1,243 research outputs found
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
Counting, Fanout, and the Complexity of Quantum ACC
We propose definitions of \QAC^0, the quantum analog of the classical class
\AC^0 of constant-depth circuits with AND and OR gates of arbitrary fan-in,
and \QACC[q], the analog of the class \ACC[q] where \Mod_q gates are also
allowed. We prove that parity or fanout allows us to construct quantum \MOD_q
gates in constant depth for any , so \QACC[2] = \QACC. More generally, we
show that for any , \MOD_q is equivalent to \MOD_p (up to constant
depth). This implies that \QAC^0 with unbounded fanout gates, denoted
\QACwf^0, is the same as \QACC[q] and \QACC for all . Since \ACC[p]
\ne \ACC[q] whenever and are distinct primes, \QACC[q] is strictly
more powerful than its classical counterpart, as is \QAC^0 when fanout is
allowed. This adds to the growing list of quantum complexity classes which are
provably more powerful than their classical counterparts.
We also develop techniques for proving upper bounds for \QACC^0 in terms of
related language classes. We define classes of languages \EQACC, \NQACC and
\BQACC_{\rats}. We define a notion of -planar \QACC operators and
show the appropriately restricted versions of \EQACC and \NQACC are
contained in \P/\poly. We also define a notion of -gate restricted
\QACC operators and show the appropriately restricted versions of \EQACC
and \NQACC are contained in \TC^0
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
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~ circuits that compute parity, where a
MAJ~ circuit is one that has a
majority gate as output, a middle layer of MOD gates and a
bottom layer of AND gates of fan-in . 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 times the
optimal size. This verifies, for the special case of ,
two conjectures made
by Due~{n}ez, Miller, Roy and Straubing (Journal of Number Theory, 2006) for general MAJ~ circuits for any odd . 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 quadratic
case as well as for
higher degrees
The power of the middle bit
The class of languages that can be recognized in polynomial time with the additional information of one bit from a #P function is studied. In particular, it is shown that every ModkP class and every class contained in PH are low for this class. These results are translated to the area of circuit complexity using MidBit (middle bit) gates. It is shown that every language in ACC can be computed by a family of depth-2 deterministic circuits of size 2 to the (log n)c power with a MidBit gate at the root and AND-gates of fan-in (log n)c at the leaves. This result improves the known upper bounds for the class ACC
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 ItalianâEnglish 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
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