Real-time dynamics of lattice gauge theories with a few-qubit quantum computer.

Gauge theories are fundamental to our understanding of interactions between the elementary constituents of matter as mediated by gauge bosons. However, computing the real-time dynamics in gauge theories is a notorious challenge for classical computational methods. This has recently stimulated theoretical effort, using Feynman's idea of a quantum simulator, to devise schemes for simulating such theories on engineered quantum-mechanical devices, with the difficulty that gauge invariance and the associated local conservation laws (Gauss laws) need to be implemented. Here we report the experimental demonstration of a digital quantum simulation of a lattice gauge theory, by realizing (1 + 1)-dimensional quantum electrodynamics (the Schwinger model) on a few-qubit trapped-ion quantum computer. We are interested in the real-time evolution of the Schwinger mechanism, describing the instability of the bare vacuum due to quantum fluctuations, which manifests itself in the spontaneous creation of electron-positron pairs. To make efficient use of our quantum resources, we map the original problem to a spin model by eliminating the gauge fields in favour of exotic long-range interactions, which can be directly and efficiently implemented on an ion trap architecture. We explore the Schwinger mechanism of particle-antiparticle generation by monitoring the mass production and the vacuum persistence amplitude. Moreover, we track the real-time evolution of entanglement in the system, which illustrates how particle creation and entanglement generation are directly related. Our work represents a first step towards quantum simulation of high-energy theories using atomic physics experiments-the long-term intention is to extend this approach to real-time quantum simulations of non-Abelian lattice gauge theories.

Realization of a scalable Shor algorithm.

Certain algorithms for quantum computers are able to outperform their classical counterparts. In 1994, Peter Shor came up with a quantum algorithm that calculates the prime factors of a large number vastly more efficiently than a classical computer. For general scalability of such algorithms, hardware, quantum error correction, and the algorithmic realization itself need to be extensible. Here we present the realization of a scalable Shor algorithm, as proposed by Kitaev. We factor the number 15 by effectively employing and controlling seven qubits and four "cache qubits" and by implementing generalized arithmetic operations, known as modular multipliers. This algorithm has been realized scalably within an ion-trap quantum computer and returns the correct factors with a confidence level exceeding 99%.

Experimental characterization of quantum dynamics through many-body interactions.

We report on the implementation of a quantum process tomography technique known as direct characterization of quantum dynamics applied on coherent and incoherent single-qubit processes in a system of trapped (40)Ca(+) ions. Using quantum correlations with an ancilla qubit, direct characterization of quantum dynamics reduces substantially the number of experimental configurations required for a full quantum process tomography and all diagonal elements of the process matrix can be estimated with a single setting. With this technique, the system's relaxation times T(1) and T(2) were measured with a single experimental configuration. We further show the first, complete characterization of single-qubit processes using a single generalized measurement realized through multibody correlations with three ancilla qubits.

Undoing a quantum measurement.

In general, a quantum measurement yields an undetermined answer and alters the system to be consistent with the measurement result. This process maps multiple initial states into a single state and thus cannot be reversed. This has important implications in quantum information processing, where errors can be interpreted as measurements. Therefore, it seems that it is impossible to correct errors in a quantum information processor, but protocols exist that are capable of eliminating them if they affect only part of the system. In this work we present the deterministic reversal of a fully projective measurement on a single particle, enabled by a quantum error-correction protocol in a trapped ion quantum information processor. We further introduce an in-sequence, single-species recooling procedure to counteract the motional heating of the ion string due to the measurement.

Experimental repetitive quantum error correction.

The computational potential of a quantum processor can only be unleashed if errors during a quantum computation can be controlled and corrected for. Quantum error correction works if imperfections of quantum gate operations and measurements are below a certain threshold and corrections can be applied repeatedly. We implement multiple quantum error correction cycles for phase-flip errors on qubits encoded with trapped ions. Errors are corrected by a quantum-feedback algorithm using high-fidelity gate operations and a reset technique for the auxiliary qubits. Up to three consecutive correction cycles are realized, and the behavior of the algorithm for different noise environments is analyzed.

14-Qubit entanglement: creation and coherence.

We report the creation of Greenberger-Horne-Zeilinger states with up to 14 qubits. By investigating the coherence of up to 8 ions over time, we observe a decay proportional to the square of the number of qubits. The observed decay agrees with a theoretical model which assumes a system affected by correlated, Gaussian phase noise. This model holds for the majority of current experimental systems developed towards quantum computation and quantum metrology.

An open-system quantum simulator with trapped ions.

The control of quantum systems is of fundamental scientific interest and promises powerful applications and technologies. Impressive progress has been achieved in isolating quantum systems from the environment and coherently controlling their dynamics, as demonstrated by the creation and manipulation of entanglement in various physical systems. However, for open quantum systems, engineering the dynamics of many particles by a controlled coupling to an environment remains largely unexplored. Here we realize an experimental toolbox for simulating an open quantum system with up to five quantum bits (qubits). Using a quantum computing architecture with trapped ions, we combine multi-qubit gates with optical pumping to implement coherent operations and dissipative processes. We illustrate our ability to engineer the open-system dynamics through the dissipative preparation of entangled states, the simulation of coherent many-body spin interactions, and the quantum non-demolition measurement of multi-qubit observables. By adding controlled dissipation to coherent operations, this work offers novel prospects for open-system quantum simulation and computation.

A study on the causes for the elevated n-3 fatty acids in cows' milk of alpine origin.

The influence of grass-only diets either from rye-grass-dominated lowland pastures (400 m above sea level) or botanically diverse alpine pastures (2000 m) on the FA profile of milk was investigated using three groups of six Brown Swiss cows each. Two groups were fed grass-only on pasture (P) or freshly harvested in barn (B), both for two experimental periods in the lowlands and, consecutively, two periods on the alp. Group C served as the control, receiving a silage-concentrate diet and permanently staying in the lowlands. Effects of vegetation stage or pasture vs. barn feeding on milk fat composition were negligible. Compared with the control, alpha-linolenic acid (18:3n-3) consumption was elevated in groups P and B (79%; P< 0.001) during the lowland periods but decreased on the alp to the level of C owing to feed intake depression and lower 18:3n-3 concentration in the alpine forage. Average 18:3n-3 contents of milk fat were higher in groups P and B than in C by 33% (P< 0.01) at low and by 96% (P < 0.001) at high altitude, indicating that 18:3n-3 levels in milk were to some extent independent of 18:3n-3 consumption. The cis-9, trans-11 CLA content in milk of grass-fed cows was higher compared with C but lower for the alpine vs. lowland periods whereas the trans-11, cis-13 isomer further increased with altitude. Long-chain n-3 FA and phytanic acid increased while arachidonic acid decreased with grass-only feeding, but none of them responded to altitude. Grass-only feeding increased milk alpha-tocopherol concentration by 86 and 134% at low and high altitude (P < 0.001), respectively. Changes in the ruminal ecosystem due to energy shortage or specific secondary plant metabolites are discussed as possible causes for the high 18:3n-3 concentrations in alpine milk.

Protein composition, plasmin activity and cheesemaking properties of cows' milk produced at two altitudes from hay of lowland and high-alpine origins.

The influence of high altitude, alpine origin of the forage and roughage-only diets on milk protein content and composition, plasmin activity and cheesemaking properties was investigated. There were four treatment groups, each consisting of six dairy cows in early to mid-lactation. Two groups were fed only with hay ad libitum either at 2000 m or at 400 m a.s.l. One group, kept in the lowlands, was pair-fed to the alpine-site group and another group received a mixed diet of silages, hay and concentrates. Two hay types, harvested either at the alpine site or in the lowlands, were offered to all cows fed with hay alone, following a change-over design in three periods each of 3 weeks. In the respective third week, milk was sampled at every milking. Hay of alpine origin significantly reduced milk protein, in particular whey proteins, which is why the casein number increased. kappa-Casein proportion in total casein was reduced and its glycosylation was increased by the alpine hay. The apparent plasminogen-derived activity was reduced when alpine hay was given, but apparent plasmin activity and rennet coagulation properties of the milk were not affected by hay type. Independent of hay type, the high altitude group showed a significantly reduced milk protein content, lower glycosylation of kappa-casein and impaired rennet coagulation properties. For several of the traits, the trend was the same in the pair-fed group. There was no effect of altitude on apparent plasmin activity. Hay-alone v. the mixed diet resulted initially in marked declines in milk protein content but did not impair cheesemaking properties. Thus the extensive diet without concentrates, typical of high-alpine conditions, contributed less to the overall effect of extensive alpine v. intensive lowland feeding systems than hay quality and altitude did. In conclusion, certain positive influences of the alpine sojourn of cows on cheese processing quality are overruled by the major adverse impact of lower milk protein content.