Small Depth Quantum Circuits

Small depth quantum circuits have proved to be unexpectedly powerful in comparison to their classical counterparts. We survey some of the recent work on this and present some open problems.National Security Agency; Advanced Research and Development Agency under Army Research Office (DAAD 19-02-1-0058

Bounds on the Power of Constant-Depth Quantum Circuits

We show that if a language is recognized within certain error bounds by constant-depth quantum circuits over a finite family of gates, then it is computable in (classical) polynomial time. In particular, our results imply EQNC^0 is contained in P, where EQNC^0 is the constant-depth analog of the class EQP. On the other hand, we adapt and extend ideas of Terhal and DiVincenzo (quant-ph/0205133) to show that, for any family F of quantum gates including Hadamard and CNOT gates, computing the acceptance probabilities of depth-five circuits over F is just as hard as computing these probabilities for circuits over F. In particular, this implies that NQNC^0 = NQACC = NQP = coC=P where NQNC^0 is the constant-depth analog of the class NQP. This essentially refutes a conjecture of Green et al. that NQACC is contained in TC^0 (quant-ph/0106017)

Uniqueness of Optimal Mod 3 Circuits for Parity

We prove that the quadratic polynomials modulo $3$ with the largest correlation with parity are unique up to permutation of variables and constant factors. As a consequence of our result, we completely characterize the smallest MAJ~$circ mbox{MOD}_3 circ { m AND}_2$ circuits that compute parity, where a MAJ~$circ mbox{MOD}_3 circ { m AND}_2$ circuit is one that has a majority gate as output, a middle layer of MOD$_3$ gates and a bottom layer of AND gates of fan-in $2$. We also prove that the sub-optimal circuits exhibit a stepped behavior: any sub-optimal circuits of this class that compute parity must have size at least a factor of $frac{2}{sqrt{3}}$ times the optimal size. This verifies, for the special case of $m=3$, two conjectures made by Due~{n}ez, Miller, Roy and Straubing (Journal of Number Theory, 2006) for general MAJ~$circ mathrm{MOD}_m circ { m AND}_2$ circuits for any odd $m$. The correlation and circuit bounds are obtained by studying the associated exponential sums, based on some of the techniques developed by Green (JCSS, 2004). We regard this as a step towards obtaining tighter bounds both for the $m ot = 3$ quadratic case as well as for higher degrees

Universal Quantum Circuits

We define and construct efficient depth-universal and almost-size-universal quantum circuits. Such circuits can be viewed as general-purpose simulators for central classes of quantum circuits and can be used to capture the computational power of the circuit class being simulated. For depth we construct universal circuits whose depth is the same order as the circuits being simulated. For size, there is a log factor blow-up in the universal circuits constructed here. We prove that this construction is nearly optimal.Comment: 13 page

Discovery of planetary nebulae using predictive mid-infrared diagnostics

We demonstrate a newly developed mid-infrared planetary nebula (PN) selection technique. It is designed to enable efficient searches for obscured, previously unknown, PN candidates present in the photometric source catalogues of Galactic plane MIR sky surveys. Such selection is now possible via new, sensitive, high-to-medium resolution, MIR satellite surveys such as those from the Spitzer Space Telescope and the all-sky Wide-Field Infrared Survey Explorer (WISE) satellite missions. MIR selection is based on how different colour-colour planes isolate zones (sometimes overlapping) that are predominately occupied by different astrophysical object types. These techniques depend on the reliability of the available MIR source photometry. In this pilot study we concentrate on MIR point source detections and show that it is dangerous to take the MIR GLIMPSE (Galactic Legacy Infrared Mid-Plane Survey Extraordinaire) photometry from Spitzer for each candidate at face value without examining the actual MIR image data. About half of our selected sources are spurious detections due to the applied source detection algorithms being affected by complex MIR backgrounds and the de-blending of diffraction spikes around bright MIR point sources into point sources themselves. Nevertheless, once this additional visual diagnostic checking is performed, valuable MIR selected PN candidates are uncovered. Four turned out to have faint, compact, optical counterparts in our H-alpha survey data missed in previous optical searches. We confirm all of these as true PNe via our follow-up optical spectroscopy. This lends weight to the veracity of our MIR technique. It demonstrates sufficient robustness that high-confidence samples of new Galactic PN candidates can be extracted from these MIR surveys without confirmatory optical spectroscopy and imaging. This is problematic or impossible when the extinction is large.Comment: 14 pages, 7 figures, 7 tables; accepted for publication in MNRA

The He abundance in the metal-deficient blue compact dwarf galaxies Tol 1214-277 and Tol 65

We present high-quality Keck telescope spectroscopic observations of the two metal-deficient blue compact dwarf (BCD) galaxies Tol 1214-277 and Tol 65. These data are used to derive the heavy-element and helium abundances. We find that the oxygen abundances in Tol 1214-277 and Tol 65 are the same, 12+logO/H=7.54+/-0.01, or Zsun/24, despite the different ionization conditions in these galaxies. The nitrogen-to-oxygen abundance ratio in both galaxies is logN/O=-1.64+/-0.02 and lies in the narrow range found for the other most metal-deficient BCDs. We use the five strongest HeI emission lines 3889, 4471, 5876, 6678 and 7065, to correct self-consistently their intensities for collisional and fluorescent enhancement mechanisms and to derive the He abundance. Underlying stellar absorption is found to be important for the HeI 4471 emission line in both galaxies, being larger in Tol 65. The weighted He mass fractions in Tol 1214-277 and Tol 65 are respectively Y=0.2458+/-0.0039 and 0.2410+/-0.0050 when the three HeI emission lines, 4471, 5876 and 6678, are used, and are, respectively, 0.2466+/-0.0043 and 0.2463+/-0.0057 when the HeI 4471 emission line is excluded. These values are in very good agreement with recent measurements of the He mass fraction in others of the most metal-deficient BCDs by Izotov and coworkers. We find that the combined effect of the systematic uncertainties due to the underlying HeI stellar absorption lines, ionization and temperature structure of the HII region and collisional excitation of the hydrogen emission lines is likely small, not exceeding ~2% (the error is 2sigma). Our results support the validity of the standard big bang model of nucleosynthesis.Comment: 22 pages, 3 Postscript figures, accepted for publication in the Astrophysical Journa

The power of the middle bit of a #P function

Peer Reviewe

A bilingual advantage in controlling language interference during sentence comprehension

This study compared the comprehension of syntactically simple with more complex sentences in Italian–English adult bilinguals and monolingual controls in the presence or absence of sentence-level interference. The task was to identify the agent of the sentence and we primarily examined the accuracy of response. The target sentence was signalled by the gender of the speaker, either a male or a female, and this varied over trials, where the target was spoken in a male voice the distractor was spoken in a female voice and vice versa. In contrast to other work showing a bilingual disadvantage in sentence comprehension under conditions of noise, we show that in this task, where voice permits selection of the target, adult bilingual speakers are in fact better able than their monolingual Italian peers to resist sentence-level interference when comprehension demands are high. Within bilingual speakers we also found that degree of proficiency in English correlated with the ability to resist interference for complex sentences both when the target and distractor were in Italian and when the target was in English and the distractor in Italian

Determining Acceptance Possibility for a Quantum Computation is Hard for PH

It is shown that determining whether a quantum computation has a non-zero probability of accepting is at least as hard as the polynomial time hierarchy. This hardness result also applies to determining in general whether a given quantum basis state appears with nonzero amplitude in a superposition, or whether a given quantum bit has positive expectation value at the end of a quantum computation