8,705 research outputs found
Quantum Computers, Factoring, and Decoherence
In a quantum computer any superposition of inputs evolves unitarily into the
corresponding superposition of outputs. It has been recently demonstrated that
such computers can dramatically speed up the task of finding factors of large
numbers -- a problem of great practical significance because of its
cryptographic applications. Instead of the nearly exponential (, for a number with digits) time required by the fastest classical
algorithm, the quantum algorithm gives factors in a time polynomial in
(). This enormous speed-up is possible in principle because quantum
computation can simultaneously follow all of the paths corresponding to the
distinct classical inputs, obtaining the solution as a result of coherent
quantum interference between the alternatives. Hence, a quantum computer is
sophisticated interference device, and it is essential for its quantum state to
remain coherent in the course of the operation. In this report we investigate
the effect of decoherence on the quantum factorization algorithm and establish
an upper bound on a ``quantum factorizable'' based on the decoherence
suffered per operational step.Comment: 7 pages,LaTex + 2 postcript figures in a uuencoded fil
Property testing of unitary operators
In this paper, we systematically study property testing of unitary operators.
We first introduce a distance measure that reflects the average difference
between unitary operators. Then we show that, with respect to this distance
measure, the orthogonal group, quantum juntas (i.e. unitary operators that only
nontrivially act on a few qubits of the system) and Clifford group can be all
efficiently tested. In fact, their testing algorithms have query complexities
independent of the system's size and have only one-sided error. Then we give an
algorithm that tests any finite subset of the unitary group, and demonstrate an
application of this algorithm to the permutation group. This algorithm also has
one-sided error and polynomial query complexity, but it is unknown whether it
can be efficiently implemented in general
Electronic and optical properties of quantum wells embedded in wrinkled nanomembranes
The authors theoretically investigate quantum confinement and transition
energies in quantum wells (QWs) asymmetrically positioned in wrinkled
nanomembranes. Calculations reveal that the wrinkle profile induces both blue-
and redshifts depending on the lateral position of the QW probed. Relevant
radiative transistions include the ground state of the electron (hole) and
excited states of the hole (electron). Energy shifts as well as stretchability
of the structure are studied as a function of wrinkle amplitude and period.
Large tunable bandwidths of up to 70 nm are predicted for highly asymmetric
wrinkled QWs.Comment: 3 pages, 4 figures. The following article has been submitted to
Applied Physics Letters. After it is published, it will be found at
http://apl.aip.or
Anisotropic Energy Gaps of Iron-based Superconductivity from Intra-band Quasiparticle Interference in LiFeAs
If strong electron-electron interactions between neighboring Fe atoms mediate
the Cooper pairing in iron-pnictide superconductors, then specific and distinct
anisotropic superconducting energy gaps \Delta_i(k) should appear on the
different electronic bands i. Here we introduce intra-band Bogoliubov
quasiparticle scattering interference (QPI) techniques for determination of
\Delta_i(k) in such materials, focusing on LiFeAs. We identify the three
hole-like bands assigned previously as \gamma, \alpha_2 and \alpha_1, and we
determine the anisotropy, magnitude and relative orientations of their
\Delta_i(k). These measurements will advance quantitative theoretical analysis
of the mechanism of Cooper pairing in iron-based superconductivity
Quantum Computation and Spin Physics
A brief review is given of the physical implementation of quantum computation
within spin systems or other two-state quantum systems. The importance of the
controlled-NOT or quantum XOR gate as the fundamental primitive operation of
quantum logic is emphasized. Recent developments in the use of quantum
entanglement to built error-robust quantum states, and the simplest protocol
for quantum error correction, are discussed.Comment: 21 pages, Latex, 3 eps figures, prepared for the Proceedings of the
Annual MMM Meeting, November, 1996, to be published in J. Appl. Phy
Quantum Bit Regeneration
Decoherence and loss will limit the practicality of quantum cryptography and
computing unless successful error correction techniques are developed. To this
end, we have discovered a new scheme for perfectly detecting and rejecting the
error caused by loss (amplitude damping to a reservoir at T=0), based on using
a dual-rail representation of a quantum bit. This is possible because (1)
balanced loss does not perform a ``which-path'' measurement in an
interferometer, and (2) balanced quantum nondemolition measurement of the
``total'' photon number can be used to detect loss-induced quantum jumps
without disturbing the quantum coherence essential to the quantum bit. Our
results are immediately applicable to optical quantum computers using single
photonics devices.Comment: 4 pages, postscript only, figures available at
http://feynman.stanford.edu/qcom
The Influence of Superpositional Wave Function Oscillations on Shor's Quantum Algorithm
We investigate the influence of superpositional wave function oscillations on
the performance of Shor's quantum algorithm for factorization of integers. It
is shown that the wave function oscillations can destroy the required quantum
interference. This undesirable effect can be routinely eliminated using a
resonant pulse implementation of quantum computation, but requires special
analysis for non-resonant implementations.Comment: 4 pages, NO figures, revte
Lossless quantum data compression and variable-length coding
In order to compress quantum messages without loss of information it is
necessary to allow the length of the encoded messages to vary. We develop a
general framework for variable-length quantum messages in close analogy to the
classical case and show that lossless compression is only possible if the
message to be compressed is known to the sender. The lossless compression of an
ensemble of messages is bounded from below by its von-Neumann entropy. We show
that it is possible to reduce the number of qbits passing through a quantum
channel even below the von-Neumann entropy by adding a classical side-channel.
We give an explicit communication protocol that realizes lossless and
instantaneous quantum data compression and apply it to a simple example. This
protocol can be used for both online quantum communication and storage of
quantum data.Comment: 16 pages, 5 figure
Quantum computation with linear optics
We present a constructive method to translate small quantum circuits into
their optical analogues, using linear components of present-day quantum optics
technology only. These optical circuits perform precisely the computation that
the quantum circuits are designed for, and can thus be used to test the
performance of quantum algorithms. The method relies on the representation of
several quantum bits by a single photon, and on the implementation of universal
quantum gates using simple optical components (beam splitters, phase shifters,
etc.). The optical implementation of Brassard et al.'s teleportation circuit, a
non-trivial 3-bit quantum computation, is presented as an illustration.Comment: LaTeX with llncs.cls, 11 pages with 5 postscript figures, Proc. of
1st NASA Workshop on Quantum Computation and Quantum Communication (QCQC 98
Experimental realization of the one qubit Deutsch-Jozsa algorithm in a quantum dot
We perform quantum interference experiments on a single self-assembled
semiconductor quantum dot. The presence or absence of a single exciton in the
dot provides a qubit that we control with femtosecond time resolution. We
combine a set of quantum operations to realize the single-qubit Deutsch-Jozsa
algorithm. The results show the feasibility of single qubit quantum logic in a
semiconductor quantum dot using ultrafast optical control.Comment: REVTex4, 4 pages, 3 figures. Now includes more details about the
dephasing in the quantum dots. The introduction has been reworded for
clarity. Minor readability fixe
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