791 research outputs found
From quantum circuits to adiabatic algorithms
This paper explores several aspects of the adiabatic quantum computation
model. We first show a way that directly maps any arbitrary circuit in the
standard quantum computing model to an adiabatic algorithm of the same depth.
Specifically, we look for a smooth time-dependent Hamiltonian whose unique
ground state slowly changes from the initial state of the circuit to its final
state. Since this construction requires in general an n-local Hamiltonian, we
will study whether approximation is possible using previous results on ground
state entanglement and perturbation theory. Finally we will point out how the
adiabatic model can be relaxed in various ways to allow for 2-local partially
adiabatic algorithms as well as 2-local holonomic quantum algorithms.Comment: Version accepted by and to appear in Phys. Rev.
Staying adiabatic with unknown energy gap
We introduce an algorithm to perform an optimal adiabatic evolution that
operates without an apriori knowledge of the system spectrum. By probing the
system gap locally, the algorithm maximizes the evolution speed, thus
minimizing the total evolution time. We test the algorithm on the Landau-Zener
transition and then apply it on the quantum adiabatic computation of 3-SAT: The
result is compatible with an exponential speed-up for up to twenty qubits with
respect to classical algorithms. We finally study a possible algorithm
improvement by combining it with the quantum Zeno effect.Comment: 4 pages, 4 figure
Multipartite entanglement in quantum spin chains
We study the occurrence of multipartite entanglement in spin chains. We show
that certain genuine multipartite entangled states, namely W states, can be
obtained as ground states of simple XX type ferromagnetic spin chains in a
transverse magnetic field, for any number of sites. Moreover, multipartite
entanglement is proven to exist even at finite temperatures. A transition from
a product state to a multipartite entangled state occurs when decreasing the
magnetic field to a critical value. Adiabatic passage through this point can
thus lead to the generation of multipartite entanglement.Comment: 4 pages, 1 figur
Geometric quantum computation using fictitious spin- 1/2 subspaces of strongly dipolar coupled nuclear spins
Geometric phases have been used in NMR, to implement controlled phase shift
gates for quantum information processing, only in weakly coupled systems in
which the individual spins can be identified as qubits. In this work, we
implement controlled phase shift gates in strongly coupled systems, by using
non-adiabatic geometric phases, obtained by evolving the magnetization of
fictitious spin-1/2 subspaces, over a closed loop on the Bloch sphere. The
dynamical phase accumulated during the evolution of the subspaces, is refocused
by a spin echo pulse sequence and by setting the delay of transition selective
pulses such that the evolution under the homonuclear coupling makes a complete
rotation. A detailed theoretical explanation of non-adiabatic geometric
phases in NMR is given, by using single transition operators. Controlled phase
shift gates, two qubit Deutsch-Jozsa algorithm and parity algorithm in a
qubit-qutrit system have been implemented in various strongly dipolar coupled
systems obtained by orienting the molecules in liquid crystal media.Comment: 37 pages, 17 figure
Quantum Cryptography with Coherent States
The safety of a quantum key distribution system relies on the fact that any
eavesdropping attempt on the quantum channel creates errors in the
transmission. For a given error rate, the amount of information that may have
leaked to the eavesdropper depends on both the particular system and the
eavesdropping strategy. In this work, we discuss quantum cryptographic
protocols based on the transmission of weak coherent states and present a new
system, based on a symbiosis of two existing ones, and for which the
information available to the eavesdropper is significantly reduced. This system
is therefore safer than the two previous ones. We also suggest a possible
experimental implementation.Comment: 20 pp. Revtex, Figures available from the authors upon request, To be
published in PRA (March 95
Temperature effects on mixed state geometric phase
Geometric phase of an open quantum system that is interacting with a thermal
environment (bath) is studied through some simple examples. The system is
considered to be a simple spin-half particle which is weakly coupled to the
bath. It is seen that even in this regime the geometric phase can vary with
temperature. In addition, we also consider the system under an adiabatically
time-varying magnetic field which is weakly coupled to the bath. An important
feature of this model is that it reveals existence of a temperature-scale in
which adiabaticity condition is preserved and beyond which the geometric phase
is varying quite rapidly with temperature. This temperature is exactly the one
in which the geometric phase vanishes. This analysis has some implications in
realistic implementations of geometric quantum computation.Comment: 5 page
Phase shifts in nonresonant coherent excitation
Far-off-resonant pulsed laser fields produce negligible excitation between
two atomic states but may induce considerable phase shifts. The acquired phases
are usually calculated by using the adiabatic-elimination approximation. We
analyze the accuracy of this approximation and derive the conditions for its
applicability to the calculation of the phases. We account for various sources
of imperfections, ranging from higher terms in the adiabatic-elimination
expansion and irreversible population loss to couplings to additional states.
We find that, as far as the phase shifts are concerned, the adiabatic
elimination is accurate only for a very large detuning. We show that the
adiabatic approximation is a far more accurate method for evaluating the phase
shifts, with a vast domain of validity; the accuracy is further enhanced by
superadiabatic corrections, which reduce the error well below .
Moreover, owing to the effect of adiabatic population return, the adiabatic and
superadiabatic approximations allow one to calculate the phase shifts even for
a moderately large detuning, and even when the peak Rabi frequency is larger
than the detuning; in these regimes the adiabatic elimination is completely
inapplicable. We also derive several exact expressions for the phases using
exactly soluble two-state and three-state analytical models.Comment: 10 pages, 7 figure
Tailoring Single and Multiphoton Probabilities of a Single Photon On-Demand Source
As typically implemented, single photon sources cannot be made to produce
single photons with high probability, while simultaneously suppressing the
probability of yielding two or more photons. Because of this, single photon
sources cannot really produce single photons on demand. We describe a
multiplexed system that allows the probabilities of producing one and more
photons to be adjusted independently, enabling a much better approximation of a
source of single photons on demand.Comment: 4 pages, LaTex, 2 figures, twocolumn and RevTex Style for PR
Quantum State Disturbance vs. Information Gain: Uncertainty Relations for Quantum Information
When an observer wants to identify a quantum state, which is known to be one
of a given set of non-orthogonal states, the act of observation causes a
disturbance to that state. We investigate the tradeoff between the information
gain and that disturbance. This issue has important applications in quantum
cryptography. The optimal detection method, for a given tolerated disturbance,
is explicitly found in the case of two equiprobable non-orthogonal pure states.Comment: 20 pages, standard LaTeX, four png figures (also available from the
authors: [email protected] and [email protected]
Quantum identification system
A secure quantum identification system combining a classical identification
procedure and quantum key distribution is proposed. Each identification
sequence is always used just once and new sequences are ``refuelled'' from a
shared provably secret key transferred through the quantum channel. Two
identification protocols are devised. The first protocol can be applied when
legitimate users have an unjammable public channel at their disposal. The
deception probability is derived for the case of a noisy quantum channel. The
second protocol employs unconditionally secure authentication of information
sent over the public channel, and thus it can be applied even in the case when
an adversary is allowed to modify public communications. An experimental
realization of a quantum identification system is described.Comment: RevTeX, 4 postscript figures, 9 pages, submitted to Physical Review
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