9,814 research outputs found
Exact two-qubit universal quantum circuit
We provide an analytic way to implement any arbitrary two-qubit unitary
operation, given an entangling two-qubit gate together with local gates. This
is shown to provide explicit construction of a universal quantum circuit that
exactly simulates arbitrary two-qubit operations in SU(4). Each block in this
circuit is given in a closed form solution. We also provide a uniform upper
bound of the applications of the given entangling gates, and find that exactly
half of all the Controlled-Unitary gates satisfy the same upper bound as the
CNOT gate. These results allow for the efficient implementation of operations
in SU(4) required for both quantum computation and quantum simulation.Comment: 5 page
Structure of strongly coupled, multi-component plasmas
We investigate the short-range structure in strongly coupled fluidlike plasmas using the hypernetted chain approach generalized to multicomponent systems. Good agreement with numerical simulations validates this method for the parameters considered. We found a strong mutual impact on the spatial arrangement for systems with multiple ion species which is most clearly pronounced in the static structure factor. Quantum pseudopotentials were used to mimic diffraction and exchange effects in dense electron-ion systems. We demonstrate that the different kinds of pseudopotentials proposed lead to large differences in both the pair distributions and structure factors. Large discrepancies were also found in the predicted ion feature of the x-ray scattering signal, illustrating the need for comparison with full quantum calculations or experimental verification
Quantum Analogue Computing
We briefly review what a quantum computer is, what it promises to do for us,
and why it is so hard to build one. Among the first applications anticipated to
bear fruit is quantum simulation of quantum systems. While most quantum
computation is an extension of classical digital computation, quantum
simulation differs fundamentally in how the data is encoded in the quantum
computer. To perform a quantum simulation, the Hilbert space of the system to
be simulated is mapped directly onto the Hilbert space of the (logical) qubits
in the quantum computer. This type of direct correspondence is how data is
encoded in a classical analogue computer. There is no binary encoding, and
increasing precision becomes exponentially costly: an extra bit of precision
doubles the size of the computer. This has important consequences for both the
precision and error correction requirements of quantum simulation, and
significant open questions remain about its practicality. It also means that
the quantum version of analogue computers, continuous variable quantum
computers (CVQC) becomes an equally efficient architecture for quantum
simulation. Lessons from past use of classical analogue computers can help us
to build better quantum simulators in future.Comment: 10 pages, to appear in the Visions 2010 issue of Phil. Trans. Roy.
Soc.
Why bayesian “evidence for H1” in one condition and bayesian “evidence for H0” in another condition does not mean good-enough bayesian evidence for a difference between the conditions
Psychologists are often interested in whether an independent variable has a different effect in condition A than in condition B. To test such a question, one needs to directly compare the effect of that variable in the two conditions (i.e., test the interaction). Yet many researchers tend to stop when they find a significant test in one condition and a nonsignificant test in the other condition, deeming this as sufficient evidence for a difference between the two conditions. In this Tutorial, we aim to raise awareness of this inferential mistake when Bayes factors are used with conventional cutoffs to draw conclusions. For instance, some researchers might falsely conclude that there must be good-enough evidence for the interaction if they find good-enough Bayesian evidence for the alternative hypothesis, H1, in condition A and good-enough Bayesian evidence for the null hypothesis, H0, in condition B. The case study we introduce highlights that ignoring the test of the interaction can lead to unjustified conclusions and demonstrates that the principle that any assertion about the existence of an interaction necessitates the direct comparison of the conditions is as true for Bayesian as it is for frequentist statistics. We provide an R script of the analyses of the case study and a Shiny app that can be used with a 2 Ă— 2 design to develop intuitions on this issue, and we introduce a rule of thumb with which one can estimate the sample size one might need to have a well-powered design
Measurement of an integral of a classical field with a single quantum particle
A method for measuring an integral of a classical field via local interaction
of a single quantum particle in a superposition of 2^N states is presented. The
method is as efficient as a quantum method with N qubits passing through the
field one at a time and it is exponentially better than any known classical
method that uses N bits passing through the field one at a time. A related
method for searching a string with a quantum particle is proposed.Comment: 3 page
The 6E Instructional Model in the Mathematics Classroom
The focus of this action research study is to compare the 6E instructional model to a traditional instructional model in the mathematics classroom. Literature shows that the 5E model has a significant positive impact on subject mastery, knowledge permanence, and students’ attitude and interest toward the content. Further, the 6E model is shown to allow for easy implementation of tiered differentiation strategies so that all students’ needs are met. Two classes of seventh grade students received instruction on the same content, with one class receiving 6E instruction and the other receiving traditional, lecture-demonstration style instruction. Results showed that the 6E instructional model had minimal impacts on students’ content mastery, but improved students’ attitudes and feelings towards mathematics
The VLSI design of a single chip Reed-Solomon encoder
A design for a single chip implementation of a Reed-Solomon encoder is presented. The architecture that leads to this single VLSI chip design makes use of a bit serial finite field multiplication algorithm
Optimized design of universal two-qubit gates
We construct optimized implementations of the CNOT and other universal
two-qubit gates that, unlike many of the previously proposed protocols, are
carried out in a single step. The new protocols require tunable inter-qubit
couplings but, in return, show a significant improvements in the quality of
gate operations. Our optimization procedure can be further extended to the
combinations of elementary two-qubit as well as irreducible many-qubit gates.Comment: 6 pages, 2 figure
Quantum Mechanics helps in searching for a needle in a haystack
Quantum mechanics can speed up a range of search applications over unsorted
data. For example imagine a phone directory containing N names arranged in
completely random order. To find someone's phone number with a probability of
50%, any classical algorithm (whether deterministic or probabilistic) will need
to access the database a minimum of O(N) times. Quantum mechanical systems can
be in a superposition of states and simultaneously examine multiple names. By
properly adjusting the phases of various operations, successful computations
reinforce each other while others interfere randomly. As a result, the desired
phone number can be obtained in only O(sqrt(N)) accesses to the database.Comment: Postscript, 4 pages. This is a modified version of the STOC paper
(quant-ph/9605043) and is modified to make it more comprehensible to
physicists. It appeared in Phys. Rev. Letters on July 14, 1997. (This paper
was originally put out on quant-ph on June 13, 1997, the present version has
some minor typographical changes
- …