1,431 research outputs found
On Quantum Algorithms
Quantum computers use the quantum interference of different computational
paths to enhance correct outcomes and suppress erroneous outcomes of
computations. In effect, they follow the same logical paradigm as
(multi-particle) interferometers. We show how most known quantum algorithms,
including quantum algorithms for factorising and counting, may be cast in this
manner. Quantum searching is described as inducing a desired relative phase
between two eigenvectors to yield constructive interference on the sought
elements and destructive interference on the remaining terms.Comment: 15 pages, 8 figure
Improved Quantum Communication Complexity Bounds for Disjointness and Equality
We prove new bounds on the quantum communication complexity of the
disjointness and equality problems. For the case of exact and non-deterministic
protocols we show that these complexities are all equal to n+1, the previous
best lower bound being n/2. We show this by improving a general bound for
non-deterministic protocols of de Wolf. We also give an O(sqrt{n}c^{log^*
n})-qubit bounded-error protocol for disjointness, modifying and improving the
earlier O(sqrt{n}log n) protocol of Buhrman, Cleve, and Wigderson, and prove an
Omega(sqrt{n}) lower bound for a large class of protocols that includes the
BCW-protocol as well as our new protocol.Comment: 11 pages LaTe
Depth-Independent Lower bounds on the Communication Complexity of Read-Once Boolean Formulas
We show lower bounds of and on the
randomized and quantum communication complexity, respectively, of all
-variable read-once Boolean formulas. Our results complement the recent
lower bound of by Leonardos and Saks and
by Jayram, Kopparty and Raghavendra for
randomized communication complexity of read-once Boolean formulas with depth
. We obtain our result by "embedding" either the Disjointness problem or its
complement in any given read-once Boolean formula.Comment: 5 page
Identification and Removal of Noise Modes in Kepler Photometry
We present the Transiting Exoearth Robust Reduction Algorithm (TERRA) --- a
novel framework for identifying and removing instrumental noise in Kepler
photometry. We identify instrumental noise modes by finding common trends in a
large ensemble of light curves drawn from the entire Kepler field of view.
Strategically, these noise modes can be optimized to reveal transits having a
specified range of timescales. For Kepler target stars of low photometric
noise, TERRA produces ensemble-calibrated photometry having 33 ppm RMS scatter
in 12-hour bins, rendering individual transits of earth-size planets around
sun-like stars detectable as ~3 sigma signals.Comment: 18 pages, 7 figures, submitted to PAS
Substituting a qubit for an arbitrarily large number of classical bits
We show that a qubit can be used to substitute for an arbitrarily large
number of classical bits. We consider a physical system S interacting locally
with a classical field phi(x) as it travels directly from point A to point B.
The field has the property that its integrated value is an integer multiple of
some constant. The problem is to determine whether the integer is odd or even.
This task can be performed perfectly if S is a qubit. On the otherhand, if S is
a classical system then we show that it must carry an arbitrarily large amount
of classical information. We identify the physical reason for such a huge
quantum advantage, and show that it also implies a large difference between the
size of quantum and classical memories necessary for some computations. We also
present a simple proof that no finite amount of one-way classical communication
can perfectly simulate the effect of quantum entanglement.Comment: 8 pages, LaTeX, no figures. v2: added result on entanglement
simulation with classical communication; v3: minor correction to main proof,
change of title, added referenc
Fast quantum algorithm for numerical gradient estimation
Given a blackbox for f, a smooth real scalar function of d real variables,
one wants to estimate the gradient of f at a given point with n bits of
precision. On a classical computer this requires a minimum of d+1 blackbox
queries, whereas on a quantum computer it requires only one query regardless of
d. The number of bits of precision to which f must be evaluated matches the
classical requirement in the limit of large n.Comment: additional references and minor clarifications and corrections to
version
Classical and quantum fingerprinting with shared randomness and one-sided error
Within the simultaneous message passing model of communication complexity,
under a public-coin assumption, we derive the minimum achievable worst-case
error probability of a classical fingerprinting protocol with one-sided error.
We then present entanglement-assisted quantum fingerprinting protocols
attaining worst-case error probabilities that breach this bound.Comment: 10 pages, 1 figur
Singlet states and the estimation of eigenstates and eigenvalues of an unknown Controlled-U gate
We consider several problems that involve finding the eigenvalues and
generating the eigenstates of unknown unitary gates. We first examine
Controlled-U gates that act on qubits, and assume that we know the eigenvalues.
It is then shown how to use singlet states to produce qubits in the eigenstates
of the gate. We then remove the assumption that we know the eigenvalues and
show how to both find the eigenvalues and produce qubits in the eigenstates.
Finally, we look at the case where the unitary operator acts on qutrits and has
eigenvalues of 1 and -1, where the eigenvalue 1 is doubly degenerate. The
eigenstates are unknown. We are able to use a singlet state to produce a qutrit
in the eigenstate corresponding to the -1 eigenvalue.Comment: Latex, 10 pages, no figure
Exact quantum query complexity of
In the exact quantum query model a successful algorithm must always output
the correct function value. We investigate the function that is true if exactly
or of the input bits given by an oracle are 1. We find an optimal
algorithm (for some cases), and a nontrivial general lower and upper bound on
the minimum number of queries to the black box.Comment: 19 pages, fixed some typos and constraint
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