1,447 research outputs found
Error suppression in Hamiltonian based quantum computation using energy penalties
We consider the use of quantum error detecting codes, together with energy
penalties against leaving the codespace, as a method for suppressing
environmentally induced errors in Hamiltonian based quantum computation. This
method was introduced in [1] in the context of quantum adiabatic computation,
but we consider it more generally. Specifically, we consider a computational
Hamiltonian, which has been encoded using the logical qubits of a single-qubit
error detecting code, coupled to an environment of qubits by interaction terms
that act one-locally on the system. Energy penalty terms are added that
penalize states outside of the codespace. We prove that in the limit of
infinitely large penalties, one-local errors are completely suppressed, and we
derive some bounds for the finite penalty case. Our proof technique involves
exact integration of the Schrodinger equation, making no use of master
equations or their assumptions. We perform long time numerical simulations on a
small (one logical qubit) computational system coupled to an environment and
the results suggest that the energy penalty method achieves even greater
protection than our bounds indicate.Comment: 26 pages, 7 figure
Asymptotic behavior of the least common multiple of consecutive arithmetic progression terms
Let and be two integers with , and let and be
integers with and . In this paper, we prove that , where is a constant depending on and .Comment: 8 pages. To appear in Archiv der Mathemati
Energy-Momentum Restrictions on the Creation of Gott Time Machines
The discovery by Gott of a remarkably simple spacetime with closed timelike
curves (CTC's) provides a tool for investigating how the creation of time
machines is prevented in classical general relativity. The Gott spacetime
contains two infinitely long, parallel cosmic strings, which can equivalently
be viewed as point masses in (2+1)-dimensional gravity. We examine the
possibility of building such a time machine in an open universe. Specifically,
we consider initial data specified on an edgeless, noncompact, spacelike
hypersurface, for which the total momentum is timelike (i.e., not the momentum
of a Gott spacetime). In contrast to the case of a closed universe (in which
Gott pairs, although not CTC's, can be produced from the decay of stationary
particles), we find that there is never enough energy for a Gott-like time
machine to evolve from the specified data; it is impossible to accelerate two
particles to sufficiently high velocity. Thus, the no-CTC theorems of Tipler
and Hawking are enforced in an open (2+1)-dimensional universe by a mechanism
different from that which operates in a closed universe. In proving our result,
we develop a simple method to understand the inequalities that restrict the
result of combining momenta in (2+1)-dimensional gravity.Comment: Plain TeX, 41 pages incl. 9 figures. MIT-CTP #225
Quantum Energies of Interfaces
We present a method for computing the one-loop, renormalized quantum energies
of symmetrical interfaces of arbitrary dimension and codimension using
elementary scattering data. Internal consistency requires finite-energy sum
rules relating phase shifts to bound state energies.Comment: 8 pages, 1 figure, minor changes, Phys. Rev. Lett., in prin
Adiabatic Quantum Computation in Open Systems
We analyze the performance of adiabatic quantum computation (AQC) under the
effect of decoherence. To this end, we introduce an inherently open-systems
approach, based on a recent generalization of the adiabatic approximation. In
contrast to closed systems, we show that a system may initially be in an
adiabatic regime, but then undergo a transition to a regime where adiabaticity
breaks down. As a consequence, the success of AQC depends sensitively on the
competition between various pertinent rates, giving rise to optimality
criteria.Comment: v2: 4 pages, 1 figure. Published versio
On the least common multiple of -binomial coefficients
In this paper, we prove the following identity \lcm({n\brack 0}_q,{n\brack
1}_q,...,{n\brack n}_q) =\frac{\lcm([1]_q,[2]_q,...,[n+1]_q)}{[n+1]_q},
where denotes the -binomial coefficient and
. This result is a -analogue of an identity of
Farhi [Amer. Math. Monthly, November (2009)].Comment: 5 page
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
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