Randomized benchmarking of single and multi-qubit control in liquid-state NMR quantum information processing

Being able to quantify the level of coherent control in a proposed device implementing a quantum information processor (QIP) is an important task for both comparing different devices and assessing a device's prospects with regards to achieving fault-tolerant quantum control. We implement in a liquid-state nuclear magnetic resonance QIP the randomized benchmarking protocol presented by Knill et al (PRA 77: 012307 (2008)). We report an error per randomized $\frac{\pi}{2}$ pulse of $1.3 \pm 0.1 \times 10^{-4}$ with a single qubit QIP and show an experimentally relevant error model where the randomized benchmarking gives a signature fidelity decay which is not possible to interpret as a single error per gate. We explore and experimentally investigate multi-qubit extensions of this protocol and report an average error rate for one and two qubit gates of $4.7 \pm 0.3 \times 10^{-3}$ for a three qubit QIP. We estimate that these error rates are still not decoherence limited and thus can be improved with modifications to the control hardware and software.Comment: 10 pages, 6 figures, submitted versio

Characterization of complex quantum dynamics with a scalable NMR information processor

We present experimental results on the measurement of fidelity decay under contrasting system dynamics using a nuclear magnetic resonance quantum information processor. The measurements were performed by implementing a scalable circuit in the model of deterministic quantum computation with only one quantum bit. The results show measurable differences between regular and complex behaviour and for complex dynamics are faithful to the expected theoretical decay rate. Moreover, we illustrate how the experimental method can be seen as an efficient way for either extracting coarse-grained information about the dynamics of a large system, or measuring the decoherence rate from engineered environments.Comment: 4pages, 3 figures, revtex4, updated with version closer to that publishe

Efficient Symmetry Reduction and the Use of State Symmetries for Symbolic Model Checking

One technique to reduce the state-space explosion problem in temporal logic model checking is symmetry reduction. The combination of symmetry reduction and symbolic model checking by using BDDs suffered a long time from the prohibitively large BDD for the orbit relation. Dynamic symmetry reduction calculates representatives of equivalence classes of states dynamically and thus avoids the construction of the orbit relation. In this paper, we present a new efficient model checking algorithm based on dynamic symmetry reduction. Our experiments show that the algorithm is very fast and allows the verification of larger systems. We additionally implemented the use of state symmetries for symbolic symmetry reduction. To our knowledge we are the first who investigated state symmetries in combination with BDD based symbolic model checking

Symmetrised Characterisation of Noisy Quantum Processes

A major goal of developing high-precision control of many-body quantum systems is to realise their potential as quantum computers. Probably the most significant obstacle in this direction is the problem of "decoherence": the extreme fragility of quantum systems to environmental noise and other control limitations. The theory of fault-tolerant quantum error correction has shown that quantum computation is possible even in the presence of decoherence provided that the noise affecting the quantum system satisfies certain well-defined theoretical conditions. However, existing methods for noise characterisation have become intractable already for the systems that are controlled in today's labs. In this paper we introduce a technique based on symmetrisation that enables direct experimental characterisation of key properties of the decoherence affecting a multi-body quantum system. Our method reduces the number of experiments required by existing methods from exponential to polynomial in the number of subsystems. We demonstrate the application of this technique to the optimisation of control over nuclear spins in the solid state.Comment: About 12 pages, 5 figure

Characterization of solar-grade silicon produced by the SiF4-Na process

A process was developed for producing low cost solar grade silicon by the reaction between SiF4 gas and sodium metal. The results of the characterization of the silicon are presented. These results include impurity levels, electronic properties of the silicon after crystal growth, and the performance of solar photovoltaic cells fabricated from wafers of the single crystals. The efficiency of the solar cells fabricated from semiconductor silicon and SiF4-Na silicon was the same

Post-copulatory opportunities for sperm competition and cryptic female choice provide no offspring fitness benefits in externally fertilizing salmon

There is increasing evidence that females can somehow improve their offspring fitness by mating with multiple males, but we understand little about the exact stage(s) at which such benefits are gained. Here, we measure whether offspring fitness is influenced by mechanisms operating solely between sperm and egg. Using externally-fertilising and polyandrous Atlantic salmon (Salmo salar), we employed split-clutch and split-ejaculate in vitro fertilisation experiments to generate offspring using designs that either denied or applied opportunities for sperm competition and cryptic female choice. Following fertilisations, we measured 140 days of offspring fitness after hatch, through growth and survival in hatchery and near-natural conditions. Despite an average composite mortality of 61%, offspring fitness at every life stage was near-identical between groups fertilised under the absence versus presence of opportunities for sperm competition and cryptic female choice. Of the 21,551 and 21,771 eggs from 24 females fertilised under monandrous versus polyandrous conditions, 68% versus 67.8% survived to the 100-day juvenile stage; sub-samples showed similar hatching success (73.1% versus 74.3%), had similar survival over 40 days in near-natural streams (57.3% versus 56.2%), and grew at similar rates throughout. We therefore found no evidence that gamete-specific interactions allow offspring fitness benefits when polyandrous fertilisation conditions provide opportunities for sperm competition and cryptic female choice

Exact and Approximate Unitary 2-Designs: Constructions and Applications

We consider an extension of the concept of spherical t-designs to the unitary group in order to develop a unified framework for analyzing the resource requirements of randomized quantum algorithms. We show that certain protocols based on twirling require a unitary 2-design. We describe an efficient construction for an exact unitary 2-design based on the Clifford group, and then develop a method for generating an epsilon-approximate unitary 2-design that requires only O(n log(1/epsilon)) gates, where n is the number of qubits and epsilon is an appropriate measure of precision. These results lead to a protocol with exponential resource savings over existing experimental methods for estimating the characteristic fidelities of physical quantum processes

Word-level Symbolic Trajectory Evaluation

Symbolic trajectory evaluation (STE) is a model checking technique that has been successfully used to verify industrial designs. Existing implementations of STE, however, reason at the level of bits, allowing signals to take values in {0, 1, X}. This limits the amount of abstraction that can be achieved, and presents inherent limitations to scaling. The main contribution of this paper is to show how much more abstract lattices can be derived automatically from RTL descriptions, and how a model checker for the general theory of STE instantiated with such abstract lattices can be implemented in practice. This gives us the first practical word-level STE engine, called STEWord. Experiments on a set of designs similar to those used in industry show that STEWord scales better than word-level BMC and also bit-level STE.Comment: 19 pages, 3 figures, 2 tables, full version of paper in International Conference on Computer-Aided Verification (CAV) 201

Cryptic choice of conspecific sperm controlled by the impact of ovarian fluid on sperm swimming behavior

Despite evidence that variation in male–female reproductive compatibility exists in many fertilization systems, identifying mechanisms of cryptic female choice at the gamete level has been a challenge. Here, under risks of genetic incompatibility through hybridization, we show how salmon and trout eggs promote fertilization by conspecific sperm. Using in vitro fertilization experiments that replicate the gametic microenvironment, we find complete interfertility between both species. However, if either species’ ova were presented with equivalent numbers of both sperm types, conspecific sperm gained fertilization precedence. Surprisingly, the species’ identity of the eggs did not explain this cryptic female choice, which instead was primarily controlled by conspecific ovarian fluid, a semiviscous, protein-rich solution that bathes the eggs and is released at spawning. Video analyses revealed that ovarian fluid doubled sperm motile life span and straightened swimming trajectory, behaviors allowing chemoattraction up a concentration gradient. To confirm chemoattraction, cell migration tests through membranes containing pores that approximated to the egg micropyle showed that conspecific ovarian fluid attracted many more spermatozoa through the membrane, compared with heterospecific fluid or water. These combined findings together identify how cryptic female choice can evolve at the gamete level and promote reproductive isolation, mediated by a specific chemoattractive influence of ovarian fluid on sperm swimming behavior