust packaging and enhanced qubit coherence is a key advance in the development of portable trapped-ion quantum sensors and clocks, providing a way towards the complete, individual control of larger numbers of ions in quantum information processing systems.

Passive cooling of a micromechanical oscillator with a resonant electric circuit.

We cool the fundamental mode of a miniature cantilever by capacitively coupling it to a driven rf resonant circuit. Cooling results from the rf capacitive force, which is phase shifted relative to the cantilever motion. We demonstrate the technique by cooling a 7 kHz cantilever from room temperature to 45 K, obtaining reasonable agreement with a model for the cooling, damping, and frequency shift. Extending the method to higher frequencies in a cryogenic system could enable ground state cooling and may prove simpler than related optical experiments in a low temperature apparatus.

Microfabricated surface-electrode ion trap for scalable quantum information processing.

Individual laser-cooled 24Mg+ ions are confined in a linear Paul trap with a novel geometry where gold electrodes are located in a single plane and the ions are trapped 40 microm above this plane. The relatively simple trap design and fabrication procedure are important for large-scale quantum information processing (QIP) using ions. Measured ion motional frequencies are compared to simulations. Measurements of ion recooling after cooling is temporarily suspended yield a heating rate of approximately 5 motional quanta per millisecond for a trap frequency of 2.83 MHz, sufficiently low to be useful for QIP.

Creation of a six-atom 'Schrödinger cat' state.

Among the classes of highly entangled states of multiple quantum systems, the so-called 'Schrödinger cat' states are particularly useful. Cat states are equal superpositions of two maximally different quantum states. They are a fundamental resource in fault-tolerant quantum computing and quantum communication, where they can enable protocols such as open-destination teleportation and secret sharing. They play a role in fundamental tests of quantum mechanics and enable improved signal-to-noise ratios in interferometry. Cat states are very sensitive to decoherence, and as a result their preparation is challenging and can serve as a demonstration of good quantum control. Here we report the creation of cat states of up to six atomic qubits. Each qubit's state space is defined by two hyperfine ground states of a beryllium ion; the cat state corresponds to an entangled equal superposition of all the atoms in one hyperfine state and all atoms in the other hyperfine state. In our experiments, the cat states are prepared in a three-step process, irrespective of the number of entangled atoms. Together with entangled states of a different class created in Innsbruck, this work represents the current state-of-the-art for large entangled states in any qubit system.

Hyperfine coherence in the presence of spontaneous photon scattering.

The coherence of a hyperfine-state superposition of a trapped 9Be+ ion in the presence of off-resonant light is studied experimentally. It is shown that Rayleigh elastic scattering of photons that does not change state populations also does not affect coherence. We observe coherence times that exceed the average scattering time of 19 photons which is determined from measured Stark shifts. This result implies that, with sufficient control over its parameters, laser light can be used to manipulate hyperfine-state superpositions with very little decoherence.

Long-lived qubit memory using atomic ions.

We demonstrate experimentally a robust quantum memory using a magnetic-field-independent hyperfine transition in 9Be+ atomic ion qubits at a magnetic field B approximately = 0.01194 T. We observe that the single physical qubit memory coherence time is greater than 10 s, an improvement of approximately 5 orders of magnitude from previous experiments with 9Be+. We also observe long coherence times of decoherence-free subspace logical qubits comprising two entangled physical qubits and discuss the merits of each type of qubit.

Implementation of the semiclassical quantum Fourier transform in a scalable system.

We report the implementation of the semiclassical quantum Fourier transform in a system of three beryllium ion qubits (two-level quantum systems) confined in a segmented multizone trap. The quantum Fourier transform is the crucial final step in Shor's algorithm, and it acts on a register of qubits to determine the periodicity of the quantum state's amplitudes. Because only probability amplitudes are required for this task, a more efficient semiclassical version can be used, for which only single-qubit operations conditioned on measurement outcomes are required. We apply the transform to several input states of different periodicities; the results enable the location of peaks corresponding to the original periods. This demonstration incorporates the key elements of a scalable ion-trap architecture, suggesting the future capability of applying the quantum Fourier transform to a large number of qubits as required for a useful quantum factoring algorithm.

Enhanced quantum state detection efficiency through quantum information processing.

We investigate theoretically and experimentally how quantum state-detection efficiency is improved by the use of quantum information processing (QIP). Experimentally, we encode the state of one 9Be(+) ion qubit with one additional ancilla qubit. By measuring both qubits, we reduce the state-detection error in the presence of noise. The deviation from the theoretically allowed reduction is due to infidelities of the QIP operations. Applying this general scheme to more ancilla qubits suggests that error in the individual qubit measurements need not be a limit to scalable quantum computation.

Realization of quantum error correction.

Scalable quantum computation and communication require error control to protect quantum information against unavoidable noise. Quantum error correction protects information stored in two-level quantum systems (qubits) by rectifying errors with operations conditioned on the measurement outcomes. Error-correction protocols have been implemented in nuclear magnetic resonance experiments, but the inherent limitations of this technique prevent its application to quantum information processing. Here we experimentally demonstrate quantum error correction using three beryllium atomic-ion qubits confined to a linear, multi-zone trap. An encoded one-qubit state is protected against spin-flip errors by means of a three-qubit quantum error-correcting code. A primary ion qubit is prepared in an initial state, which is then encoded into an entangled state of three physical qubits (the primary and two ancilla qubits). Errors are induced simultaneously in all qubits at various rates. The encoded state is decoded back to the primary ion one-qubit state, making error information available on the ancilla ions, which are separated from the primary ion and measured. Finally, the primary qubit state is corrected on the basis of the ancillae measurement outcome. We verify error correction by comparing the corrected final state to the uncorrected state and to the initial state. In principle, the approach enables a quantum state to be maintained by means of repeated error correction, an important step towards scalable fault-tolerant quantum computation using trapped ions.

Quantum dense coding with atomic qubits.

We report the implementation of quantum dense coding on individual atomic qubits with the use of two trapped 9Be+ ions. The protocol is implemented with a complete Bell measurement that distinguishes the four operations used to encode two bits of classical information. We measure an average transmission fidelity of 0.85(1) and determine a channel capacity of 1.16(1).

Deterministic quantum teleportation of atomic qubits.

Quantum teleportation provides a means to transport quantum information efficiently from one location to another, without the physical transfer of the associated quantum-information carrier. This is achieved by using the non-local correlations of previously distributed, entangled quantum bits (qubits). Teleportation is expected to play an integral role in quantum communication and quantum computation. Previous experimental demonstrations have been implemented with optical systems that used both discrete and continuous variables, and with liquid-state nuclear magnetic resonance. Here we report unconditional teleportation of massive particle qubits using atomic (9Be+) ions confined in a segmented ion trap, which aids individual qubit addressing. We achieve an average fidelity of 78 per cent, which exceeds the fidelity of any protocol that does not use entanglement. This demonstration is also important because it incorporates most of the techniques necessary for scalable quantum information processing in an ion-trap system.

Toward Heisenberg-limited spectroscopy with multiparticle entangled states.

The precision in spectroscopy of any quantum system is fundamentally limited by the Heisenberg uncertainty relation for energy and time. For N systems, this limit requires that they be in a quantum-mechanically entangled state. We describe a scalable method of spectroscopy that can potentially take full advantage of entanglement to reach the Heisenberg limit and has the practical advantage that the spectroscopic information is transferred to states with optimal protection against readout noise. We demonstrate our method experimentally with three beryllium ions. The spectroscopic sensitivity attained is 1.45(2) times as high as that of a perfect experiment with three non-entangled particles.

Quantum information processing with trapped ions.

Experiments directed towards the development of a quantum computer based on trapped atomic ions are described briefly. We discuss the implementation of single-qubit operations and gates between qubits. A geometric phase gate between two ion qubits is described. Limitations of the trapped-ion method such as those caused by Stark shifts and spontaneous emission are addressed. Finally, we describe a strategy to realize a large-scale device.

New experimental constraints on non-Newtonian forces below 100 microm.

We have searched for large deviations from Newtonian gravity by means of a finite-frequency microcantilever-based experiment. Our data eliminate from consideration mechanisms of deviation that posit strengths approximately 10(4) times Newtonian gravity at length scales of 20 microm. This measurement is 3 orders of magnitude more sensitive than others that provide constraints at similar length scales.