Deutsch-Jozsa algorithm as a test of quantum computation

A redundancy in the existing Deutsch-Jozsa quantum algorithm is removed and a refined algorithm, which reduces the size of the register and simplifies the function evaluation, is proposed. The refined version allows a simpler analysis of the use of entanglement between the qubits in the algorithm and provides criteria for deciding when the Deutsch-Jozsa algorithm constitutes a meaningful test of quantum computation.Comment: 10 pages, 2 figures, RevTex, Approved for publication in Phys Rev

Universal fault-tolerant gates on concatenated stabilizer codes

It is an oft-cited fact that no quantum code can support a set of fault-tolerant logical gates that is both universal and transversal. This no-go theorem is generally responsible for the interest in alternative universality constructions including magic state distillation. Widely overlooked, however, is the possibility of non-transversal, yet still fault-tolerant, gates that work directly on small quantum codes. Here we demonstrate precisely the existence of such gates. In particular, we show how the limits of non-transversality can be overcome by performing rounds of intermediate error-correction to create logical gates on stabilizer codes that use no ancillas other than those required for syndrome measurement. Moreover, the logical gates we construct, the most prominent examples being Toffoli and controlled-controlled-Z, often complete universal gate sets on their codes. We detail such universal constructions for the smallest quantum codes, the 5-qubit and 7-qubit codes, and then proceed to generalize the approach. One remarkable result of this generalization is that any nondegenerate stabilizer code with a complete set of fault-tolerant single-qubit Clifford gates has a universal set of fault-tolerant gates. Another is the interaction of logical qubits across different stabilizer codes, which, for instance, implies a broadly applicable method of code switching.Comment: 18 pages + 5 pages appendix, 12 figure

A study of video frame rate on the perception of moving imagery detail

The rate at which each frame of color moving video imagery is displayed was varied in small steps to determine what is the minimal acceptable frame rate for life scientists viewing white rats within a small enclosure. Two, twenty five second-long scenes (slow and fast animal motions) were evaluated by nine NASA principal investigators and animal care technicians. The mean minimum acceptable frame rate across these subjects was 3.9 fps both for the slow and fast moving animal scenes. The highest single trial frame rate averaged across all subjects for the slow and the fast scene was 6.2 and 4.8, respectively. Further research is called for in which frame rate, image size, and color/gray scale depth are covaried during the same observation period

The effects of video compression on acceptability of images for monitoring life sciences experiments

Future manned space operations for Space Station Freedom will call for a variety of carefully planned multimedia digital communications, including full-frame-rate color video, to support remote operations of scientific experiments. This paper presents the results of an investigation to determine if video compression is a viable solution to transmission bandwidth constraints. It reports on the impact of different levels of compression and associated calculational parameters on image acceptability to investigators in life-sciences research at ARC. Three nonhuman life-sciences disciplines (plant, rodent, and primate biology) were selected for this study. A total of 33 subjects viewed experimental scenes in their own scientific disciplines. Ten plant scientists viewed still images of wheat stalks at various stages of growth. Each image was compressed to four different compression levels using the Joint Photographic Expert Group (JPEG) standard algorithm, and the images were presented in random order. Twelve and eleven staffmembers viewed 30-sec videotaped segments showing small rodents and a small primate, respectively. Each segment was repeated at four different compression levels in random order using an inverse cosine transform (ICT) algorithm. Each viewer made a series of subjective image-quality ratings. There was a significant difference in image ratings according to the type of scene viewed within disciplines; thus, ratings were scene dependent. Image (still and motion) acceptability does, in fact, vary according to compression level. The JPEG still-image-compression levels, even with the large range of 5:1 to 120:1 in this study, yielded equally high levels of acceptability. In contrast, the ICT algorithm for motion compression yielded a sharp decline in acceptability below 768 kb/sec. Therefore, if video compression is to be used as a solution for overcoming transmission bandwidth constraints, the effective management of the ratio and compression parameters according to scientific discipline and experiment type is critical to the success of remote experiments

Quantum Inference on Bayesian Networks

Performing exact inference on Bayesian networks is known to be #P-hard. Typically approximate inference techniques are used instead to sample from the distribution on query variables given the values $e$ of evidence variables. Classically, a single unbiased sample is obtained from a Bayesian network on $n$ variables with at most $m$ parents per node in time $\mathcal{O}(nmP(e)^{-1})$, depending critically on $P(e)$, the probability the evidence might occur in the first place. By implementing a quantum version of rejection sampling, we obtain a square-root speedup, taking $\mathcal{O}(n2^mP(e)^{-\frac12})$ time per sample. We exploit the Bayesian network's graph structure to efficiently construct a quantum state, a q-sample, representing the intended classical distribution, and also to efficiently apply amplitude amplification, the source of our speedup. Thus, our speedup is notable as it is unrelativized -- we count primitive operations and require no blackbox oracle queries.Comment: 8 pages, 3 figures. Submitted to PR

Deterministic and cascadable conditional phase gate for photonic qubits

Previous analyses of conditional \phi-phase gates for photonic qubits that treat cross-phase modulation (XPM) in a causal, multimode, quantum field setting suggest that a large (~\pi rad) nonlinear phase shift is always accompanied by fidelity-degrading noise [J. H. Shapiro, Phys. Rev. A 73, 062305 (2006); J. Gea-Banacloche, Phys. Rev. A 81, 043823 (2010)]. Using an atomic V-system to model an XPM medium, we present a conditional phase gate that, for sufficiently small nonzero \phi, has high fidelity. The gate is made cascadable by using using a special measurement, principal mode projection, to exploit the quantum Zeno effect and preclude the accumulation of fidelity-degrading departures from the principal-mode Hilbert space when both control and target photons illuminate the gate