2,531 research outputs found
A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
A quantum system will stay near its instantaneous ground state if the
Hamiltonian that governs its evolution varies slowly enough. This quantum
adiabatic behavior is the basis of a new class of algorithms for quantum
computing. We test one such algorithm by applying it to randomly generated,
hard, instances of an NP-complete problem. For the small examples that we can
simulate, the quantum adiabatic algorithm works well, and provides evidence
that quantum computers (if large ones can be built) may be able to outperform
ordinary computers on hard sets of instances of NP-complete problems.Comment: 15 pages, 6 figures, email correspondence to [email protected] ; a
shorter version of this article appeared in the April 20, 2001 issue of
Science; see http://www.sciencemag.org/cgi/content/full/292/5516/47
Using Classical Probability To Guarantee Properties of Infinite Quantum Sequences
We consider the product of infinitely many copies of a spin-
system. We construct projection operators on the corresponding nonseparable
Hilbert space which measure whether the outcome of an infinite sequence of
measurements has any specified property. In many cases, product
states are eigenstates of the projections, and therefore the result of
measuring the property is determined. Thus we obtain a nonprobabilistic quantum
analogue to the law of large numbers, the randomness property, and all other
familiar almost-sure theorems of classical probability.Comment: 7 pages in LaTe
Derivation of the Quantum Probability Rule without the Frequency Operator
We present an alternative frequencists' proof of the quantum probability rule
which does not make use of the frequency operator, with expectation that this
can circumvent the recent criticism against the previous proofs which use it.
We also argue that avoiding the frequency operator is not only for technical
merits for doing so but is closely related to what quantum mechanics is all
about from the viewpoint of many-world interpretation.Comment: 12 page
Improved Error-Scaling for Adiabatic Quantum State Transfer
We present a technique that dramatically improves the accuracy of adiabatic
state transfer for a broad class of realistic Hamiltonians. For some systems,
the total error scaling can be quadratically reduced at a fixed maximum
transfer rate. These improvements rely only on the judicious choice of the
total evolution time. Our technique is error-robust, and hence applicable to
existing experiments utilizing adiabatic passage. We give two examples as
proofs-of-principle, showing quadratic error reductions for an adiabatic search
algorithm and a tunable two-qubit quantum logic gate.Comment: 10 Pages, 4 figures. Comments are welcome. Version substantially
revised to generalize results to cases where several derivatives of the
Hamiltonian are zero on the boundar
Exact solution for the dynamical decoupling of a qubit with telegraph noise
We study the dissipative dynamics of a qubit that is afflicted by classical
random telegraph noise and it is subject to dynamical decoupling. We derive
exact formulas for the qubit dynamics at arbitrary working points in the limit
of infinitely strong control pulses (bang-bang control) and we investigate in
great detail the efficiency of the dynamical decoupling techniques both for
Gaussian and non-Gaussian (slow) noise at qubit pure dephasing and at optimal
point. We demonstrate that control sequences can be successfully implemented as
diagnostic tools to infer spectral proprieties of a few fluctuators interacting
with the qubit. The analysis is extended in order to include the effect of
noise in the pulses and we give upper bounds on the noise levels that can be
tolerated in the pulses while still achieving efficient dynamical decoupling
performance
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