Shannon X. Wang

Quantum computers are able to outperform classical algorithms. This was long recognized by the visionary Richard Feynman who pointed out in the 1980s that quantum mechanical problems were better solved with quantum machines. It was only in 1994 that Peter Shor came up with an algorithm that is able to calculate the prime factors of a large number vastly more efficiently than known possible with a classical computer. This paradigmatic algorithm stimulated the flourishing research in quantum information processing and the quest for an actual implementation of a quantum computer. Over the last fifteen years, using skillful optimizations, several instances of a Shor algorithm have been implemented on various platforms and clearly proved the feasibility of quantum factoring. For general scalability, though, a different approach has to be pursued. Here, we report the realization of a fully scalable Shor algorithm as proposed by Kitaev. For this, we demonstrate factoring the number fifteen by effectively employing and controlling seven qubits and four "cache-qubits", together with the implementation of generalized arithmetic operations, known as modular multipliers. The scalable algorithm has been realized with an ion-trap quantum computer exhibiting success probabilities in excess of 90%.

Quantum computers hold the promise to solve certain problems exponentially faster than their classical counterparts. Trapped atomic ions are among the physical systems in which building such a computing device seems viable. In this work we present a small-scale quantum information processor based on a string of $^{40}$Ca${^+}$ ions confined in a macroscopic linear Paul trap. We review our set of operations which includes non-coherent operations allowing us to realize arbitrary Markovian processes. In order to build a larger quantum information processor it is mandatory to reduce the error rate of the available operations which is only possible if the physics of the noise processes is well understood. We identify the dominant noise sources in our system and discuss their effects on different algorithms. Finally we demonstrate how our entire set of operations can be used to facilitate the implementation of algorithms by examples of the quantum Fourier transform and the quantum order finding algorithm.

Fluorescence collection sets the efficiency of state detection and the rate of entanglement generation between remote trapped ion qubits. Despite efforts to improve light collection using various optical elements, solid angle capture is limited to ~10% for implementations that are scalable to many ions. We present an approach based on fluorescence detection through a transparent trap using an integrated photodetector, combining collection efficiency approaching 50% with scalability. We microfabricate transparent surface traps with indium tin oxide and verify stable trapping of single ions. The fluorescence from a cloud of ions is detected using a photodiode sandwiched with a transparent trap.

Electrical charging of metal surfaces due to photoelectric generation of carriers is of concern in trapped ion quantum computation systems, due to the high sensitivity of the ions' motional quantum states to deformation of the trapping potential. The charging induced by typical laser frequencies involved in doppler cooling and quantum control is studied here, with microfabricated surface electrode traps made of aluminum, copper, and gold, operated at 6 K with a single Sr$^+$ ion trapped 100 $μ$m above the trap surface. The lasers used are at 370, 405, 460, and 674 nm, and the typical photon flux at the trap is 10$^{14}$ photons/cm$^2$/sec. Charging is detected by monitoring the ion's micromotion signal, which is related to the number of charges created on the trap. A wavelength and material dependence of the charging behavior is observed: lasers at lower wavelengths cause more charging, and aluminum exhibits more charging than copper or gold. We describe the charging dynamic based on a rate equation approach.

A novel approach to optics integration in ion traps is demonstrated based on a surface electrode ion trap that is microfabricated on top of a dielectric mirror. Additional optical losses due to fabrication are found to be as low as 80 ppm for light at 422 nm. The integrated mirror is used to demonstrate light collection from, and imaging of, a single 88 Sr+ ion trapped $169\pm4 μ$m above the mirror.

We fabricate superconducting ion traps with niobium and niobium nitride and trap single 88Sr ions at cryogenic temperatures. The superconducting transition is verified and characterized by measuring the resistance and critical current using a 4-wire measurement on the trap structure, and observing change in the rf reflection. The lowest observed heating rate is 2.1(3) quanta/sec at 800 kHz at 6 K and shows no significant change across the superconducting transition, suggesting that anomalous heating is primarily caused by noise sources on the surface. This demonstration of superconducting ion traps opens up possibilities for integrating trapped ions and molecular ions with superconducting devices.

We demonstrate quantum control techniques for a single trapped ion in a cryogenic, surface-electrode trap. A narrow optical transition of Sr+ along with the ground and first excited motional states of the harmonic trapping potential form a two-qubit system. The optical qubit transition is susceptible to magnetic field fluctuations, which we stabilize with a simple and compact method using superconducting rings. Decoherence of the motional qubit is suppressed by the cryogenic environment. AC Stark shift correction is accomplished by controlling the laser phase in the pulse sequencer, eliminating the need for an additional laser. Quantum process tomography is implemented on atomic and motional states using conditional pulse sequences. With these techniques we demonstrate a Cirac-Zoller Controlled-NOT gate in a single ion with a mean fidelity of 91(1)%.

Dense array of ions in microfabricated traps represent one possible way to scale up ion trap quantum computing. The ability to address individual ions is an important component of such a scheme. We demonstrate individual addressing of trapped ions in a microfabricated surface-electrode trap using a magnetic field gradient generated on-chip. A frequency splitting of 310(2) kHz for two ions separated by 5 um is achieved. Selective single qubit operations are performed on one of two trapped ions with an average of 2.2+/-1.0% crosstalk. Coherence time as measured by the spin-echo technique is unaffected by the field gradient.

Electric field noise from fluctuating patch potentials is a significant problem for a broad range of precision experiments, including trapped ion quantum computation and single spin detection. Recent results demonstrated strong suppression of this noise by cryogenic cooling, suggesting an underlying thermal process. We present measurements characterizing the temperature and frequency dependence of the noise from 7 to 100 K, using a single Sr+ ion trapped 75 um above the surface of a gold plated surface electrode ion trap. The noise amplitude is observed to have an approximate 1/f spectrum around 1 MHz, and grows rapidly with temperature as T^beta for beta from 2 to 4. The data are consistent with microfabricated cantilever measurements of non-contact friction but do not extrapolate to the DC measurements with neutral atoms or contact potential probes.