David Hanneke

Complete Methods Set for Scalable Ion Trap Quantum Information Processing

Hi Fi Quantum Computing In quantum information processing, one goal is to control the entangled states of objects such that they can interact during logical operations but otherwise have minimal interactions with their environment. In one scheme for quantum computing, ions are trapped within and physically moved by electric fields. One drawback is that the entangled states can be sensitive to stray magnetic fields. Home et al. (p. 1227, published online 6 August 2009) show that coupling of the ions (in this case, 9Be+) with a second ion (24Mg+) can create states that are relatively insensitive to magnetic fields and also allows for recooling of the ions during operation. This approach can minimize the loss of fidelity that occurs during ion transport. Coupling of different ions creates states that are insensitive to stray magnetic fields and more robust for quantum computing. Large-scale quantum information processors must be able to transport and maintain quantum information and repeatedly perform logical operations. Here, we show a combination of all of the fundamental elements required to perform scalable quantum computing through the use of qubits stored in the internal states of trapped atomic ions. We quantified the repeatability of a multiple-qubit operation and observed no loss of performance despite qubit transport over macroscopic distances. Key to these results is the use of different pairs of 9Be+ hyperfine states for robust qubit storage, readout, and gates, and simultaneous trapping of 24Mg+ “re-cooling” ions along with the qubit ions.

Cavity Control of a Single-Electron Quantum Cyclotron: Measuring the Electron Magnetic Moment

Measurements with a one-electron quantum cyclotron determine the electron magnetic moment, given by

Entangled mechanical oscillators

g/2 = 1.001\,159\,652\,180\,73\,(28)\,[0.28~\textrm{ppt}]

Coherent diabatic ion transport and separation in a multizone trap array.

, and the fine structure constant,

Realization of a programmable two-qubit quantum processor

\alpha^{-1}=137.035\,999\,084\,(51)\,[0.37~\textrm{ppb}]

Randomized benchmarking of multiqubit gates.

. Brief announcements of these measurements are supplemented here with a more complete description of the one-electron quantum cyclotron and the new measurement methods, a discussion of the cavity control of the radiation field, a summary of the analysis of the measurements, and a fuller discussion of the uncertainties.

MORE ACCURATE MEASUREMENT OF THE ELECTRON MAGNETIC MOMENT AND THE FINE STRUCTURE CONSTANT

Hallmarks of quantum mechanics include superposition and entanglement. In the context of large complex systems, these features should lead to situations as envisaged in the ‘Schrödinger’s cat’ thought experiment (where the cat exists in a superposition of alive and dead states entangled with a radioactive nucleus). Such situations are not observed in nature. This may be simply due to our inability to sufficiently isolate the system of interest from the surrounding environment—a technical limitation. Another possibility is some as-yet-undiscovered mechanism that prevents the formation of macroscopic entangled states. Such a limitation might depend on the number of elementary constituents in the system or on the types of degrees of freedom that are entangled. Tests of the latter possibility have been made with photons, atoms and condensed matter devices. One system ubiquitous to nature where entanglement has not been previously demonstrated consists of distinct mechanical oscillators. Here we demonstrate deterministic entanglement of separated mechanical oscillators, consisting of the vibrational states of two pairs of atomic ions held in different locations. We also demonstrate entanglement of the internal states of an atomic ion with a distant mechanical oscillator. These results show quantum entanglement in a degree of freedom that pervades the classical world. Such experiments may lead to the generation of entangled states of larger-scale mechanical oscillators, and offer possibilities for testing non-locality with mesoscopic systems. In addition, the control developed here is an important ingredient for scaling-up quantum information processing with trapped atomic ions.

New determination of the fine structure constant from the electron g value and QED

We investigate the dynamics of single and multiple ions during transport between and separation into spatially distinct locations in a multizone linear Paul trap. A single 9Be+ ion in a ~2 MHz harmonic well was transported 370 μm in 8 μs, corresponding to 16 periods of oscillation, with a gain of 0.1 motional quanta. Similar results were achieved for the transport of two ions. We also separated chains of up to 9 ions from one potential well to two distinct potential wells. With two ions this was accomplished in 55 μs, with excitations of approximately two quanta for each ion. Fast transport and separation can significantly reduce the time overhead in certain architectures for scalable quantum information processing with trapped ions.

New measurement of the electron magnetic moment using a one-electron quantum cyclotron

A simple programmable quantum processor has been created using trapped atomic ions. The system can be programmed with 15 classical inputs to produce any unitary operation on two qubits. This trapped-ion approach is amenable to scaling up for creating more complex circuits.

Erratum: New determination of the fine structure constant from the electron g value and QED (Physical Review Letters (2006) 97 (030802))

We describe an extension of single-qubit gate randomized benchmarking that measures the error of multiqubit gates in a quantum information processor. This platform-independent protocol evaluates the performance of Clifford unitaries, which form a basis of fault-tolerant quantum computing. We implemented the benchmarking protocol with trapped ions and found an error per random two-qubit Clifford unitary of 0.162±0.008, thus setting the first benchmark for such unitaries. By implementing a second set of sequences with an extra two-qubit phase gate inserted after each step, we extracted an error per phase gate of 0.069±0.017. We conducted these experiments with transported, sympathetically cooled ions in a multizone Paul trap-a system that can in principle be scaled to larger numbers of ions.